SAT Flashcards
(164 cards)
1
Q
ONE OF EVER X dollars =
A
1/X DOLLARS
2
Q
A meteorologist estimates that on a sunny day, the air temperature decreases by about 4F for every 1,000feat of elevation gain.
On a certain day, the air temperature outside an airplane flying above Seattle is -58F∘ and the ground level temperature in Seattle is 70F . If x is the height above Seattle, in feet, at which the plane is flying, which of the following best models the situation?
70 = - 4x/1000 +58 70 = - 4x/1000 -58 70 = 4x.1000-58 70 = 4x/1000 -58
A
y = ax + b
b : is the initial one - the ground height is 70ft and its go up by 1000ft , while the temperature decreases 4F ( -4)
a: is the variation, slope
-58 = -4x/1000 + 70
But it does not appear like this in the answer, let’s chng the ax position
-58 +4x/1000 = -70
It is not : 70 = - 4x /1000 - 58 . Since it is temp decreases for every of ELEVATION GAIN
3
Q
Oliver mows lawns in his neighborhood. He charges $10 for each regular yard he mows, and he charges an extra $5dollar sign, 5 for each large yard that he mows. In one week he mowed 6 more large yards than regular yards and made$265 If r represents the number of regular yards that Oliver mowed, which equation best models the situation? 10 ( r+6) = 265 10r + 5 ( r+6) = 265 10r + 15( r+6) = 265 10r + 15r + 6 = 265
A
” an extra $5dollar sign, 5 for each large yard “ = 10+5 = 15$ each large
10r + 15 ( r+ 6) = 265
4
Q
Cecilia rents a moving truck that uses a gallon of gas every 10 miles for $29.95dollar sign, 29,95 per day. She incurs an additional charge of $0.89 for each mile traveled and must return the truck with the same amount of gas in the tank as when she rented it. Cecilia travels x miles and replaces the gas she used with gas that costs$2.25. She returns the moving truck on the same day, and calculates that she spent a total of $65.63Which of the following equations best models the situation?
A
Total = rent fee + additional mile charge + gas return ( = when she rented it)
2.25$x /10 = the gallon used
29,95$ + 0,89$.x + ( replaces the gas she used with gas that costs$2.25.) 2.25$x /10= 65.63
5
Q
Camille and Hiroki have decided to start walking for exercise. Camille is going to walk 7 miles the first day and 3 miles each day after that. Hiroki is too busy to walk on the first 2 days, so he decides to walk 5 miles each day until he has walked the same number of miles as Camille. If Camille and Hiroki will have walked the same number of miles, how many days will Camille have walked?
A
Camile miles = Hiroki miles
Camile walked 2 days extra : 7 + 3 ( d-1)
Hiroki walked 2 days fewer: 5 (d -2)
7 + 3 (d -1) = 5 (d-2)
4 + 3d = 5d - 10
-2d = -6
d = 3 days
6
Q
range :
the min should be the result of __
the max should be the result of __
On a highway, drivers are required to maintain a speed of between 55and 65miles per h.$7penalty is assessed for each 1mph a driver’s speed is outside this range. If a driver receives a 42 penalty, what are possible values for his speed?
A
min : substraction : 55-6 = 49
max : plus 42 = 6 = 71
42/7 = 6 mph
7
Q
At the county fair, the operator of a game guesses a contestant’s weight. For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive $3A contestant weighing xpounds received $15 when the operator guessed 120pounds. Which of the following equations could be used to solve for the weight of the contestant?
A
! If the options do not have one that has + - in the answer, it doesn’t matter if it was more weighted or less
To only know what it differs : 120 - x
When its differed , the constant earn 3$ : ( 120-x)3
At final, the constant earn a total of $15 :
( 120-x)3 = 15
8
Q
A taut string of length 10 inches is plucked at the center. The vibration travels along the string at a constant rate of c inches per millisecond in both directions. If x represents the position on the string from the left-most end, so that 0≤x≤100, which of the following equations can be used to find the location x of the vibration after 0.3 milisec
1/c (x -5) =0. 3
cx - 5 = 0,3
x - 10 = 0,3c
A
rate x time = distance
plucked at the center = 5
c . 0,3 = ( 5 -x)
the answer does not appear like this way , so divide “c”
0,3 = (5-x)1/c
9
Q
T=0.125(I−8,225)
The amount of tax, T, in dollars to be paid by an individual with an income of III between 8{,}225$ 34{,}500$ is given by the equation above. Tax is paid from the portion of income above 8,225$ and the remaining amount becomes a part of disposable income. What percentage of income above 8,225 remains after paying tax for an individual whose income falls within the specified range?
A
Rearrange method
m = 0,125 = 🔺y/🔺x = Taxes/Income = 12,5% of Income PAID to Taxes.
The remain is : 100% (income) - 12,5% = 87,5
10
Q
C=1.25S
A factory determines that the mass of a chocolate-dipped strawberry in grams, C, is related to the mass of an undipped strawberry in grams, S as shown in the equation above. For a chocolate-dipped strawberry, what percent of its mass is chocolate?
A
Dipped-chocolate - Undipped = chocolate
= 1,25S - S = 0,25
Chocolate/ chocolated-dipped strawberry = 0,25/ 1,25 = 1/5 = 20%
11
Q
A food truck owner has determined that her maximum revenue occurs when she sells 950sandwiches per month. For every sandwich above or below 950that she sells, her revenue decreases by $0.10Which of the following could be s, the number of sandwiches sold in a month if the owner’s revenue decreased $45 from the maximum? Round the answer to the nearest whole number.
A
“above or below 950 sandwiches” :
( 950-s) decreases
“VARIES , decreases by 0.10$”
0,10 ( 950-s) = 45
12
Q
A stack of 20 stainless steel sheets is supposed to be 40mm thick. The allowable amount of variation in thickness (tolerance) is 0.08mm for an individual sheet. Which of the following are the smallest and largest allowable thicknesses for a stack of 20sheets?oi
A
smallest and the largest : (40 - x)
“is 0.08mm for an individual sheet. “: 40-x/ 20 sheets
the allowable variation is 0,08:
40-x/ 20 = 0,08
largest = 40 + x smallest = 40 - x
13
Q
A company that produces thumb drives has determined that its maximum profit occurs when it sells 5000. For every 500 units above or below 5000 company sells, its profit decreases by $1500 Which of the following could be the number of units sold in a month if the company’s profit decreased $12,000 from the maximum? Round the answer to the nearest whole number.
A
“bove or below 5000 company sells”
( 5000 - x)
“For every 500 units…. decreases $1500”
500/1500 ( 5000-x) = 12000
14
Q
From 1990 to 2010, the annual profit of a company was $350 times the numbers of years either before or after 200 less than $750. For which of the following years could the annual profit have been $575
A
see
15
Q
In the year 2006, the average home price per square foot in a certain county was $98. For each year before or after 2006, the average price per square foot increased by approximately $3.50 In which of the following years could the average home price per square foot be $119
A
“each year befo or after 2006”
2006 - x
Increased by $3,5 + the already existing in 2006
(2006-x) .3,5 + 98 = 119
16
Q
Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 12 by 12 inches, with 0.75 inch margins on all 4 sides. India measures 3,214 kilometers from north to south and 2,933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If k is the number of kilometers per inch in Uche’s scale, which equation best models the situation?
A
lET'S TAKE ONLY ONE side margin 0,75 of 2 sides : 12 - ( 0,75.2) = 10,5 k = number of kilometers per inch = km/inch = 3,214 km/10,5inch
k.10,5 = 3,214
17
Q
The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?
A
50miles — x
21 miles — 1gallon
y=mx + b
G= 🔺y/🔺x . t + initial
BUT, since x or t is always multipying the numerator, it should be 50t above the 21
G = 50t/21 ( miles per G) - 17
Is minus 17, cuz G is the REST of the G
18
Q
Line l with equation 5x-6y= 3 is graphed in the x-y plane. Line k with equation 2x+ny=5 is perpendicular with line. What is the value of n
A
Perpendicular: solpe 2 is negative inverse = slope 1
Slope 1 : -A/B = -5/-6
Slope 2: 5/6 => -6/-5 = 6/5
B (n) = -A/B = 6/5 = 2/n ( multiples crossing)
6n= 10 : n = 5/3
19
Q
in the x-y plane , line p has equation y=ax-4 where a is a constant. If line p intersects the x axis at x = 3,what is the value of a
A
WHEN LINE INTERSECTS THE X AXIS -> Y= 0
0 = a.3-4
20
Q
Which of the following is an equation of the line A graphed in the xy plane that passes through the point (-1, 3.5)and is perpendicular to the line B whose equation is x + 4.5 = 0
x= 3.5
y= 4.5
y=3.5
x=-1
A
x = -4,5 . This means that if y=0 , the x will be always -4,5. While, if y is not 0, the y will be constant
x= -4,5 and y= 3.5
21
Q
A line in the x y-plane passes through the point (4, -1)and is perpendicular to the line with equation y = x + 5y Which of the following is an equation of the line ?
