Math Is Fun Forum

I would very much appreciate the help on checking if these are correct

Solve the quadratic equations in questions 1 – 5 by factoring.
1.
Q. x2 – 49 = 0

A. x = -7, 7

2.
Q. 3x3 – 12x = 0

A. x = -2, 2

3.
Q. 12x2 + 14x + 12 = 18

A. x = -3/2, 1/3

4.
Q.  –x3 + 22x2 – 121x = 0

A. x = 11, 11

5.
Q. x2 – 4x = 5

A. x = -1, 5

6.
Q. Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

A. x2 – 4x - 21

7.
Q. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

A. x2 – 14x + 24

8.
Q. Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4.

A. x2 – 7/2x -2
And if we want to get rid of the fraction:
2(x2 – 7/2x -2)
2x2 – 14/2x – 2
(2 goes into 14, 7 times)
Final Answer: 2x2 – 7 - 4

9.
Q. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0.

A. x2 + 0x + 0

10.
Q. Write a quadratic equation that cannot be factored.

A. x2 + x + 3

11.
Q. The product of two consecutive positive integers is 72. Find the integers.

A.
n(n + 1) = 72
n2 + n = 72
n2 + n – 72 = 0
(n + 9)(n – 8) = 0
Solution becomes -9 and 8. Problem asks for two positive numbers. We reject -9. Since n = 8 and there is n+ 1, we do 8 + 1 which comes up to 9.
Answer: 8, 9

12.
Q. The product of two consecutive negative integers is 10506. Write a quadratic equation that you could solve to find the integers.

A.
n(n + 1) = 10506
n2 + n = 10506
n2 + n – 10506 = 0
(n + 103)(n – 102) = 0
Solution comes to an obvious -103 and 102. Problem asks for two negative numbers.
n + 1 = -103 + 1 = -102
Answers: -102, -103

13.
Q. The product of two consecutive odd integers is 63. Write a quadratic equation that you could solve to find the integers, then find the integers.

A.
n(n + 2) = 63
n2 + n = 63
n2 + n – 63 = 0
(n + 9)(n – 7)
Answer: -9, 7

14.
Q. A tennis ball is launched with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:
4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0

A. I believe the last equation is the correct one: -4.9t2 + 24.5t + 117.6 = 0

15.
Q. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)
t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.

A. I believe the third one is correct: t = 3 as in it will take 3 seconds for the ball to hit the ground.

16.
Q. Using the same equation, determine when the ball is at a height of 49 meters.

A. It will take 7 seconds for the ball to reach 49 meters.

I am having a hard time understanding how to do these correctly. Could someone please help explain how to do them step by step?

1. (3x + 6x)/3x

2. (21x3 + 14x) / 7

3. (4x5 + 8x2) / 4x

4. [2(x – 1) + 3(x – 1)] / (x – 1)

5. [3(2x – 3) – x(2x – 3)] / (2x - 3)

6. [x2(5x + 6) – 3(5x + 6)] / (5x + 6)

7. [3x2(2x - 3) + 27x3(2x - 3)] / [3x(3 – 2x)]

For my studies. I'm not to sure how to do them. Especially number 2.

1. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?

2. After watching hours of those home improvement shows, you decide you want to paint you bedroom. You don’t want to paint all four walls the same color (how boring!), but instead, you want to paint one wall a different color. The electric orange paint you’ve chosen for the "special" wall is more expensive, and you’re on a budget, so you need to know the area of the wall so you can buy the smallest amount of paint possible. You know that the height of the wall is half the length. You also know that the perimeter of the rectangular wall is 48 feet. What is the area of the wall?

A The area of the wall is 128 sq.ft.
BThe area of the wall is 116 sq. ft.
CThe area of the wall is 144 sq. ft.
DThe area of the wall is 140 sq. ft.
E The area of the wall is 416 sq. ft.
F The area of the wall is 136 sq. ft.