other math

Question 1

How to get interior angles?

Answer 1

n-2 x 180

n= number of sides
(e,g, triangle= 3-2x180

Question 2

Solve for x: log₁₀(x) + log₁₀(5) = 2

Answer 2

x = 20

Using the log rule: log(a) + log(b) = log(ab) => log₁₀(5x) = 2 => 5x = 100 => x = 20

Question 3

If logₐ(64) = 3, what is the value of a?

Answer 3

a = 4

logₐ(64) = 3 means a³ = 64 => a = 64^(1/3) = 4

Question 4

A television is sold at a 15% discount for $595. What was its original price?

Answer 4

Original price = $700

Let original price be x. => x - 0.15x = 595 => 0.85x = 595 => x = 595 / 0.85

Question 5

If $500 is invested at 4% simple interest per annum for 3 years, what is the total amount?

Answer 5

Total amount = $560

Simple interest = P × R × T / 100 = 500 × 4 × 3 / 100 = $60; Total amount = 500 + 60

Question 6

A car travels 180 km in 3 hours. What is its average speed?

Answer 6

Average speed = 60 km/h

Speed = Distance / Time = 180 / 3

Question 7

If 5 workers can build a wall in 12 days, how long will 3 workers take to build the same wall?

Answer 7

3 workers take 20 days

Work = workers × days = 5 × 12 = 60 => 3 workers take 60 / 3

Question 8

Find the area of a triangle with base 8 cm and height 5 cm.

Answer 8

Area = 20 cm²

Area = 1/2 × base × height = 1/2 × 8 × 5

Question 9

A rectangular prism has dimensions 5 m, 3 m, and 2 m. What is its volume?

Answer 9

Volume = 30 m³

Volume = length × width × height = 5 × 3 × 2

Question 10

An object is thrown upwards with a velocity of 20 m/s. How high will it go?

Answer 10

Solution not available.

Question 11

A car accelerates from rest at 4 m/s². What is its speed after 5 seconds?

Answer 11

Speed = 20 m/s

v = u + at = 0 + 4 × 5

Question 12

Find the sum of the first 5 terms in the geometric sequence: 2, 4, 8,…

Answer 12

Sum = 62

S₅ = a(r⁵−1)/(r−1) = 2(2⁵−1)/(2−1)

Question 13

What is the 10th term of the arithmetic sequence: 3, 7, 11,…?

Answer 13

10th term = 39

Common difference d = 4. T₁₀ = 3 + (10-1)×4

Question 14

Find the product of matrices A = [[1, 0], [0, 1]] and B = [[5, 6], [7, 8]].

Answer 14

Result = [[5, 6], [7, 8]]

Multiplying with identity matrix gives same matrix

Question 15

If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]], find A + B.

Answer 15

A + B = [[3, 2], [4, 7]]

A + B = [[1+2, 2+0], [3+1, 4+3]]

Question 16

How many sides does a regular polygon have if each internal angle is 120°?

Answer 16

n = 6

Sum of internal angles = (n−2)×180; Each angle = 120

Question 17

Find the area of a circle with radius 7 cm.

Answer 17

Area ≈ 153.94 cm²

Area = πr² = π×7²

Question 18

If it is currently 2:30 PM, what time will it be after 2 hours and 45 minutes?

Answer 18

5:15 PM

Question 19

A train departs at 13:45 and arrives at 16:20. How long is the journey?

Answer 19

Journey = 2 hrs 35 mins

Question 20

A bus travels 300 km in 5 hours. What is its speed?

Answer 20

Speed = 60 km/h

Speed = Distance / Time = 300 / 5

Question 21

If a person walks at 4 km/h, how far will they walk in 1.5 hours?

Answer 21

Distance = 6 km

Distance = speed × time = 4 × 1.5

Question 22

Find the mean of the numbers: 5, 10, 15, 20, 25.

Answer 22

Mean = 15

Mean = (5+10+15+20+25)/5

Question 23

What is the median of the numbers: 3, 1, 7, 9, 5?

Answer 23

Median = 5

Arrange: 1, 3, 5, 7, 9 → Median = 5

Question 24

speed=

Answer 24

distance/time