Question
page 9 of 9
Question 1
A)
A customer paid a total of $16 for 74 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.
Each black-and-white copy cost $0.15.
Each color copy cost $0.29.
Which system of equations can be used to find b
b
, the number of black-and-white copies, and c
c
, the number of color copies that the customer paid for at the print shop?
(1 point)
Responses
Question 2
A)
A system of equations is graphed on the grid.
Which system of equations is best represented by the graph?
(1 point)
Responses
Question 3
A)
What is the solution to this system of equations?
3x+y=30
3
x
+
y
=
30
x−3y=0
x
−
3
y
=
0
(1 point)
Responses
(9,3)
(
9
,
3
)
open paren 9 comma 3 close paren
(15,−6)
(
15
,
−
6
)
open paren 15 comma negative 6 close paren
There is no solution.
There is no solution.
There are an infinite number of solutions.
There are an infinite number of solutions.
Question 4
A)
What is the value of x
x
in the solution to this system of equations?
2x+4y=−17
2
x
+
4
y
=
−
17
y=−3x+2
y
=
−
3
x
+
2
(1 point)
Responses
-2.5
-2.5
5.5
5.5
2.5
2.5
-5.5
-5.5
Question 5
A)
The tables of ordered pairs represent some points on the graphs of lines f
f
and g.
g
.
Which system of equations represents lines f
f
and g
g
?
(1 point)
Responses
y=1.75x+3.5
y
=
1.75
x
+
3.5
y=−4x−8
y
=
−
4
x
−
8
y is equal to 1 point 7 5 x plus 3 point 5 y is equal to negative 4 x minus 8
y=1.75x+3.5
y
=
1.75
x
+
3.5
y=−4x−2
y
=
−
4
x
−
2
y is equal to 1 point 7 5 x plus 3 point 5 y is equal to negative 4 x minus 2
y=3.5x+1.75
y
=
3.5
x
+
1.75
y=−4x−8
y
=
−
4
x
−
8
y is equal to 3 point 5 x plus 1 point 7 5 y is equal to negative 4 x minus 8
y=3.5x+1.75
y
=
3.5
x
+
1.75
y=4x−2
y
=
4
x
−
2
y is equal to 3 point 5 x plus 1 point 7 5 y is equal to 4 x minus 2
Question 1
A)
A customer paid a total of $16 for 74 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.
Each black-and-white copy cost $0.15.
Each color copy cost $0.29.
Which system of equations can be used to find b
b
, the number of black-and-white copies, and c
c
, the number of color copies that the customer paid for at the print shop?
(1 point)
Responses
Question 2
A)
A system of equations is graphed on the grid.
Which system of equations is best represented by the graph?
(1 point)
Responses
Question 3
A)
What is the solution to this system of equations?
3x+y=30
3
x
+
y
=
30
x−3y=0
x
−
3
y
=
0
(1 point)
Responses
(9,3)
(
9
,
3
)
open paren 9 comma 3 close paren
(15,−6)
(
15
,
−
6
)
open paren 15 comma negative 6 close paren
There is no solution.
There is no solution.
There are an infinite number of solutions.
There are an infinite number of solutions.
Question 4
A)
What is the value of x
x
in the solution to this system of equations?
2x+4y=−17
2
x
+
4
y
=
−
17
y=−3x+2
y
=
−
3
x
+
2
(1 point)
Responses
-2.5
-2.5
5.5
5.5
2.5
2.5
-5.5
-5.5
Question 5
A)
The tables of ordered pairs represent some points on the graphs of lines f
f
and g.
g
.
Which system of equations represents lines f
f
and g
g
?
(1 point)
Responses
y=1.75x+3.5
y
=
1.75
x
+
3.5
y=−4x−8
y
=
−
4
x
−
8
y is equal to 1 point 7 5 x plus 3 point 5 y is equal to negative 4 x minus 8
y=1.75x+3.5
y
=
1.75
x
+
3.5
y=−4x−2
y
=
−
4
x
−
2
y is equal to 1 point 7 5 x plus 3 point 5 y is equal to negative 4 x minus 2
y=3.5x+1.75
y
=
3.5
x
+
1.75
y=−4x−8
y
=
−
4
x
−
8
y is equal to 3 point 5 x plus 1 point 7 5 y is equal to negative 4 x minus 8
y=3.5x+1.75
y
=
3.5
x
+
1.75
y=4x−2
y
=
4
x
−
2
y is equal to 3 point 5 x plus 1 point 7 5 y is equal to 4 x minus 2
Answers
GPT-4o mini
Let's address each question one by one:
### Question 1
A customer paid a total of $16 for 74 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.
