AnswersINMT3 Integrated Math 3 Sem 1 26-27Solving One-Variable Equations with Systems

Solving Quadratic Equations by Factoring Answers

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The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x – 2x2. For what number of tabletops does the company make a profit of $0?

A
100 tabletops
B
120 tabletops
C
240 tabletops
D
480 tabletops
2
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A rectangular field has an area of 1,764 m2. The width of the field is 13 m more than the length. What is the perimeter of the field?

A
121 m
B
144 m
C
168 m
D
170 m
3

What are the solutions to the equation (x – 6)(x + 8) = 0?

A
x = –6 or x = 8
B
x = –6 or x = –8
C
x = 6 or x = –8
D
x = 6 or x = 8
4

The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x – 2x2. For what number of tabletops does the company make a profit of $0?

A
100 tabletops
B
120 tabletops
C
240 tabletops
D
480 tabletops
5

The solutions to the equation are or

Question illustration
Answer not available
6

The square of a number is 12 less than 7 times the number. What is the number?

A
–4 or –3
B
–4 or 3
C
–3 or 4
D
3 or 4
7

Use the zero product property to find the solutions to the equation x2 + 12 = 7x.

A
x = –4 or x = 3
B
x = –4 or x = –3
C
x = –3 or x = 4
D
x = 3 or x = 4
8

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased?

A
2 ft
B
4 ft
C
8 ft
D
10 ft
9

The square of 9 less than a number is 3 less than the number. What is the number?

A
–12 or 7
B
–12 or –7
C
–7 or 12
D
7 or 12
10

Use the zero product property to find the solutions to the equation x2 – 13x + 30 = 0.

A
x = –10 or x = –3
B
x = –10 or x = 3
C
x = –3 or x = 10
D
x = 3 or x = 10
11

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle?

A
20 in.
B
26 in.
C
120 in.
D
138 in.
12

Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

A
x = –6 or x = 1
B
x = –3 or x = –2
C
x = –1 or x = 6
D
x = 2 or x = 3
13

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle?

A
20 in.
B
26 in.
C
120 in.
D
138 in.
14

Use the zero product property to find the solutions to the equation x2 + 12 = 7x.

A
x = –4 or x = 3
B
x = –4 or x = –3
C
x = –3 or x = 4
D
x = 3 or x = 4
15

What are the solutions to the equation 3(x – 4)(x + 5) = 0?

A
x = –4 or x = 5
B
x = 3, x = 4, or x = –5
C
x = 3, x = –4, or x = 5
D
x = 4 or x = –5
16

The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
17

A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What does the value of x in her solutions represent?

A
one possible length and one possible width
B
two possible amounts for the widths
C
two possible amounts for the lengths
D
two possible amounts by which the dimensions were changed
18

What are the solutions to the equation (2x – 5)(3x – 1) = 0?

A
x = or x =
Option A
B
x = or x = 3
Option B
C
x = or x =
Option C
D
x = 5 or x = 1

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