A
x = 1.x => a=1
perpendicular => -1
y=-1x + b
(4, -1)
-1 = -1.4 + b
3 = b
y = -1x + 3
22
Q
when x + 3 or y + 3 = 0 , the x or y is a ___
Which of the following is the equation of the line A graphed in the x y-plane that passes through the point (-2,2)and is parallel to the line B whose equation is y - 3 = 0
a) x + 2 = 0
b) y + 2 = 0
c) y-2 = 0
d) x-2= 0
A
y is constant
y = 2 => y-2=0 ( y-3=0 : y=+3)
y-2=0
23
Q
What is the equation, in which its slope is 7/8 and y-intercept is 3
a) 7x+8y= 24
b) 7x - 8y = -3
c) 7x-8y= 24
d) 7x+8y = 3
e) 7x-8y= -24
A
slope = -A/B -> - (-7) /8
y intercept = 3 = C/B = C/8 = 24
-7X+8y = 24
HOWEVER, in the answers the “Ax” are all positive:
(-7X+8y = 24) x -1
+7x -8y = -24
24
Q
If the slope is + , the line will be
A
m + => line rising up
25
x-1-y = 0 switch into the y=mx+b form
x = 1x = mx
- y ( go to the opposite) => +y = 1y
- 1 = b
```
+1y= 1x - 1
0 = x-1-y
```
26
how is the graph of 4x - 10 = 0 gonna look like
there is no y , so the line will be entirely vertical line passing through the x value when f(x) = 0 :
x = +10/4 = 5/2 = 2,5
27
The equations x+y=3x and 5x−5y=−15 are graphed in the xy plane. Which of the following must be true of the graphs of the two equations?
a) the slope of "x+y=3" is 1 and the slope of another is -1
b) they are perpendicular
c)
a) 1/1=0 |. -A/B -1/-1=1
| b
28
If there is no "x" or "y" in the equation question, the one that is existed will remain ___.
Which of the following is the equation of the line A graphed in the XY plane that passes through the point (-2,2) and is parallel to the line B whose equation is y - 3 = 0
Justify
a) x-2= 0
b) y+2 = 0
c) x + 2 = 0
d) y - 2 = 0
constant;
y= +3
So, there need to be :
y= 2 => 2-2= 0
It's not x+2 = 0 -> -2+2 = 0 .
Because there will be no y.
Y exist and is constant to "2". X is the one who does not exist
29
A jar of jelly bean candies weighs 8ounces. A container of caramel candies weighs 40 ounces. Lúcia buys 10pounds worth of jelly bean candy jars and caramel candy containers for her big party. Given that there are 16 ounces in a pound, which of the following equations correctly relates the number of jars of jelly bean candies, j, and the number of containers of caramel candies, c, that Lúcia bought?
8ounces ----- x pounds
16 ----- 1 = 8/16 ( = 40/16)
8j/16 + 40c/16 = 10pounds
30
A forest that is populated by crows and doves currently contains a total of 1,500 and dove nests. Crows use approximately 8 grams of twigs when building a nest, and doves use approximately 6grams of twigs when building a nest. Which of the following equations best approximates the relationship between C, the total amount, in grams, of twigs used for crow nests and D, the total amount, in grams, of twigs used for dove nests?
8g ---- 1 nest
Cg ---- x nest = C/8 ( = D/6)
C/8 + D/6 = 1,500 NEST
31
A company produces candy bags that each hold about 528cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about 361candies. When a bag contains only gummy bear candies, then it has about 697candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies, l, in the bag and the approximate number of gummy bear candies, g, in the bag?
A) l/361 + g/697 = 528
b) 361l + 697g= 1
c) l/361 + g/697 = 1
d) 361l + 697g= 528
c
! 528 = inches cubes = volume
the "l" and "g" and 261,697 are UNITS
1 = max capacity
l ( number existed)/ 361 ( the max lolipopo)
32
Jacob's classroom contains tables and chairs, each with 4 legs. Jacob puts a pad on the end of every leg so that the tables and chairs will not make noise when they are moved around. If Jacob needs exactly 80pads for his classroom, which of the following equations correctly relates the number of chairs, c, to the number of tables, t ?
1 leg = 1 pad
```
4t+4c = 80pads
4c= 80-4t
c = 80/4 - 4t/4
c = 20 - t
```
33
Sterling silver is an alloy of silver that is 92.5% pure silver. If x grams of sterling silver are mixed with y grams of an 88% silver alloy to produce a 91%silver alloy, which of the following equations correctly relates xand y?
A. 0.075x+0.12y = 0
B. 0.015x -0.03y = 0
C. 0.925x +0.88y = 91
D. 0.925x +0.88y = 0.91xy
```
X = sterling silver has 0,925g of Pure Silves
Y= silver alloy has 0,88g of Pure Silver
```
Since X and Y is mixed together:
92,5%x + 88%y
91% is pure silver
92,5%x + 88%y = 91% (x+y)
BUT, there is not this in the alternatives -> Change to other form : = 0
92,5%x + 88%y - 91% (x+y) = 0
92,5x + 88y - 91x+91y = 0
0.015x−0.03y=0
34
When is f(x) mentioned to be in the equation:
Ebuka needs to take a taxi, which costs$3.50 and an additional cost of 3,5per mile. Which of the following gives the number of miles, m(d) that Ebuka can ride a taxi as a function of the amount of dollars, d that he has?
a) 3.5d + 3.5 = m(d)
b) 3.5d/3.5 = m (d)
c) 1 + d/3.5 = m (d)
d) 1 - d/3.5 = m (d)
m(d)3.5 + 3.5 = d
3. 5 - d = -3.5m(d)
3. 5 - d = m (d)
3. 5/ 3.5 - d/3,5 = m (d)
1-d/3,5 = m (d)
35
When is f(x) in the equation
Surya's fence is 340eet long. It is made from both 6‑foot fence panels and 9‑foot fence panels. Which of the following shows the number of 9‑foot fence panels, l(s), , in Surya's fence as a function of the number of 6‑foot fence panels, s, in Surya's fence?
6s + 9l(s) = 340
6s - 340 = 9 l (s)
6s/9 - 340/9 = l (s)
36
The first is not 0, and has a n < y < n2 :
Over the course of 4 years of training for the 100-meter dash, Erica's best time at each end-of-year track meet improved linearly by 0.30 per year. Her best time at her first end-of-year track meet was 13seconds. Which of the following equations shows Erica's best time, b after y years of training for 1
( y-1)
b = 13 - 0,3 ( y-1)
37
A used car dealer would like to cover their vehicles using 220 liters of paint and 400 liters of clear coat. It takes 13liters of paint and 9 liters of clear coat to cover one car. It takes 1.5 times those amounts to cover one truck. Which of the following shows f(c) the maximum number of trucks the dealer can cover if the dealer covered c cars?
a) f(c)= 220 - 13(1,5)c / 13
b) f (c) =220-13c/13.1,5
c) f(c) = 220-9c/13
f(c) = number of trucks
13c + 13.1,5.f(c) = 220
13.1,5 f (c) = 220 - 13c
f(c) = 220 -13 c/ 13.1,5
38
A construction company is going to build two styles of houses in a particular area. The company will build x houses that each require 4,000 bricks and y houses that each require 8,000 bricks. For the construction project, the company ordered 350,00, so that as many as 4%, percent can break and there will still be enough for the houses. Which of the following equations expresses y in terms of x?
```
y= 2x + 350,00.0,96/8000
y = 1x/2 - 350,00.0,96/8000
y= 2x - 350,00.0,96/8000
```
4000x + 8000y = 350,00 . ( 100% - 4%)
350,00. 0,96 - 4000x = 8000y
350,00. 0,96 - 4000x/8000 = y
350,00.0,96/8000 - 1x/2 = y
39
In tennis, a player must win at least 6 games to win a set. If g is the number of games the player won and s is the number of sets the player won, which of the following inequalities must be true?
