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Nookie1986 [14]
2 years ago
9

The graph of which of the following will be parallel to the graph of 4x – 3y = –12?

Mathematics
1 answer:
Fudgin [204]2 years ago
8 0
First, we need to write the equation into the form y=mx + b which is as follows:

<span>4x – 3y = –12
y = (4/3)x + 12

For an equation to be parallel, they should have the same slope. For this case, the slope should be 4/3. I believe the correct answer is option A. </span>The graph of y=4/3x - 3/2 <span>will be parallel to the graph of 4x – 3y = –12.</span>
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Step-by-step explanation:

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A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. At a certain screening
-BARSIC- [3]

Answer:

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving  a system of linear equations.

First we write the system equations :

C+S+A=750

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

3C+5S+7A=3450

This equation represents the totaled receipts.

The system :

C+S+A=750\\3C+5S+7A=3450

has the following associated matrix :

\left[\begin{array}{cccc}1&1&1&750\\3&5&7&3450\end{array}\right]

By performing elementary matrix operations we find that the matrix is equivalent to

\left[\begin{array}{cccc}1&0&-1&150\\0&1&2&600\\\end{array}\right]

The new system :

C-A=150\\S+2A=600

Working with the equations :

C = 150 + A\\S = 600-2A

Our solution vector is :

\left[\begin{array}{c}C&S&A\end{array}\right] =\left[\begin{array}{c}150+A&600-2A&A\end{array}\right]

For example :

If 0 adults attended ⇒ A = 0

C = 150 + 0 \\C = 150\\S = 600 - 2A\\S = 600

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S = 600 -2A

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

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3 years ago
Underline all the ordered pairs (x,y) that are solutions to the equation y=2x+1.
Romashka [77]

Answer:

<u>(3,7)</u> (7,3) (−1,14) <u>(0,1)</u> <u>(12,25)</u>

<u>(5,11)</u> (0,12) (1,8) (12,0) <u>(−1,−1)</u>

Step-by-step explanation:

We have the following function:

y = 2x+1.

We are going to check if each ordered pair is a solution.

(3,7)

If when x = 3, y = 7, it is a solution.

y = 2x + 1 = 2(3) + 1 = 7

This ordered pair is a solution.

(7,3)

If when x = 7, y = 3, it is a solution.

y = 2x + 1 = 2(7) + 1 = 15

This ordered pair is not a solution.

(-1,14)

If when x = -1, y = 14, it is a solution.

y = 2x + 1 = 2(-1) + 1 = -1

This ordered pair is not a solution.

(0,1)

If when x = 0, y = 1, it is a solution.

y = 2x + 1 = 2(0) + 1 = 1

This ordered pair is a solution.

(12,25)

If when x = 12, y = 25, it is a solution.

y = 2x + 1 = 2(12) + 1 = 25

This ordered pair is a solution.

(5,11)

If when x = 5, y = 11, it is a solution.

y = 2x + 1 = 2(5) + 1 = 11

This ordered pair is a solution.

(0,12)

If when x = 0, y = 12, it is a solution.

y = 2x + 1 = 2(0) + 1 = 1

This ordered pair is not a solution.

(1,8)

If when x = 1, y = 8, it is a solution.

y = 2x + 1 = 2(1) + 1 = 3

This ordered pair is not a solution.

(12,0)

If when x = 12, y = 0, it is a solution.

y = 2x + 1 = 2(12) + 1 = 25

This ordered pair is not a solution.

(-1,-1)

If when x = -1, y = -1, it is a solution.

y = 2x + 1 = 2(-1) + 1 = -1

This ordered pair is a solution.

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2 years ago
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Answer:

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Step-by-step explanation:

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