Negative Exponents Answers

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Which statement correctly explains how Andre could find the solution to the following system of linear equations using elimination?

Question illustration
A
Multiply the first equation by –7 and the second equation by 8, and then subtract.
B
Multiply the first equation by -7 and the second equation by 8, and then add.
C
Multiply the first equation by 2 and the second equation by 9, and then add.
D
Multiply the first equation by –2 and the second equation by 9, and then subtract.
2
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Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for these graphs?

A
none
B
one
C
two
D
infinitely many
3

Which graph can be used to find the solution(s) to 4x = –4x?

A
mc020-1.jpg
Option A
B
mc020-2.jpg
Option B
C
mc020-3.jpg
Option C
D
mc020-4.jpg
Option D
4

The constraints of a problem are listed below. What are the vertices of the feasible region?

Question illustration
A
mc008-2.jpg
Option A
B
mc008-3.jpg
Option B
C
mc008-4.jpg
Option C
D
mc008-5.jpg
Option D
5

A charity bingo game costs $2 per round and has a $13 entry fee for an adult. It costs $3 per round and a $10 entry fee for a child. For how many rounds of bingo are the costs the same for an adult and a child?

A
2
B
3
C
4
D
5
6

Which ordered pair (c, d) is the solution to the given system of linear equations?

Question illustration
A
(–1, 6)
B
(–1, 7)
C
(6, –1)
D
(7, 10)
7

Which graph shows the solution to the following system of inequalities?

Question illustration
A
mc020-2.jpg
Option A
B
mc020-3.jpg
Option B
C
mc020-4.jpg
Option C
D
mc020-5.jpg
Option D
8

A deli is offering two specials. The roast beef special gives a profit of $2.30 per sandwich, and the turkey special gives a profit of $3.10 per sandwich. The roast beef special uses two slices of bread and three slices of cheese. The turkey special uses two slices of bread and four slices of cheese. The deli has 120 slices of bread and 160 slices of cheese available for the specials. The deli wants to maximize its profit selling specials. Let x represent the number of roast beef specials and y represent the number of turkey specials. What are the constraints for the problem?

A
mc023-1.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-5.jpg
Option C
D
mc023-7.jpg
Option D
9

Which equation can pair with x – y = –2 to create a consistent and dependent system?

A
6x + 2y = 15
B
–3x + 3y = 6
C
–8x – 3y = 2
D
4x – 4y = 6
10

Which statement describes the solution to the system of equations?

Question illustration
A
The system has exactly one solution.
B
The system has exactly two solutions.
C
The system has no solutions.
D
The system has infinitely many solutions.
11

Which ordered pair (a, b) is the solution to the following system of equations?

Question illustration
A
mc027-2.jpg
Option A
B
mc027-3.jpg
Option B
C
mc027-4.jpg
Option C
D
mc027-5.jpg
Option D
12

Becca graphs the equations y = –3(x – 1) and y = x – 5 to solve the equation –3(x – 1) = x – 5. Her graph is shown below.What are the solution(s) of –3(x – 1) = x – 5?

Question illustration
A
–5 and 3
B
–3
C
1 and 5
D
2
13

What is the maximum value of P = 24x + 30y, given the constraints on x and y listed below?

Question illustration
A
120
B
132
C
138
D
150
14

Which region represents the solution to the given system of inequalities?

Question illustration
A
A
B
B
C
C
D
D
15

A small organic food store makes two types of fruit smoothies: tropical and sport. Each tropical smoothie uses 9 oz of orange juice and 6 oz of milk. Each sport smoothie uses 3 oz of orange juice and 3 oz of milk. The store buys the orange juice in a 210-oz container and milk in a 150-oz container. The store sells the tropical smoothies for $4 and sells the sport smoothie for $3. What is the maximum in smoothie sales the store can make from 1 container each of orange juice and milk?

A
$100
B
$110
C
$150
D
$280
16

Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?

A
There are no intersection points.
B
There is exactly one intersection point.
C
There are exactly two intersection points.
D
There are infinitely many intersection points.
17

Which system of equations can be graphed to find the solution(s) to ?

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
mc004-4.jpg
Option C
D
mc004-5.jpg
Option D
18

The constraints of a problem are listed below. What are the vertices of the feasible region?

Question illustration
A
(0, 0), (0, 4), , (3, 0)
Option A
B
(0, 0), , , (6, 0)
Option B
C
(0, 4), , (3, 0)
Option C
D
, , (6, 0)
Option D
19

How many solutions exist for the system of equations below?

Question illustration
A
none
B
one
C
two
D
infinitely many
20

Michael graphs the equations and y = x + 1 to solve the equation . His graph is shown below. What are the solution(s) of ?

Question illustration
A
–1 and 8
B
1 and 4
C
2
D
3

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