6g < = s
6s < = g
6s > = g
6g > = s
s < = 6g
s > = 6g
6s < = g
" AT LEATS X TO ( or for) y " :
g/ s = 6/1
1g = 6s
6s < = g
40
( Inequality) "At most" = ___
A sundae requires 3] ice-cream scoops and 4strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries. Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries. Let's form a system of inequalities to represent Ramses's conditions. Let S denote the number of sundaes he makes and M the number of milkshakes he makes. Which system of inequalities best describes this situation
at most = at least
3S + 2M < = 25
4S + 6M < =
41
Elena is designing a paint can with thickness t millimeters and height h centimeters. She calculates that the thickness of the can in millimeters must be at least 0.10 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2 + t + 0.5h) cents, must be at most 12.2. Which of the following systems of inequalities best models the relationship
between height and thickness described above?
t < = 12 - 0,5h
10t > = h
t > = 12 - 0,5h
10t < = h
t > = 12 - 0,5h
t < = 10 h
"thickness at least 0.10 x h"
(mm) t > = 0.10h ( cm).10
Since we are using "h" as x, we should :
10t = h
(0.2 + t + 0.5h) < = 12,2 ( at most = at least)
t < = 12,2 - 0,5h - 0,2
t < = 12 - 0,5h
42
At least x for each y =
A barge must carry steel pieces for a construction project such that the total weight of the steel pieces is under 1,500kg. Each steel piece is either a beam, which weighs 363kg. There must be at least 2 connector plates for each beam. If b is the number of beams and c is the number of connector plates, which of the following systems of inequalities must be true?
a) 363b + 6c < = 1500
2c < = b
```
b) 363b + 6c < 1500
2c > = b
c) 363b + 6c < 1500
2b < = c
d) 363b + 6c < 1500
2b > = c
```
"AT LEAST 2c FOR EACH b' =
c/b > = 2/1
1c > = 2b
d
43
A taxicab company charges $2.05 for the first mile, $1.56for every successive mile after that. Which of the following functions best represents the amount charged, in dollars, by the taxicab company after m miles (m > 4)
a) f(m)=2.05+1.56(m−4)
b) f(m) = 3,61 + 1;22 (m-4)
c) f (m) = 6.73 + 1.22 (m-4)
d) f(m) = 7.21 + 1.22 (m-4)
c) 2.05 + 1.56x3 miles = 6.73 + 1.22 (m-4)
44
At t it has x , then, at t2 it has x2 :
Snow from the most recent storm fell at a constant rate for the 10 hours the storm lasted. Three hours into the storm, there were 8.48 inches of snow on the ground. Six hours into the storm, there were 10.5 of snow on the ground. If it has been thours since the start of the storm, which of the following best approximates the amount of snow, S in inches, that is on the ground?
S(t)=2.8t
S(t)=3.5t
S(t)=0.7t+6.3
(3, 8.48) and ( 6, 10.5)
m = 10.5 - 8.48 / 6-3 = 2.1/3 = 0.7
```
S(t) = 0.7t + b
8.48 = 0.7x3 + b = 6.3
```
S(t)=0.7t+6.3
45
A physicist measures the energies of atoms A and B to be the positive values a and b respectively. He determines that the energy of atom B is between one percent more than and one percent less than twice the energy of atom A. Which of the following systems of inequalities best models the possible range of values for the energies of atoms A and B?
a<2.02b
a>1.98b
a<2b+0.02
a>2b−0.02
B > 2A x 1,01
B < 2A x 0,99
B> 2,02a
B < 0,98a
46
The supply and demand curves for a product are given by functions Sand D, respectively. For a given number of units, Q, S is the minimum price, in dollars, that the supplier should accept. D is the maximum price, in dollars, where consumers will purchase that number of units.
S(Q) = 45 + 0.04Q
D(Q) = 110 - 0.003Q
For the above equations, which of the following combinations of price and quantity fall between the maximum consumer price and minimum supplier price?
500 units at $105
1000 units at , 80
1500 units at $ 110
2450units at 110
Replace each answer to the equations. The value should be more than S and less than D
47
A business analyst is deciding the amount of time allotted to each employee for meetings and training. He wants the sum of meeting and training time to be no more than 16 hours per month. Also, there should be at least one training hour for every two meeting hours. Finally, there should be at least 2 meeting hours per month to discuss short-term goals. What is the difference between the maximum and minimum number of monthly training hours that could be allotted to an employee? A)10 B)13 C)14 D)1
"t least one training hour for every two meeting hours. " :
1training < = 2meeting
t < = 1/2
m + 1m /2 < = 16hour
the max = 16 hour
the min is 2 meeting hour + 2.1/2 = 3
48
A study by a group of cardiologists determined that maximal heart rate in humans, a parameter used as a basis for prescribing exercise programs, depends on age. Maximal heart rate is around 201 beats per minute for a 10 years old, and decreases at a constant rate of 7bpm every 10 years. Which of the following inequalities best describes the ages, a, for which maximal heart rate is less than 180bpm for a≥10
208−0.7a<180
208−0.7a≥180
201-0.7a<180
201−0.7a≥180
- 7bpm/ 10 years = variation = m
initial stage = 201 ( 10years old) = b
201-0.7a<180
49
Joanne and Richard volunteer at a hospital. Joanne volunteers 4 hours more per week than Richard does. In a given week, they do not volunteer for more than a combined total of 16 hours. If x is the number of hours that Richard volunteers, which inequality best models this situation?
x+4≤16
2x+4≤16
2x+8≤16
2x−4≤16
Richard(x) = J - 4
J + x = 16
x+4 + x <16
2x+4≤16
50
From 2005 to 2011, the world's forests were decreasing in area by about 55.776
per year. In 2008
240,351,492 km squared of forest land. If x represents years since 2005, which of the following best predicts the area of the world's forests, a, for 0< a < 60
" x years since 2005" ( x - 2005)
If 2008 was 240.351, so 2005 was :
240.351 = ( 2008 - 2005). 55.776 - initial value
initial value = 73023
```
y = mx+ b
y = 55.776 ( x-2005) - 73023
```
51
**a is constant** and there are infinitive solution :
What is the value of a
a( y-1/3) + x/2 =0
3y - x -1 = 0
1) Convert to standard form :
y = mx+b
2) Find the slope
3) If "a" is a constant, and INFINITIVE solution, then both slopes are equal
1) ay - a/3 = -x/2
y = (-x/2 + a/3 )/ a
y = (-x/2a + 1/3 )
y = +1/3 + x/3
2) slope = xm
- 1/2a .x and 1/3 . x
3) - 1/2a = 1/3
- 3 = 2a
- 1,5 = a
52
**a is a constant and there are NO SOLUTIONS "
```
ay = 2x + 1
y = 2x + 2
```
1) Find the slope
2) Parallel = no solutions = same slope
```
y = 2x / a + 1/a
2x = 2x/a ( false - so it's no solution)
```
a = 1
53
0.5(8w+2v) = 3
8w =2−v+4w
Which of the following accurately describes all solutions to the system of equations shown above?
a) v=1 , w = 1/4
b) v=2 , w = -1/4
c) infinitive solution
d) no solution
4w + 1v = 3
4w + v = 2
FALSE ! => 0 SOLUTION
54
"How many solutions" :
1.70p−0.34q = 0
0.17(q+1)−0.85(p−1) = 0
Consider the system of equations above. How many (p, q)( solutions does this system have?
1) Convert into standard form
2) find the slope
3) compare two slope
! (p,q) = (x,y)
q = -1.70p / 0.34
q = -1.70p / 0.34 - 1.02/ 0.17
2) -1.70p / 0.34 and -1.70p / 0.34
3) We have SAME SLOPES but y-intercept DIFFERENT => PARALLEL = 0 SOLUTIONS OR IFINITIVE
4) Replace the m and compare 2 equations
5p - 0.12 = q
5p = q
INCOHERENT - 0 SOLUTIONS
55
44(j+2k) = 12
22k =−11j+16
** How many solutions:*
Consider the system of equations above. How many solutions (j,k)does this system have?
How many solutions : convert to y=mx + b and FIND THE SLOPE
```
44(j+2k) = 12
88K = 12 - 44j
k = 12/88 - 44j /88
```
22k =−11j+16
k = -11j/22+ 16 /22
- 44j /88 (½) = -11j/22
Ifinitive solutions
56
19−38y = 76 x
24x =−6(2y−1)
**How many solutions ** :
Consider the system of equations above. How many solutions (x,ydoes this system have?
How many solutions : convert to y=mx + b and find the SLOPE
19−38y = 76 x
24x =−6(2y−1)
y = 76x/-38 - 19/-38
+12y = -24x/12 + 6/12
- 24x/12 = 76x/-38
- 2x = -2x
There are IFINITIVE solutions
57
3x+2y =4(x−y−6)
6(y+x) =7x−24
Which of the following accurately describes all solutions to the system of equations shown above?
Since in the answers there are "ifnitive solutions " "No solutions", let's identify the SLOPE first
1) Isolate y :
3x+2y =4(x−y−6)
6y = x - 24
y = x/6 - 4
6(y+x) =7x−24
6y = 6x - 24
y = x/6 - 4
2) Same slope : x/6 = x/6
IFINITIVE SOLUTIONS
58
12t =4v−3
−6t=4v+6
If (t, v) is the solution to the system of equations above, what is the value of t - v?
12t - 4v = 3 (.+1)
−6t - 4v =+6
6t = 9
t= 3/2
-6 ( 3/2) - 4v = 6
-4v = 6 + 9
v = 15/4
3/2 - 15/4
6/4 - 15/4 = -9/4 ❌
6/4 > - 15/4 => +-9/4
59
3−m=2(ℓ−4)
m=ℓ−4
Consider the system of equations above. If (ℓ,m) is the solution to the system, then what is the value of l ?
3−m=2 . m => m=ℓ−4
3 = 2m + m
3 =3m
1= m
```
1 = l - 4
l = 5
```
60
When the 2 equations are equivalent:
−20x+12y = 24
−5x+3y = 6
Consider the system of equations above. How many (x,y)solutions does this system have?
