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4 years ago

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8. Suppose y varies directly as x. If y = -4 when x = 32, find x when ys -0.

1 answer:

Nata [24]4 years ago

4 0

Answer:

$x=0$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

in this problem

For x=32, y=-4

Find the value of the constant of proportionality k

$k=y/x$

substitute

$k=-\frac{4}{32}$

simplify

$k=-\frac{1}{8}$

so

The linear equation is

$y=-\frac{1}{8}x$

Find x when the value of y=0

Remember that

In a proportional relationship <u><em>the line passes through the origin</em></u>

so

If y=0

then

the value of x must be equal to zero

therefore

$x=0$

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Ares is making 14 jars of honey peanut butter. He wants to use 45 milliliter (ML) of honey in each jar. How much honey (in ML) w

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8) Find the endpoint Cif M is the midpoint of segment CD and M (2, 4) and D (5,7)

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Answer:

8. c. (-1, -1)

9. a. (-6, -1)

b. True

Step-by-step Explanation:

8. Given the midpoint M(2, 4), and one endpoint D(5, 7) of segment CD, the coordinate pair of the other endpoint C, can be calculated as follows:

let $D(5, 7) = (x_2, y_2)$

$C(?, ?) = (x_1, y_1)$

$M(2, 4) = (\frac{x_1 + 5}{2}, \frac{y_1 + 7}{2})$

Rewrite the equation to find the coordinates of C

$2 = \frac{x_1 + 5}{2}$ and $4 = \frac{y_1 + 7}{2}$

Solve for each:

$2 = \frac{x_1 + 5}{2}$

$2*2 = \frac{x_1 + 5}{2}*2$

$4 = x_1 + 5$

$4 - 5 = x_1 + 5 - 5$

$-1 = x_1$

$x_1 = -1$

$4 = \frac{y_1 + 7}{2}$

$4*2 = \frac{y_1 + 7}{2}*2$

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Coordinates of endpoint C is (-1, 1)

9. a.Given segment AB, with midpoint M(-4, -5), and endpoint A(-2, -9), find endpoint B as follows:

let $A(-2, -9) = (x_2, y_2)$

$B(?, ?) = (x_1, y_1)$

$M(-4, -5) = (\frac{x_1 + (-2)}{2}, \frac{y_1 + (-9)}{2})$

$-4 = \frac{x_1 - 2}{2}$ and $-5 = \frac{y_1 - 9}{2}$

Solve for each:

$-4 = \frac{x_1 - 2}{2}$

$-4*2 = \frac{x_1 - 2}{2}*2$

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$-8 + 2 = x_1 - 2 + 2$

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$x_1 = -6$

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b. The midpoint of a segment, is the middle of the segment. It divides the segment into two equal parts. The answer is TRUE.

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