Math Questions With Answers (4)

A set of comprehensive math questions are presented. Answers to these questions are also provided and are located at the lower part of the page.

Question 1

How much water should be added to 20 ounces of a 20% acid solution to reduce it to a 10% solution?

Question 2

Solve for C the following equation: B = 2 B D + 2 C E + 2 C L

Question 3

Thomas can paint the house in 6 days, while it takes Joe 12 days to paint the same house. How long would it take Thomas and Joe, working together, to paint the house?

Question 4

Solve the following system of equations
3x - 4y = 25
-2x + y = -10

Question 5

An airliner can make a 3,000 mile trip with tailwind (wind in the same direction as the airliner) in 4 hours and make the return trip against the wind (with the same speed) in 4 hours 48 minutes (4.8 hours). Find the ground speed of the airliner.

Question 6

Write as a single interval if possible: (-9 , 2) U (1 , 30)

Question 7

Solve the equation: |5x - 2| - 2 = 6

Question 8

Solve the inequality: |4x + 6| < 30

Question 9

Solve the inequality: |4x + 5| - 5 > 6

Question 10

Solve the inequality: √ (3x - 2)² < 5

Question 11

Solve the equation: |-2x + 5| = 2x - 5

Question 12

Solve the equation: |4x - 2| = 8x - 12

Question 13

Evaluate and write in standard form: (4 - 2i)(-3 + 3i), where i² = -1.

Question 14

Evaluate and write in standard form: (2 - 3i) / (2 - 2i), where i² = -1. (where i is the imaginary unit)

Question 15

Evaluate and write in standard form: (-3 + 2i)² - 3(3 - i)(-2 + 2i), where i² = -1. (where i is the imaginary unit)

Question 16

Solve the equation: -(x - 2)² - 2 = 7

Question 17

Solve the equation: (-x + 3)² - 12 = 8

Question 18

Solve the equation: 3 + 30/x² = -21/x

Question 19

Solve the equation: -x / (x² + 2x - 3) + 5 / (x + 3) = 1

Question 20

The sum of a number and its reciprocal is 82 / 9. Find the number.

ANSWERS TO ABOVE QUESTIONS

1) 20 ounces
2) C = B(1 - 2D) / (2E + 2L)
3) 4 days
4) (3 , -4)
5) 687.5 miles/hour
6) (-9 , 30)
7) x = 2 , x = - 6 / 5
8) -9 < x < 6
9) (- infinity , -4) U (3/2 , + infinity)
10) (-1 , 7/3)
11) [5/2 , + infinity)
12) x = 5/2
13) -6 + 18 i
14) 5/4 - i / 4
15) 17 - 36 i
16) x = 2 + 3 i , x = 2 - 3 i
17) x = 3 + 2 SQRT(5) , x = 3 - 2 SQRT(5)
18) x = -2 , x = -5
19) x = 1 + i , x = 1 - i
20) Two possible solutions: x = 9 and x = 1 / 9

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