2 equations 're equivalent => there are IFINITIVE solutions
1) Isolate f(x) ,y
2) Do the system of addition
24 + 20x = 12y
6 + 5x = 3y (x4) => 24 + 20x = 12y
61
x² + 13x/2 + 15/2 = 0
If x = a and x = b are the solutions to the equation above, hat is the value of ab
! ab is LITERALLY the product of ab ( the roots )
DON'T NEED TO FIND ROOTS
ab = c/ a
15/2 /x
15/2x
62
( x + 3)² - 4 = 0
| Find the roots
(x + 3 ) ( x+3) ❌
3.3 = 9 - 4 = 5
3+3 = 6
Sum 6 = 1+5
Product: 5 = 1.5
the roots are : INVERT THE SIGNALS
-1 and -5
63
the one with "x" is the __ of the roots.
The one with no "x" is the __ of the roots
Describe each formulas
with "x": Sum = -b/a
| no "x" : Prod = c/a
64
Sara has whole milk, which contains 3.25% butterfat by volume , and one type of low - fat milk, which contains 1% butterfat by volume. Which of the following systems could be used to determine the amount of whole ,ilk,w, in ounces, and the amount of low-fat milk, l, in ounces, that Sarah should mix to obtain 32 ounces of a low-fat milk with 2% butterfat by volume
a) l + w =
__ l + ___ w =
l ounces + w ounces = 32 ounces
1% = 0.01
0.01l + 0.325w = total of % of the final volume
0;01l + 0.325w = 32.0.02
65
In 1960. the population of Colombia was about 16 million and the population of Argentina was about 20.6 million. Between 1960 and 2010the population of Colombia increased by about 530,000 people per year, and the population of Argentina increased by about 340,000 people per year. Let P represent the population, in millions, and t represent the number of years since 1960. Which of the following system of equations can be used to find the year when both countries had approximately the same population?
P =
P =
```
Unit = number million
530,000 = 0.53 million
340,000 = 0.43 million
```
Poplutation the same :
P = 16 + 0.53.t
P = 20.6 + 0.43 .t
66
A television network must air 16minutes of commercials during a 1 hour show. All commercials aired on this network are either 30seconds or 45 seconds. The network would like to run exactly 24commercials during a certain 1hour program. Which of the following systems could be used to determine the number of 30‑second commercials, x, and the number of 45‑second commercials, y that it should air during this program
x+y =
_x + _ y =
x and y = number of commercials
x+y = 24 commercials
16 MINUTES instead of sec
30/60 + 45/60 = 16min
67
y =0.25x+12
y =K(x+3)
In the system of equations above, K is a constant. For which value of K does the system have no solution?
no solution = parallell = same slopes
0.25 x = slope 1
kx + k 3 = y => "K"x is the slope 2
kx = 0.25x
k= 0.25
68
Two airplanes, which start 3.300 miles apart, fly toward each other. The two planes fly at a constant speed, but their speeds differ by 80 . After 5 hours, the planes pass each other. What is the speed of the faster plane?
! distance = v.t
! x = the fast velocity
3300 - x5 = (x-80) . 5
3300 + 400 = 5x + 5x
3700 = 10x
x = 370
69
Ji-Hun and Kana are running a marathon. Due to the volume of people running, the starts occur in waves. Kana starts at 9:35 and runs at an average rate of 7 miles per hour . Ji-Hun starts at 10am and runs at an average rate of 8mph. Assuming constant paces and no stops, to the nearest tenth of a mile, in how many miles will Ji-Hun catch up to Kana?
10 am - 9:35 = 25min
veloc. time = distance
7 . t = 8 ( 25-t)
70
If the constant is not mutiplying "x" to do the ratio equity and multiply cross, you should convert the equations in ____ form. And ___ 2 equations
x = 1/3 ( y +4)
4x - 3y = 3(a-x) - 2x
In the system of equations above, a is a constant. For what value of a does the system of linear equations have infinitely many solutions?
1) Convert to Ax +By = C
x = 1/3 ( y +4)
x - 1y/3 = 4
4x - 3y = 3(a-x) - 2x
9x - 3y = 3a ( simplify with 3)
3x - y = a
2) Compare
x - 1y/3 = 4
3x - y = a
a = 4
71
If the constant is not multipying x, you should not do the crossover multiplication. Intead, convert the equations into __ form and then, ___ the 2.
8 (x - 9y) = 8 - 6x +24
4x - Ay = -3x + 16
In the system of equations above, A is a constant. For what value of A does the system of linear equations have infinitely many solutions?
8 (x - 9y) = 8 - 6x +24
4x - Ay = -3x + 16
1) Ax + By = C :
14x - 72y = 38 ( SIMPLIFY 2) =>
7x- 36y = 16
7x - Ay = 16
A = 36
72
From 1970 to 1990 the average per person annual consumption of whole milk declined at a constant rate from 101 to 41 quarts per year. During the same period, the average annual consumption of low fat milk increased at a constant rate from 25 to 60quarts per year. What was the average annual per person consumption when the consumption of whole milk and low fat milk was the same?
```
x = number of years since 1970
y = mx+ b : "B" is the INITIAL and "m" is the Variation
```
"20" divide: per year
110 - 110-41x/ 20 = 25 + 60-25x/20
73
A local grocer wants to mix candied pecans, priced at $14.00 and candied cashews, priced at $10.00 How many pounds of candied cashews must he mix with 8lbs of candied pecans to make a mixture that costs $12.5 per lb? (Round the answer to the nearest tenth of a pound.)
c + 8 = total weight
14.8 + c.10 = total weight x 12.5
! 12.5 $ PER LB
Solve the system = 4.8 c
74
2 constants in quadratic form, we should:
x(x−a)−b(a+b)=0
In the equation above, a and b are constants. What are the solutions to the equation?
1) (x + c) (x + d)
2)c+ d = the one who multiplies "x"
= -a
cd = (a+b)b
3) Identify who is c and d
cd = -(a+b)b => c is -(a+b) and d is b
4) replace in (x+c) (x+d) = 0
5) each parentisis = 0
(x - (a+b) = 0
x = + (a+b)
(x + b) = 0
x = -b
75
kx² - 3x = -2
In the equation above, k is a constant. For what value of k does the equation have no real solutions?
no real solutions = discriminant < 0
kx² - 3x = -2
```
(-3)² - 4.2.k < 0
9 - 8k < 0
-8k < -9
(CHANGE THE <> WHEN IS NEGATIVE TO POSITIVE)
k > 9/8
```
76
If k is a constant, and the equation has one solution. What is the k value
2x² + 5x - k = 0
```
1 solution = discriminant = 0
5² - 4.(-k). 2 = 0
25 + 8k = 0
8k= -25
k = -25/8
```
77
kx² + 5x=−7k
In the equation above, k is a constant. Which of the following represents all values of k for which the equation has two distinct real solutions
2 solutions= discriminant > 0
5² - 4. 7.k > 0
25 - 28k > 0
-28 k > -25
k < +25/ 28
CHANGE the < > when change negative to positive.
78
(y-k) y = 1/3
In the equation above, k is a constant. One of the solutions to the equation is:
3 + √9+4 ( 1/3) /3
1) convert into the normal form
y² - ky - 1/3 =0
2) Compare with the Báskara formula
b+- v b² - 4.a.c /2a => k is b
3 + √9+4 ( 1/3) /3
3) b is 3 => k is 3
79
A (q) = 86 (0.9) ^ q/4
The function above models A, the number of active players, in thousands, of a mobile game q quarter years after 2018. Based on the function, how many quarter years does it take for the number of active players to decreases by 10% percent ?
it will take 4 quarter years :
A (q) = 86 (0.9) ^ 4/4
86.0.9¹ => 0.9 is 100%-10%
80
P(q)=−0.01(q−250)(q−80)
The equation above gives the profit, P(q) in dollars, earned by a cupcake bakery when q cupcakes are produced. What is the best interpretation of the number 808080 in this context?
a) 80cis a number of cupcakes for which the profit is equal to $0
b) 80 is the number of cupcakes that corresponds to the minimum profit.
c) is the maximum profit, in dollars.
d) 80 is the minimum profit, in dollars
a) equal the $ that is P(q) in 0
0 =−0.01(q−250)(q−80)
(q - 80) = 0 and (q - 250) = 0
81
1 quarter = ____
D=32(1.16) ^ q/4
The equation above models the total number of downloads in thousands, DDD, of a mobile game q quarter years after it officially launches. Based on the model, which of the following statements is true?
a) It will increase 64% per year
b) It will decrease 16% per quarter
c) it will decrease 64% per quarter
d) it will increase 16% per year
1 quarter = 1 trimestre
1 year we have 4 trimestres => 3.4 = 12 months
1.16 = 100% + 16%
a
82
E(s) = 6.11.10 ^7.5T/ 382 - 92T
The saturation vapor pressure over water,
E (s) measured in hectopascals, is the vapor pressure of the air when the number of water molecules condensing equals the number evaporating from a flat surface of water. The equation shown above models the relationship between
E(s) and T, of the air and water. Which of the following best describes the meaning of 6.11
a) This is the saturation vapor pressure when the temperature is 0degrees Celsius.
b) This is the saturation vapor pressure when the temperature is 1 Celsius.
c) This is the saturation vapor pressure when the temperature is 10degrees Celsius.
d) This is the saturation vapor pressure when the temperature is 100degrees Celsius.
a) if t = 0 -> 10^0 = 1
| 1. 16 x 1 = 1.16 = E(s)
83
The equation below can be used to calculate the kinetic energy, K, of an object having a mass, mmm, and a velocity, v.