- Let \( b \) be the number of black-and-white copies.
- Let \( c \) be the number of color copies.
We have two pieces of information to create equations:
1. The total number of copies:
\[
b + c = 74
\]
2. The total cost of the copies:
\[
0.15b + 0.29c = 16
\]
The system of equations that represents this situation is:
\[
\begin{align*}
b + c &= 74 \\
0.15b + 0.29c &= 16
\end{align*}
\]
### Question 2
Since there’s no graph displayed here, I can't provide a response. You'll need to analyze the graph and identify the lines and their equations based on their intersections or slopes.
### Question 3
To find the solution to this system of equations:
1. The first equation:
\[
3x + y = 30 \quad (1)
\]
2. The second equation:
\[
x - 3y = 0 \quad (2) \implies x = 3y \quad \text{(finding } x \text{ in terms of } y)
\]
Substituting \( x = 3y \) into equation (1):
\[
3(3y) + y = 30 \implies 9y + y = 30 \implies 10y = 30 \implies y = 3
\]
Substituting \( y = 3 \) back into \( x = 3y \):
\[
x = 3(3) = 9
\]
Thus, the solution is \( (9, 3) \).
### Question 4
To find the value of \( x \) in the solution to the system of equations:
1. The first equation:
\[
2x + 4y = -17 \quad (1)
\]
2. The second equation:
\[
y = -3x + 2 \quad (2)
\]
Substituting (2) into (1):
\[
2x + 4(-3x + 2) = -17
\]
\[
2x - 12x + 8 = -17 \implies -10x + 8 = -17
\]
\[
-10x = -17 - 8 \implies -10x = -25 \implies x = 2.5
\]
### Question 5
Without the tables provided, I cannot provide an answer. You’d need to identify the slopes and intercepts (if possible) of the lines represented by the ordered pairs in the tables to match them with the equations given.
If you need further clarification or help on particular questions, let me know!
### Question 1
A customer paid a total of $16 for 74 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.
- Let \( b \) be the number of black-and-white copies.
- Let \( c \) be the number of color copies.
We have two pieces of information to create equations:
1. The total number of copies:
\[
b + c = 74
\]
2. The total cost of the copies:
\[
0.15b + 0.29c = 16
\]
The system of equations that represents this situation is:
\[
\begin{align*}
b + c &= 74 \\
0.15b + 0.29c &= 16
\end{align*}
\]
### Question 2
Since there’s no graph displayed here, I can't provide a response. You'll need to analyze the graph and identify the lines and their equations based on their intersections or slopes.
### Question 3
To find the solution to this system of equations:
1. The first equation:
\[
3x + y = 30 \quad (1)
\]
2. The second equation:
\[
x - 3y = 0 \quad (2) \implies x = 3y \quad \text{(finding } x \text{ in terms of } y)
\]
Substituting \( x = 3y \) into equation (1):
\[
3(3y) + y = 30 \implies 9y + y = 30 \implies 10y = 30 \implies y = 3
\]
Substituting \( y = 3 \) back into \( x = 3y \):
\[
x = 3(3) = 9
\]
Thus, the solution is \( (9, 3) \).
### Question 4
To find the value of \( x \) in the solution to the system of equations:
1. The first equation:
\[
2x + 4y = -17 \quad (1)
\]
2. The second equation:
\[
y = -3x + 2 \quad (2)
\]
Substituting (2) into (1):
\[
2x + 4(-3x + 2) = -17
\]
\[
2x - 12x + 8 = -17 \implies -10x + 8 = -17
\]
\[
-10x = -17 - 8 \implies -10x = -25 \implies x = 2.5
\]
### Question 5
Without the tables provided, I cannot provide an answer. You’d need to identify the slopes and intercepts (if possible) of the lines represented by the ordered pairs in the tables to match them with the equations given.
If you need further clarification or help on particular questions, let me know!