Hi there!

6. x² + 6x = 27
subtract 27 on both sides to make the equation equal to 0.
x² + 6x - 27 = 0
(x - 3)(x + 9) = 0
x - 3 = 0 x + 9 = 0
x = 3 x = -9

7. k² - 13k + 36 = 0
(k - 9)(k - 4) = 0
k - 9 = 0 k - 4 = 0
k = 9 k = 4

8. g(x) is translated up 5 from f(x).

9. g(x) is reflected by x-axis, then translated 3 down from f(x).

Hope this helped! :)

7 0

3 years ago

What is the rate of change for f(x) =7 sin x-1 on the interval from x=0 to x=piover 2

Oksi-84 [34.3K]

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------$

$\bf f(x)= 7sin(x)-1 \qquad 
\begin{cases}
x_1=0\\
x_2=\frac{\pi }{2}
\end{cases}\implies \cfrac{f\left( \frac{\pi }{2} \right)-f(0)}{\frac{\pi }{2}-0}
\\\\\\
\cfrac{[7\cdot 1-1]~-~[7\cdot 0-1]}{\frac{\pi }{2}}\implies \cfrac{6-(-1)}{\frac{\pi }{2}}\implies \cfrac{6+1}{\frac{\pi }{2}}\implies \cfrac{7}{\frac{\pi }{2}}\implies \cfrac{14}{\pi }$

7 0

4 years ago