K = 1/2 mv²
If the velocity of Niklas's car slows to 2/3
of its previous velocity, what will be the effect on the kinetic energy of the car?
A) The kinetic energy will become 1/9of the previous
B) will become 2/4
c) will become 1/16
d) will become 4/9
k is proportional to v²
| If v vary in 2/3, k will vary on (2/3)² = 4/9
84
[ H+] = 10^- ph
What is the effect on pH if the hydrogen ion concentration is multiplied by 10?
A) it decreases by 1
B) it multiplies by 10
c) it divides by 10
d) it increases by 1
[ H+] = 10^- ph
10 H+ = 10^-ph .10
10^-ph . 10¹ => -ph + 1 => 10^- ( ph -1)
A
85
h=x(V−5x)
The equation shown above gives the height, h, in meters, of a spray of water from a particular lawn sprinkler at a distance, x meters from the sprinkler when the water is traveling at a velocity, V, in meters per second. The maximum spraying distance is the horizontal distance from the sprinkler where the water reaches the ground. If the velocity is quadrupled, how does the maximum spraying distance change?
"the max spraying dist is where the water reaches the ground"
0 = xV - 5x²
5X²/ X = V
5X = V
V.4 :
5X²/ X = V .4
5X . 4 = V
IS QUADRUPLED
86
B(n)=2^n
A binary codeword of length n is a string of 0's and 1's with n digits. For example, 1001 is a binary codeword of length 4. The number of binary code words, B(n), of length n, is shown above. If the length is increased from n to n+1, how many more binary code words will there be?
a) 2 ^ n+1
b) 2
c) 2^n
d) 2²
```
2^n+1
"many more "
2^n - 2^n+1 = 2^n - 2 + 2^n
2^n ( 2 - 1)
= 2^n
```
87
A steel ball is traveling through water with a speed of x meters per second, where x is positive. The drag force, F in newtons
F = 0.5 + 0.004(x + 50)(x-2.5)
At what speed in meters per second does the ball have a force of 0.5N?
1) turn all x non- related to 0
0.5 = 0.5 + 0.004(x + 50)(x-2.5)
0.5 - 0.5 = 0 = 0.004(x + 50)(x-2.5)
0 /0.04 = (x + 50)(x-2.5)
0.= (x + 50)(x-2.5)
2) each parentesis equal to 0
(x+50) = 0
x = -50
x -2.5 = 0
x = +2.5
88
t days
After how many days did the total number of people viewing the video double from the original number of people?
18.16^0.0125t
1) simplify the 16 = 2^4
2) 0.0125.t = 1 => so it can be 16¹
t = 20 days
89
A mug of warm apple cider is gradually cooling. Its temperature in degrees Celsius can be modeled with the expression 23+24.2^-0.014t
, where the variable t represents the time in minutes. Approximately how many minutes will it take for the temperature to reach 29C?
```
29-23 = 24.2^ - 0.014t
6/24= 24.2^ - 0.014t /24
1/4 = 2^ - 0.014t
4-¹ = 4^1/2. - 0.014t -> 1/2. - 0.014t = -1
t = 142.86
```
! 1/4 = 4-¹ ; 2 = 4^1/2
90
A dish with 2 grams of nutrient is being used to model the change in a microbe population with limited resources. The growth rate of the population, r in millions of microbes per hour h hours after introducing the bacteria is given by:
r = 42h - 3h²
How many hours after introduction does the growth rate become negative?
```
=0 -> less than 0 is negative
3h ( 14 - h) = 0
14 - h = 0/3h
14 = h
or h = 0
```
91
Hung Lam plans to enclose a rectangular area for his chickens in his backyard using the sides of his apartment building for 2 of the sides, as seen in the figure at left. If Hung Lam has exactly 40 feet of chicken wire, what is the largest area, in square feet, he can enclose for his chickens?
🟫 |
__
the 2 lines are the 2 of the sides
LARGEST AREA = VERTEX
Min or Max? Depend on the "m" signal
2l + 2w = 40 ->
l.
92
Hung Lam plans to enclose a rectangular area for his chickens in his backyard using the sides of his apartment building for 2 of the sides, as seen in the figure at left. If Hung Lam has exactly 40 feet of chicken wire, what is the largest area, in square feet, he can enclose for his chickens?
🟫 |
__
the 2 lines are the 2 of the sides
LARGEST AREA = VERTEX
Min or Max? Depend on the "m" signal
2l + 2w = 40 ->
l.
93
Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately 12years. That is, every 12 years, the amount of tritium decreases by 50%. If a new tritium EXIT sign contains 25curies of tritium, approximately how many curies of tritium will remain after 24 years?
every 12 years , decreases by 50% ( 0.5)
0.5^tyears/12
25 - 0.5^24/12 = 25 - 0.5^2
94
Travel at SAME DIST, but DIFFERENT SPEED
A forest ranger travels up a river by boat to collect soil samples. The boat travels at a speed of v miles per hour for a distance of 2 miles. After collecting the samples, the ranger travels the same distance back, but the boat travels 5 miles per hour slower than it did on the way up the river. If the ranger spent 3 hours travelling up and back, which of the following equations could be used to determine the speed of the boat on the way up the river?
T1 + T2 = Ttotal
T = d/v
2/v + 2/(v-5) = 3 hours
( simplify with "v") : 2 + 2v/ v-5 = 3v
(simplify with "v-5" by multiplying v-5) :
2v - 10 + 2v = 3v (v-5)
2v-10 + 2v - 3v² - 15v = 0
95
Two climate scientists are creating models for global rising sea levels. One scientist proposes a 10-year doubling model, which predicts that the change in sea level, R(t), will grow according to the following function:
R(t) = 125/256 . (2)^t/10
where t is the number of years after 2005. The other scientist proposes a steady increase model where the change in sea level will increase by 5 centimeters ( per year. Both models predict that in the year 2105, the sea level will increase by 500cm. To the nearest centimeter, how much greater is the predictions of the steady increase model than the 10-year doubling model for the change in sea level in the year 2055?
2005 - 2055 = 50 years
"increase 50cm per year" = +50.y
```
50.50 = 250
R(t) = 125/256 . (2)^50/10 = 16cm
```
250-16
96
Rocio drops a ball from a height of 4 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, as shown at left. Which of the following equations correctly models the ball's peak height, h, in meters, after b bounces?
h=4⋅0.79 ^(b−1)
h=4⋅0.79 ^b
h=4−0.79⋅b ²
h=4⋅(1−0.79⋅b²)
h=4⋅0.79 ^b
When b=0 : 4.1 = 4= h
when there was 0 bounces, the height is the INITIAL value
97
S=500(1.02) ^t
The equation above models the amount of money in dollars, S, in a savings account t years after the initial deposit was made. If the interest rate remains constant, which of the following equations models the amount of money in the savings account d decades after the initial deposit was made?
S=500(1.02)^10/d
S=500(1.02)^10d
S=500(1.22)^10d
S=500(1.002)^d
When the original icognite is SMALLER than the new one, is going to be ___
multiplying :
year < decade
1 year = 10d
98
√16x²y^16 + 25x^16y²
DON'T ____ WHEN IS SUM UNDER THE SAME √
DON'T SIMPLIFY WHEN IS ...
√16x²y^16 + 25x^16y²
1) Isolate the same values:
xy √ ( 16y^14 + 25x^14)
! is √ -> so, 16 - 2 = 14 -> y^14
99
(bd) ^1/4 . ( b/d)^4
| Which of the following expressions is equivalent to the expression above assuming d is nonzero?
