Final Review Flashcards
(36 cards)
When simplyifing always remember to
simplify the numbers e.q 9/36 to 1/4
<= or full circle
[x,y]
< or emty circle
(x,y)
Infinite sign
(x,y)
When you simplify a negative exponent e.q (y^-6/ 3x^5)^-4 What should you do?
As we can see the 3 is on the denominator, so before you start multiply 3 with -4 you convet the exponent 4 to positive by moving 3 to the numerator and then you start multypling. BUTTT, for the y sinci it has -6 we can multiply it with the exponent -4 and it will give us a positive answer withought needing to move it (unless the answer is negative we move it).
How to solve for y in the following problem 4/5=y+5/ 15
Solving a proportion of the form (x+a)/b = c/d
We multiply 4 by 15 and 5 by y+5 (the opposites) and we continue to solve for y
How to solve the following word problem?
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $25 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has a $12 monthly fee and charges an additional $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
To slove the following problem we will need to write the first plan as follows 25 + 0.12x (we add the x because we do not know the number of calls. It was stated on the problem as for each minute of calls) and the second as 12 + 0.16x and then we combine them 25 + 0.12x = 12 + 0.16x and we start to solve for x
Solve for y, where y is a real number y^1/4 = -2
Solving an equation with exponent 1/a: Problem type 1
We put the two sides in parantheses by the exponent 4 (y^1/4)^4 = (-2)^4 and then we start to solve. We will get y = 16. So we will need to check: 2= -2 they are not like each other so it is not true and answer is NO SOLUTION
Solve w^3=-9 where w is a real number.
Solving an equation using the odd-root property: Problem type 1
The answer will be -3 square root of 9. The negative is outside the square root because - means -1 and if we multiply it inside the squar root it will give us -1 so we move it to be outside the square root
How to solve a radical quation solving for v such as the following *square root of v = -3 *
We raise both sides of the equation to an exponent of 2 (since a square root means 2) and then we will get v=9 as the answer. BUT because it is negative we have to check by replacing v with 9 on the first form of the equation e.q square root of 9 = -3 this will give us 3 = -3 which is not true. The answer is NO SOULTION
TO solve any equation with a square root you have to
multily it with 2 so you free the equation from the square root and you start solving
How to solve the radiacal x= square root of x + 6
We do the same as always which is raising both sides of the equation to an exponent of 2. This time x is on both sides and we have to solve for x so we will get x^2 = x + 6 we will need to move the x + 6 to the other side and start factoring. We will get (x-3)(x +2) or x= 3,-2 but before we write them asthe answer we should check by replacing x with the 3 and -2 in the first form of the equation. We will see that 3 is true while -2 is not true so we will only write 3 as the answer
How to simplify a square root of w^7
= square root of w^6 and square root of w
= w^3 and square root of w
Why w^3? Well because multiplying 2 by 3 will give us 6
How to simplify a radical expression such as square root of 5y^2u and square root of 10yu^6
Simplifying a product of radical expression: Multivariate
We combine all the nubers and vaiables inside one quare root and multiply them with each other. We will get square root of 50y^3u^7. We silplify it to be 5yu^3 square root of 2yu
How to simplify a radical expression such as square root of 12x^4w^9 and square root of 3x^6w^4
Simplifying a product of radical expression: Multivariate
We will do the same as the others which is multiplying and combining them to one suare root. We will get square root 36x^10w^13. This one is a boit diffrent to simplify it we will do the following: square root 36x^10w^12w
(6)^2(w^5)^2(w^6)^2 square root of w.
Answer: 6w^5w^6 square root of w
In a radical expression like this 8u square root of 48uy - y and square root of 27u YOU
MULTIPLY when movig a number inside the root to outside it you multiply it with the number that was outside
In a radical expression like this u square root of 2u - 4u square root of 18uy YOU
SUBTRACT based on the order that was given. For example you got uy - 12 the answer will be -11
When simplyfing a higher radical expression do not forget to
Put the expression on the upper left of the square root
Write the following as an exponential expression: 4 on the upper left of the square root and a square root of y^3
y^3/4
Numerator = exponent
Denominator = upper left of the square root
Do the opposite if youu were asked write it as a radical expression.
How to write a radical on its simplified form
To simplify it we write the radical using exponents e.q upper left of the square 6 with square root of y^2 will be y^6/2
SECOUND: if it was multilpy it meanse addition and if it was division it means subtraction.
How to solve a system of equations that have fractions
We first find the LCD and then we multiply the LCD by each side. Then, wwe continue to solve the system as the others.
What should you do if you were asked to solve a system of eyuation that wants (x,y) or (x,y)?
We combine the first equation with the second equation so they become one. Then we factor to get the x(s). Then we take the x(s) or the answe and put them as the first form of the equation to get the y(s)
How to solve the following word problem?
A phone company offers two monthly plans. Plan A costs $26 plus an additional $0.11 for each minute of calls. Plan B has no initial fee but costs $0.13 for each minute of calls.
(A) For what amount of calling do the two plans cost the same?
(B) What is the cost when the two plans cost the same?
So, we write the quation for the first plan which is 26+0.11x and the second plane which is 0.13x (we write the x because wh do not know how many calls or the problem did not state how much) then we combine them as 26+0.11x = 0.13x and start to solve.
(A) will be the soultion for x which is 1300
(B) we will take the soultion and put it on the place of the x in one of the equation. For example, 0.13(1300). The answer will be 169
How to factor the following: 20v^3x^3x^7-12v^9w^5
We look at the common multiplication whic is 4 and the smalles exponent on the variables v and w which is 3 so the answer will be 4v^3w^3(5x^7-3v^6w^2)