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3 years ago

6

If f(x) = -x2 – 1, and g(x) = x + 5, then f(g(x)) = [ ? ]x2+[? ]x+[?]

1 answer:

Misha Larkins [42]3 years ago

8 0

Answer:

-x^2-10x-26

Step-by-step explanation:

f(x) = -x^2 – 1, and

g(x) = x + 5

f(g(x)) = Plug g(x) in for x in f(x)

= -(x+5)^2 -1

= -(x^2 +10x+25) -1

= -x^2 -10x-25 -1

=-x^2-10x-26

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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)

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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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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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$-5 = \frac{y_1 - 9}{2}$

$-5*2 = \frac{y_1 - 9}{2}*2$

$-10 = y_1 - 9$

$-10 + 9 = y_1 - 9 + 9$

$-1 = y_1$

$y_1 = -1$

Coordinates of endpoint B is (-6, -1)

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Answer:

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