(bd) ^1/4 . ( b/d)^4
b^1/4 . d ^1/4 . ( b^4 : d^4)
b^1/4 . b^1/4 . d^4 /d^4
^1/4 + ^4 . ^1/4 - ^4
'17/4 . -15/4
'17/4 + -15/4
100
√x.√y =
| 2 ³√ 4 . 2 ³√2
√x.√y = √x.y :
4 ³√4.2 = 4³√8
4.2 = 8
101
SAME √ =
³√6^4 + 3 ³√6^4 = 6.4^A
wHAT IS the value of A
Resolve the base
1 ³√6^4 + 3 ³√6^4 = 6.4^A
1 + 3 = 4 ³√6^4
```
4 ³√6^4 = 6.4^A
(SIMPLIFY) :4 ;
³√6^4 = 6^A
6 ^4/3 = 6^A
4/3 = A
```
102
The quotient of 5√m^4 / 4√m³ and
√m /5√m^6 is
THE QUOTIENT
multiply
5√m^4 / 4√m³ x √m /5√m^6
m^4/5 . m ½ : m³/4 . m^6/5
( do the sum between the multiplication)
( do the subctraction between the results of the multiplication )
103
x³/² ( 1/ x^5/²)²
x³/² . ( 1²/ x^10/²)² -> (x^5)² - 2.5
x³/² / x^5 -> ³/² - 5 = -7/2
x^ -7/2 = 1/x^ +7/2 => 1/ √x^7
104
8-¹/² . 8 ^7/6
^7/6 + (-¹/²) = 8²/³
not finished yet
³raiz 8 ² = 2² = 4
105
(1/9) -³/² . ( 1/8) ²/³
(1/9) -³/² => ( 1/8) ²/³ / (1/9) +³/²
| 3√1²/ 3 √8²): (2√ 1³ / 2 √ 9 ³
1/2² : 1/3³ = 1/4 / 1/27 = 27/4
106
√25h²+144h² + ³√h²
SUM UNDER THE SAME √:
Sum it , don't rationalize first
√25h²+144h² + ³√h²
√169h² + ³√h²
13h + h ²/³
107
(s-2) (7s³/3 + 7s²/3 - 7s + 4/3)
```
take out (s-2) :
s - 7s= 6s
-2 + 4/3 = -6/3 + 4/3 = -2/3
```
(7s³/3 + 7s²/3 - 6s -2/3) ISOLATE THE COMMON
1/3 ( 7s³ + 7s² - 18s -2)
108
(3y-2) (y+a) = 3y² +by - 24
a and b are constants. what is the vaue of b
DISTRIBUTION
3y² +3ya - 2y -2a = 3y² +by - 24
ISOLATE THE COMMON
3y² + y(3a - 2) -2a = 3y² +by - 24
COMPARE THE EQUALITY
```
-2a= -24 => a = 12
y(3a-2) = by
3a-2 = b
12.3-2 = 34
```
109
what is odd and even numbers
```
odd = 1,3,,5,7,9
even = that can divided into 2 equals part = 2,4,
```
110
(Parabola graph) : x-intercepts 1.5 and 9.
y-intercept -3.
Parabola is down, with maximum (5, 3.25)
What is the equation that represent it
a) - 1/4 ( x-5)² + 3.25
a) - 1/4 ( x+5)² + 3.25
a) - 1/2 ( x-5)² + 3.25
d) x² - 1/4x + 3.25
Have parabola = vertex form : a(x-h) ²+ k
maximum is + 5 for -h = -(+5) = -5 -> (x-5)²
to discover a, replace y for -3 and x for 0
111
The equations y= 3/x+4 and y= 3/x+4 +3 are graphed in thex-yplane. What are the correct option regarding there ASSYNDOTE
a) Their vertical assymptote = 4
b) Their vertical assyndote = -4
c) their vertical assyndote is 3 for y=0
d) their horizontal assyndote is -3
Horizontal Assyndote : when y=0 . In this case
a/ x - k +h = y
3/ -4 + 4= 0
b
112
vertical asymptote is when :
how to calculate :
horizontal asymptote is when :
how to calculate :
vertical is when y=0 . Turn y=0 . While the x , has numerous values
horizontal is when y=0, and 1 value for x. Find the one that intercept a x number , with y=0
113
Graph with 2 parabolas + 1 line . Here are the equations of this graph :
y=x²
y= -x² + 2
y = x + 2
Which of the following list all of the solutions of these equations
a) (-1,1)
b) (-1,-1) (0,2) ( 1,1) ( 2,4)
c) (0,2)
The intercept that has ALL OF THE PARABOLAS INTERCEPTING
114
Two parabolas graphed in thex, y-plane have the equations y=2(x-4)² + 2 y=-(x-a)²+12 where a is a constant. For what value of a will the two parabolas have the same axis of symmetry?
A) 4
B) -4
C) -8
D) 8
y=2(x-4)² + 2 y=-(x-a)²+12
a ( x-h) + k
-h : - (+4) = -4
115
The functions y=3(x+2)² -4 and y= -3(x+2)² - 4
are graphed in the x, y-plane. Which of the following must be true of the graphs of the vertexes and axes of symmetry of the two functions?
a) they have different vertexes
b) they have different axes of symmetry
c) the first function has a max value, while the second has the minimum
d) the first function has a min value, while the second has the maximum
a) they have same vertexes = +k = +(-4) = -4
b) same axes of symetry = -h = -( +2) = -2
d) yes ; +3 = +a -> parabola facing upwards = vertex is minimum
116
how to calculate:
- axes fo symetry
- vertex
- f(x) be symetric of g(x) respect to y-axis
a(x -h) + k
- -h
- +k
- +x = -x
117
The functions f(x)=8( 2/5) ^x and g(x)=8(b)^x are graphed in the x, y‑plane. For what value of b would the graphs of functions f and g be symmetric with respect to the y-axis?
be symetric = be reflected = be the opposite ( signal)
| f8( 2/5) ^ - x=> 8.2.5^x
118
The functions f(x)=5(2)^x and g(x)=5(b)^x are graphed in the x, y‑plane. If the graph of function g is always increasing and f(x)>g(x) for all x>0, then which of the following could be the value of b?
a) 0.25
b) 2
c) 1.25
d) 5
f(x)=5(2)^x > g(x)=5(b)^x
LET'S SAY that x = 1
5. 2 = 10
5. b¹ < 10
5. 0.25 or 5.1.25
Now, x=2
5. 4 = 20
5. 0.25² = 0.3125 and 1,25 ( DECREASED)
5. 1.25² = 7.8125 and 6.25 ( INCREASED)
So, is 1.25
! b> 1 = always increasing
b<1 = always decreasing
119
```
if f(x) = -g(x)
when the values of f(x) are ( c,d) , the values of g(x) =
```
(c , -d) -> (x , -y)
120
f(x) = - 2 ( 1/3)^x and g(x)= 2 ( 1/3)^x
are graphed in the x, y‑plane. If (a,b) is a point on the graph of f, then which of the following is a point on the graph of g?
the g(x) would be the same values of f(x) , but the parabola face down
121
g(x) is a transformation of {f(x)}. The graph to the left shows f(x), solid line, g(x). as a dashed line. What is g(x)s in terms of f(x)
a) f(x - 5)
b) f (x+5)
c) f(x) - 5
d) f(x) + 5
Justify all options
a) f(x - 5) : it means that g(x) is more RIGHT for 5 values than f(x)
b) f (x+5): it means that g(x) is more LEFT for 5 values than f(x)
c) f(x) - 5 : it means that g(x) is more DOWN for 5 values than f(x)
d) f(x) + 5 : it means that g(x) is more UP for 5 values than f(x
122
graph parabola
f(x) and h (-x). How is the h(-x) graph related to f(x)
what about f(x) and -h(x)
Let's say that the parabola of f(x) is more inclined to the right. So, graph of h(-x) will be more inclined to the OPPOSITE ( reflection) - to the left
Let's say the parabola of f(x) is face UPwards. Then, -h(x) is faced DOWN-wards
123
```
The functions f(x)=-2.5(x+2)² +8
and g(x)=-2.5(x+2)^2+b
are graphed in the xy plane as y=f(x) and y=g(x Let a be the y‑coordinate of the vertex of function f and b be the y‑coordinate of the vertex of function g. If a is 5 less than b, then what is the value of b ?
```
y-coordinate of the vertex = k ( a(x-h) + k ;
a = 8
8+5 = 13 = b
124
y =10 + 16x - x²
y = 3x + 50
what is the sum of y1 and y2
139
125
2x(x-2) + 3 (4-x²)
a) (6+x) (2-x)
b) (x-6) (x+2)
c) x² + 12
d) x² -4x +12
- x² - 4x +12
1) factor out the common = -1
- 1 (x² +4x - 12)
2) factor the quadratic
- 1 (x-2 ) ( x+6) -> -1 (x-2) = x+2
3) Distribute the common factored out
- 1 (x-2 ) (x+6)
4) (-x+2) (x+6) => ( 2 - x) ( x+6) = A
a) (6+x) (2-x)
b) (x-6) (x+2)
126
(w-3)^5 - (w-3)²
a) (w-3)³
b) w^5 - w² +293
c) (w-3)² (w-3)³
d) (w-3)² ( (w-3)³ - 1))
Let A = (w-3)
127
If 64x² + px + 81 = (8x +q)². WHat is the value of p/q
16
128
x² + 3x-a / x- 2 = x+5
Given that x != 2, what is the value of a
10
129
CHECK CORRECT ANSWER
1 feet = __ inches
A rectangular swimming pool measures 12 feet 24f . A scale drawing of the pool uses a scale of 1:24. What is the area of the pool in the scale drawing in square inches
1 feet = 12inches
12feet = 144in
24f = 288in
1---- 24
x --- 144.288
144.288/ 24 : SIMPLIFY 24 with 144 and 288
If, 12x12 = 144 and 12x2 = 24. Then, 24 x 12/2= 24x6 = 288
12.6/ 1 = 72
130
A stack of 10 flyers on glossy paper weighs 0.3oz A publisher ships 64 flyers in a box that weighs }0.5oz. Shipping costs $0.98for the first ounce and $0.21 for each additional ounce rounded up to the nearest ounce. How much, in dollars, does it cost the publisher to ship the box with 64 flyers inside
10 --- 0.30z
64 --- xoz = 1.92oz + 0.5 ( box weight) = 2,42oz
0.98 ( 1oz) + 2.0.21= 1,4
2,42 -1 = 1,42 -> ROUND -> 2
131
k=xy
In the equation above, kis a constant. If the value of x were multiplied by 3, how would the value of y change?
a) y x3
b) y not change
c) y x1/3
d) y x2/3
x.y inver. proportional
| c
132
y= x/k
In the equation above, k is a constant. If x were multipled by 1\ 2how would the value of y change?
a) y = x/2k
b) y x2
c) y x1\ 2
d) y not change
y= ⬆x/k ⬇
direct proportional
y
133
Andi has a total of 55 horses, sheep, and chickens on her farm. If she has 3 horses, and the ratio of the number of sheep to the number of chickens is 8to 5, what is the difference between the number of sheep and the number of chickens Andi has?
