AnswersMOHEGAN - ALGEBRA 1AIntroduction to Compound Inequalities

Introduction to Compound Inequalities — Unit test Answers

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The formula for the area of a triangle is , where b is the length of the base and h is the height.Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.

Question illustration
A
3 units
B
5 units
C
8 units
D
9 units
2
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Nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. In the first part of the race, her average speed was 8.75 kilometers per hour. For the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. Which expression represents Nikita’s distance for the second part of the race?

Question illustration
A
6t
B
0.65 – t
C
6(0.65) – t
D
6(0.65 – t)
3

Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.What is the missing step of her solution?

Question illustration
A
Add 10.4 to both sides.
B
Add negative 10.4 to both sides.
C
Multiply both sides of the equation by 10.4.
D
Divide both sides of the equation by 10.4.
4

A metalsmith is mixing two molten metals, each containing different percentages of silver. The table shows the amount of each molten metal used.

Question illustration
A
(15)(0.75) and 0.7(15 – x) + 0.9x
B
(15)(0.75) and 0.7(15 – x)(0.9x)
C
15 + 0.75 and 0.7(15 – x) + 0.9x
D
15 + 0.75 and 0.7(15 – x)(0.9x)
5

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

A
2.3p – 10.1 = 6.4p – 4
B
2.3p – 10.1 = 6.49p – 4
C
230p – 1010 = 650p – 400 – p
D
23p – 101 = 65p – 40 – p
E
2.3p – 14.1 = 6.4p – 4
6

Which compound inequality is represented by the graph?

Question illustration
A
x < –4 or x ≥ 3
B
x < –4 and x ≥ 3
C
x ≤ –4 or x < 3
D
x ≤ –4 and x < 3
7

Which compound inequality could be represented by the graph?

Question illustration
A
–4 ≤ x ≤ 4
B
–2 ≤ x ≤ –1
C
x ≤ –1 or x ≥ 0
D
x ≤ 3 or x ≥ –1
8

To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?

A
12 < x ≤ 12.2
B
12 > x ≤ 12.2
C
x > 12 or x ≤ 12.2
D
x < 12 or x ≤ 12.2
9

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.$8$9$11$13$14

A
$8
B
$9
C
$11
D
$13
E
$14
10

Which compound inequality is represented by the graph?

Question illustration
A
x < –4 or x ≥ 3
B
x < –4 and x ≥ 3
C
x ≤ –4 or x < 3
D
x ≤ –4 and x < 3
11

Tickets to a school production cost $5 for a student ticket and $10 for an adult ticket. A total of 67 tickets were purchased at a cost of $440.

Question illustration
A
67
B
440
C
67 – a
D
440 – a
12

At a pumpkin patch, if Armando guesses the weight of his pumpkin within 0.3 pounds, he gets to take the pumpkin home for free. If his pumpkin weighs 4.9 pounds, which two equations can be used to find the minimum and maximum weights he can guess in order to get his pumpkin for free?

A
x – 0.3 = 4.9 and x – 0.3 = –4.9
B
x + 0.3 = 4.9 and x + 0.3 = –4.9
C
x + 4.9 = 0.3 and x + 4.9 = –0.3
D
x – 4.9 = 0.3 and x – 4.9 = –0.3
13

The axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.What is the equation when solved for a?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends of her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week?

Question illustration
A
(10h + 60) = (10h)
Option A
B
(10h + 60h) = (10h)
Option B
C
h(10 + 60) = h(10)
Option C
D
(10 + 60h) = (10h)
Option D
15

Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.What percentage of blue pigment is in ink B?

A
45%
B
49%
C
60%
D
75%
16

Alex has 84 quarters and nickels worth a total of $17.80.

A
0.25q + 0.05(q – 84) = 17.80
B
0.05q + 0.25(84 – q) = 17.80
C
0.25(q – 84) + 0.05q = 17.80
D
0.05(84 – q) + 0.25q = 17.80
17

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s=180(n−2), where n is the number of sides.Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°? Round to the nearest whole number.

A
6 sides
B
7 sides
C
8 sides
D
9 sides
18

Sara wants to find the input value that produces the same output for the functions represented by the tables.

Question illustration
A
–2
B
–1
C
1
D
2
19

The axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.What is the equation when solved for a?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh.

A
= h
Option A
B
= h
Option B
C
Pmg = h
D
= h
Option D

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