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Lady bird [3.3K]
2 years ago
6

For geometry:( will give brainist to the correct answer!!!

Mathematics
1 answer:
Over [174]2 years ago
7 0

Answer:

y = ⅔x - 5

Step-by-step explanation:

The line that passes through (-3, -7) will have the same slope (m) as the line, 2x - 3y = 24. This is because if two lines that are parallel to each other would have the same slope.

Rewrite 2x - 3y = 24, in the slope-intercept form, y = mx + b.

Thus:

2x - 3y = 24, rewritten would give us y = ⅔x - 8.

The slope of the line, 2x - 3y = 24, is ⅔.

Thus, the slope of the line that is parallel to 2x - 3y = 24, is also ⅔.

To find the equation, substitute a = -3, b = -7, and m = ⅔ into y - b = m(x - a).

Thus:

y + 7 = ⅔(x + 3)

Rewrite to make the equation in slope-intercept form.

Thus:

y + 7 = ⅔(x + 3)

3(y + 7) = 2(x + 3) ---› multiplication property of equality

3y + 21 = 2x + 6 ----› distributive property

3y = 2x + 6 - 21 ----› subtraction property of equality

3y = 2x - 15

y = ⅔x - 5 (division property of equality)

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There is a 10% sales tax on a purchase of $13.50 how much is the tax
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1.35

Step-by-step explanation:

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In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat
NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

    35x = -0.05(x² - 800x + 160000) + 9492

    35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

    35x = -0.05x² +40x - 8000 + 9492

    35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492}  }{2X0.05}   = \frac{5 +/- \sqrt{25 + 298.4}  }{0.1} =  \frac{5 +/- \sqrt{323.4}  }{0.1}\\=  \frac{5 +/- 17.983 }{0.1}\\=  \frac{5 - 17.983 }{0.1}  or  \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or  \frac{22.983 }{0.1}\\= -129.83 or 229.83

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

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Answer:

Can not be determined.

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  1 to 5

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