8:5 -> total : 8+5= 13
52 / sheep = 13/ 8 = 32 sheeps
52 / chicken = 13/ 5 = 20 chickens
32 - 20 = 12
134
On average, a commercial bakery bakes 800blueberry pies in 1hour of baking. Each blueberry pie requires 4 cups of blueberries. Rounded to the nearest tenth of an hour, how many baking hours does it take for the bakery to use 30,000 cups of blueberries?
nearest TENTH OF AN HOUR =
nearest TENTH OF AN HOUR =
800 x 4 = 3200 cups --- 60min
30,000 cups ---- x min = 562min
5.62min
135
A marine aquarium has a small tank and a large tank, each containing only red and blue fish. In each tank, the ratio of red fish to bluefish is 3 to 4. The ratio of fish in the large tank to fish in the small tank is 46 to 5. What is the ratio of blue fish in the small tank to red fish in the large tank?
15: 184
10: 69
69: 10
184: 15
( 1 blue fish in small tank ) 1 . 3r/4b = 46l/5s
SIMPLIFY CROSS MULTIPLY
1. 3r/2b = 23l/5s (:2)
MULTIPLY NORMALLY : 3.23 and 2.5
1: 69/10 = prportion
SIMPLIFY x10
10 : 69
b
136
A gardener purchases a 1.67 gallon bottle of weed killer. The ratio of the total weed killer volume to its active ingredient, glyphosate, is 1:2, colon. If the manufacturer charges $58.00 per gallon for the glyphosate in the weed killer and charges $40.00 per gallon for the other ingredients in the weed killer, then, rounded to the nearest dollar, how much does the manufacturer charge for the 1.67gallon bottle of weed killer?
1w/2g = 1.67/g => 0.83g
0.83 x 58$ = 48$
the rest : 1.67 - 0.83 = 0.83
0.83 x 40$= 33$
48 + 33 = 82
137
In the west region of the US, the ratio of densely vegetated land to sparsely vegetated land is 11:18. In the central region of the US, the ratio is 3:1 What is the difference in percentage of densely vegetated land from the west region to the central region?
11:18 -> 11+18 = total 29
11/29 . 100% = 38%
3+1 = total 4
3/4. 100% = 75%
75%-38%=37%
138
Owen answered a set of math and history Quiz Bowl questions. Owen correctly answered 72%percent of all the 200 questions. However, Owen answered 53.3% of the math questions correctly. If 45% of the questions were in math, what percent of history questions did Owen answer correctly?
200 questions . 45% = 90 MATH questions
90 x 53.3% = 48 Correct Math Q.
200 - 90 = 110 HISTORY questions
200. 72% correct = 144 total correct - 48 = 96 hist correct
96/110 . 100% = 87% correct history que
139
An organization determined most of its sales only occurred after at least 4 contacts. However, 44% percent of its salespeople gave up on a customer after the 1th contact didn't make a sale. Of the remaining salespeople, 40% t contact. Finally, 41%, percent of the salespeople who made a 3th contact gave up when that call did not make a sale. To the nearest percent, what percent of the original salespeople made 4 or more contacts if the first 3 contacts did not result in sales?
```
1th contact) 100% - 44% = 56% - remaining
2th) 56% . 40% = 0.224 = 22,4%
56% - 22,4% = 33,6%
3th) 33,6% . 41% = 13,77%
33,6% - 13,77 = 19,83% - remaining
```
20% remains
140
The population of Springville is on the rise. Each year, on January 11, the town holds its own census and the population is recorded. In 2010 the town recorded a population of 12000. The 2011 census reported a 5% percent increase from the 2010 population, and the 2012 census reported a 7% percent increase from the 2011population. By how many people did the population of Springville increase over the 2-year period?
INCREASE = 100% + 5% = 105% = 1.05
1.05 x 1.07 = 1,1235
1,1235 x 12000 = 13482
13482 - 12000 = 1482
141
Daniela has a three-season acting contract for a new TV show. Her pay for Season 1 is p dollars. Then, her pay will increase by 5percent from Season 1 to Season 2 and by 10 percent from Season 2 to Season 3. Which of the following represents Daniela's Season 3 pay in terms of p?
A) 1.15p
b) 1.05p
c) p/1,05
d) (1.05)(1.1)P
d
SUCCESSIVE INCREASE = SUCCESIVE % MULITPLICATION
1.1 ( season 2) x 1.05 ( +5% for season3)
142
It takes 20 drops of rain to make 1 milliliter. How many drops would it take to fill a 50-gallon rain barrel?
1 gallon =3.785liter;1L= 1000 milliliters ; 20 drops = 1mm)
20drops/1mm = x drops/50 gallon
20drops/1mm . 1000mm/1L
CUT mm with mm
20000drops/1L . 3.785L/ 1 gallon
CUT L with L
75,700drops /1 gallon = x drops/50 gallon
x = 378500
143
Dr. Li Jie measures the absorption of radiation coming from his X-ray device to be 5⋅10 ^ - 18
t square centimeters per square nanosecond but needs to report the finding in "grays", where grays are equivalent to square meters per square second. If there are 10^9 nanoseconds in a second, what is the absorption of radiation in grays?
A) 5.10^-40
B) 5.10^11
C) 5.10^-11
D) 5.10^-4
m² = means 10^-4 for cm²
ns² means (10^9)² for s²
5.10^-18 = 10^-4 /9^18
SIMPLIFY: CUT THE SAME ONES : 10^18
5 = 10^-4
D
144
6.5.10^-² kJ per cs . A watt is equivalent to 1 joule per second . What is the number equal to W
```
1cs= __ s
1KJ = __ J
```
```
1cs = 0.01s
1KJ = 1000J
```
6.10^-2 kJ/cs = W. J/s = 1000J/1KJ
CUT KJ with kj
6.10¹ J / 1cs = 1cs/0.01s
CUT cs with cs =
60/ 0.01s = ¹ - (-²) = 1 + 2 = 6.10³
145
Osmium is the densest naturally occurring element, with a density of 22.59 grams per cubic cm. What is the desntiy in lb per cubic inch, rounded to the nearest tenth
1g= 0.0022lb and 1cm³ = 0.061in³
start unit . linking unit/starting unit . final unit/linking unit = final unit
22.59 . g/cm³ = 1cm³/0.061in³
CUT cm³ with cm³
22.59g/ 0.061in³ . 0.0022lb/1g = lb/in³
Cut g with g
22.59 . 0.0022lb/ 0.061in³ = 0,81
146
NET Credit sales : 72,000
Average accounts receivable: 9,000
The accounts receivable turnover ratio is the ratio of net credit sales to average accounts receivable. The turnover ratio shows the average number of times per year that the company collects its debts. For example, a turnover ratio of 12 means the company takes about 1 month to collect its debts, while a turnover ratio 2/3 means the company takes about 18 months to collect its debts. How many months does it take the company whose accounts are shown in the table above to collect its debts?
72000/9000 = 8 turnover
8 / 1 year = 8 /12months = 2times / 3months
2times / 3months = 1times/ x month = 1.5
147
Guilherme can mow his 4acre lawn in 2 hours. His lawnmower cuts 3 foot wide swaths. He can drive his car 132miles in 2 hours, also. How many times as fast is Guilherme's car as his lawnmower?
(1mi² = 640ac; 1mi=5280ft)
4ac x 1mi²/ 640ac = 1mi²/ 160mi²
Cut "ac" and simplify
3ft x 1mi/5280ft = 1mi/1760mi
Cut "ft" and simplify
1mi²/ 160mi² = 1mi/1760mi . lenght = 11mi
11mi now is linear to compare with 132mi
132/11 = 12
Now, 50mi = lenght is linear with 132miles
132 - 50 = 82
148
The maximum recorded speed for the American antelope is 88.5kilometers per hour. At this speed, how long, to the nearest tenth of a second, does it take for an American antelope to run 1 kilometer?
1) How MANY seconds , the antalope takes to run 1 km
1hour/3600s . 88.5km/ 1 hour ❌ Cuz, this will be 88.5km per sec. We want 1 km per x sec
88.5km --- 1 hr
1 km ------- x = 0.011
0.011 x 3600s = 40.6 sec
INVERT THEN
3600s/1h . 1hour / 88.5km = 40.7 sec per 1km
149
A company conducts a study to understand how employees act during meetings. They observe a total of 300 different meetings and determine whether employees are choosing to multitask or not. The following incomplete table shows the results.
