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Gekata [30.6K]
2 years ago
15

Here are two rectangles.

Mathematics
1 answer:
Drupady [299]2 years ago
3 0
The two rectangles are similar and the scale factor is 3:4
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Find the value of $B - A$ if the graph of $Ax + By = 3$ passes through the point $(-7,2),$ and is parallel to the graph of $x +
Salsk061 [2.6K]

Answer:

-6

Step-by-step explanation:

We know that since Ax + By = 3 passes through (-7, 2), then if we plug -7 in for x and 2 in for y, the equation is satisfied. So, let's do that:

Ax + By = 3

A * (-7) + B * 2 = 3

-7A + 2B = 3

We also know that this line is parallel to x + 3y = -5, which means their slopes are the same. Let's solve for y in the second equation:

x + 3y = -5

3y = -x - 5

y = (-1/3)x - (5/3)

So, the slope of this line is -1/3, which means the slope of Ax + By = 3 is also -1/3. Let's solve for y in the first equation:

Ax + By = 3

By = -Ax + 3

y = (-A/B)x + 3/B

This means that -A/B = -1/3. So, we have a relationship between A and B:

-A/B = -1/3

A/B = 1/3

B = 3A

Plug 3A in for B into the equation we had where -7A + 2B = 3:

-7A + 2B = 3

-7A + 2 * 3A = 3

-7A + 6A = 3

-A = 3

A = -3

Use this to solve for B:

B = 3A

B = 3 * (-3) = -9

So, B = -9 and A = -3. Then B - A is:

B - A = -9 - (-3) = -9 + 3 = -6

The answer is -6.

<em>~ an aesthetics lover</em>

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