Multitask : Phone ( ) In-person( ) Web ( 68) Video(10)
❌Multi: Phone (11) In-person (7) Web ( ) Video (3)
Total: P (160) In ( ) Web ( ) Vid (13)
Overall, employees chose to multitask during 90%, percent of all the meetings observed. Based on the information above, as a decimal, what is the probability that employees choose to multitask during an in-person meeting?
Multitask : Phone ( ) = 160 -11 = 149
90% . 300 = 270
270 = 149 + 68 + 10 + In-person( ) = 43
In person Total = 43+7 = 50
Multitask : Phone ( 149 ) In-person( 43 ) Web ( 68) Video(10)
❌Multi: Phone (11) In-person (7) Web ( ) Video (3)
Total: P (160) In ( 50) Web ( ) Vid (13)
Multitask In-person / Total In-person = 43/50
150
A holistic veterinarian conducts a study of the use of slippery elm to treat gastrointestinal symptoms. Overall, the prescription of this medication showed positive outcomes within two days for approximately 80%, percent of all dogs in this study. This result was consistent for dogs in each weight category. Based on the information provided, approximately what percentage of dogs in this study were larger than 50 pounds?
+50pounds : 137 ( + ) 39 (-)
29-50 pounds: 312 ( )
14-29pounds: 236 ( )
6-14pounds ( ) 115
"This result was consistent for dogs in each weight category. " =>
total = positive outcomes/ 0.8
OR 137+39 =176
Apply to others to discover the TOTAL DOGS = 1436
171/1436
151
Of the 500 people surveyed, 54.6% said they were offered paid vacation. Based on the information provided, what is the probability of randomly selecting a person who has paid vacation if given that they are a part-time worker?
PAID : 114 ( Part-time) ( ) Full time
X PAID: ( ) 16
100% - 54.6 = 45.4% total that X PAID
500 x 45.4% = 227
227 - 16 = total Part times not paid + 114 = 325 ( total part-time)
114/325
152
Donte and his friends ordered pizza for a birthday party. They asked all the guests at the party whether they wanted sauce or no sauce and whether they wanted cheese or no cheese. The results are displayed in the table above.
Sauce: ( ) 🧀 ( ) No🧀 18 Total
No Sau: ( ) ( ) 8
Total: 20 6 26
Donte found that 1/5 of the people who wanted cheese did not want sauce. What fraction of the people who wanted sauce also wanted cheese
a) 8/13
b) 1/5
c) 4/5
d) 8/9
d
153
The bar graph above shows the number of sites occupied by peregrine falcons in Canada from 1990to 2010By approximately what percent did the number of occupied sites increase from 1990 to 2010 ?
(graph)
1990 --- 300
2010 -- 600
a) 33%
b) 50%
c) 30%
d) 100%
(x) 50%
Difference/ Initial value . 100 %
600-300/300 . 100% = 100%
154
The graph at left in the LF plane of a particular thickness of guitar string to the frequency in Hertz Hz at which it will vibrate. By what factor does the frequency decrease between string lengths of 0.5m and 0.6 m
graph :
0. 5m --- 400
0. 6m --- 300
a) 0.16
b) 0.5
c) 0.31
d) 0.75
By what factor = 400. x = 300
| x = 300/400 = 0.75
155
A physics book author received a one-time advance of $5000 from a publisher for her latest book. In addition, she will receive a royalty of $9.50 for each book sold. Her total revenue, R, is the amount of the advance plus her royalties. Which of the following graphs represents the relationship between revenue, R, in thousands of dollars, and number of books sold, x, in hundreds of books? Write the 2 points (x,y) that the correct graph should have
THE GRAPH'S NUMBERS ARE IN UNITS
R, IN THOUSANDS of dollars; books,x, IN HUNDREDS of books
1 book ---- 9.5 $
100 books----> 950$
5000 -> 5 in the graph of y-axis of thousands of dollars
(0, 5) ( 10 , 950)
950-5/10 = 9.45
156
The rectangular floor of a playpen has a perimeter of 24feet. Which of the following graphs in the , A-plane could represent the relationship between the width, w, in feet, and the floor area, A, in square feet, of the playpen?
Area is y-axis and Width is x-axis
```
perimeter = 2(w+l)
24 = 2 (w+l) -> 12 = w+l
```
```
Area = w. l -> w ( 12-w) = 0
w = 0; 12-w= 0 , w=12
```
The parabola ( because is 12w - w²) should start at 0 and finish at 12 in the x-axis
157
The number of medical publications that mention evolutionary medicine each year is shown at left, with the data for 2007 and 2008 missing. Based on the entire trend of the data, what is the best estimate of the number of publications that mentioned evolutionary medicine in 2008?
```
21 ------- 2000
29------- 2001
40 ------- 2002
57 -------- 2003
79 --------- 2004
111 -------- 2005
156 ------- 2006
```
their differences in subtraction differs a lot. So, it is EXPONENTIAL.
Let's check the RATIO diffrences
29/21 = 1.38
156/111 = 1.40
Nearly similar - let's PADRONIZE to 1.40
2007 is 1.4 times the 2006, and 2008 is 1.4times the 2007:
1.4 x 1.4 x 156 = 307
158
The table on the left models the GDP in America across 7 decades, with one value missing. Which of the following is the most reasonable estimate of the GDP in 1980?
```
1950 ------ 0.320
1960 --------- 0.614
1970 ----------- 1.179
1980 -------------- x
1990 -------------- 4.347
2000 --------------8.347
```
1. 744
2. 264
2. 763
3. 218
They seems to be 2x , let's check
0.614/0.320 = 1.91 -- less that 2x
1.179 x 2 = 2.358
is less than 2x, so the result also need to be less than 2.358 ; B 2.264
159
The table at left partially summarizes the percent of residents in different counties who participate in performing arts at least once a month. The percentages have a range of 12.9% What could be the percentage of county G residents who participate in performing arts at least once a month?
9.9% ------ A
8.8% ===== B
7.8 ------------ C
5.2 ---------- D
17.3 ---------- E
4.7 ---------- F
X ------------ G
4.7 -----------H
range = max - min
17.3 - 4.7 = 12.6
12.9 - 12.6 = 0.3
If the range % is constant for all, then, we just need to see the range of 0.3% in G. Since the only matter is the max and the min
4.7 - 0.3 = 4.4
17.3 + 0.3 = 17.6
Testify:
if G = 4.4, then the overal range is : 17.3 - 4.4 = 12.9
If G = 17.6, then the overall range is : 17.6 - 4.7 = 12.9
160
The table above lists the weights, in kilograms, of a litter of newborn piglets. Of the mean, range, and standard deviation of the values listed, which will decrease if the 0.98KG measurement is removed from the data?
0. 98 ; 1.13
1. 13 ; 3.36
1. 52 ; 1.66
0.98 is the smallest value . If range is max value - min value , so if the min value turn to be a higher value, the difference ( the range) will decrease.
Standard aviation = the spread of the mean = the range of the mean; Therefore, if the min value is removed, the distance from the starting to the mean is decreased.
If the min value is removed, the average ( the mean) will increase. Since this low value contributes to lowering down the average
161
18=12C+13S
A batch of hard candy needs C gallons of corn syrup and S gallons of sucrose to create 18 pounds of sweetener as shown in the equation above. What is the increase in the amount of corn syrup in gallons if the amount of sucrose decreases by 1 gallon?
If S decreases, then C should increase to MAINTAIN BALANCE since the result should be CONSTANT
1 gallon of sucralose = 13
13 decrease in sucralose = 13 increase in C
New value/ Original value = increased amount
13/12
162
M⋅V=P⋅Q
The quantitative theory of money states that given M dollars in circulation in a year, a monetary velocity of V, a price level of P, and a real output of Q dollars, the above equation is correct. An economist considers the case where the dollars in circulation and the real output are known constants. Which of the following expressions is the change in monetary velocity as the price level increases by 1?
A) Q
B) M
C) Q/M
D) M/Q
M will be DEPENDENT one , and P the INDEPENDENT
M = P.Q/M
C
163
T=0.125(I−8,225) in dollars to be paid by an individual with an income of I between 8,22534,500 dollars is given by the equation above. Tax is paid from the portion of income above 8,225dollars and the remaining amount becomes a part of disposable income. What percentage of income above 8,225dollars remains after paying tax for an individual whose income falls within the specified range?
I - 8,225 will result a real value , and it will need to multiply 0.125. Therefore, 0.125 is the one that will alter the real value to become the Taxes
Taxes = - 12.5 % of the real income above 8,225 dollars
The ANOTHER PART IS : 100% - 12,5% = 87,5%
164
t= 1/4p+2
Ana uses the equation above to determine the number of hours, t, to roast a ppp-pound turkey. How many more minutes would it take Ana to roast a 13-pound turkey than a 12-pound turkey?
We can eliminate "2" since it will add up for both values
the only value that will alter according to each value, is 1/4
1/4 hour = 60min/4 = 15min
