F(x)= -(x+7)²+4. Which of the following is true for f(x). Check all that apply

Mathematics

1 answer:

3241004551 [841]3 years ago

4 0

A and D seem to be the only correct ones. Hope this helps

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What is the volume of an equilateral triangular prism?

Nata [24]

Actually, the "slant height" is 4, but the vertical height or "altitude" of the equilateral triangle is not 4

but anyway..... $\bf \begin{array}{cllll}
\textit{height of an equilateral triangle}\\\\
h=\cfrac{s\sqrt{3}}{2}\\
----------\\
\textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}
\end{array}\qquad s=\textit{length of one side}$

and the volume, is the area of the triangle, times the length, so, whatever you get for the area of the triangle * 10

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Given points A (-3,-4) and B (2,0), points P (-1,-12/5) partitions line AB in the ratio

kvv77 [185]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&A&(~ -3 &,& -4~) 
&P&(~ -1 &,& -\frac{12}{5}~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AP=\sqrt{[-1-(-3)]^2+[-\frac{12}{5}-(-4)]^2}
\\\\\\
AP=\sqrt{(-1+3)^2+(-\frac{12}{5}+4)^2}\implies AP=\sqrt{2^2+\left( \frac{8}{5} \right)^2}
\\\\\\
AP=\sqrt{4+\frac{64}{25}}\implies AP=\sqrt{\cfrac{164}{25}}\implies AP=\cfrac{\sqrt{164}}{\sqrt{25}}
\\\\\\
\boxed{AP=\cfrac{2\sqrt{41}}{5}}$

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&P&(~ -1 &,& -\frac{12}{5}~) 
&B&(~ 2 &,& 0~)
\end{array}
\\\\\\
PB=\sqrt{[2-(-1)]^2+[0-\left(-\frac{12}{5} \right)]^2}
\\\\\\
PB=\sqrt{(2+1)^2+\left( \frac{12}{5} \right)^2}\implies PB=\sqrt{9+\frac{144}{25}}\implies PB=\sqrt{\cfrac{369}{25}}
\\\\\\
PB=\cfrac{\sqrt{369}}{\sqrt{25}}\implies \boxed{PB=\cfrac{3\sqrt{41}}{5}}$

so, let's check the ratio of AP:PB

$\bf AP:PB\implies \cfrac{AP}{PB}\implies \cfrac{\frac{2\sqrt{41}}{5}}{\frac{3\sqrt{41}}{5}}\implies \cfrac{2\underline{\sqrt{41}}}{\underline{5}}\cdot \cfrac{\underline{5}}{3\underline{\sqrt{41}}}\implies \cfrac{2}{3}$

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Gnoma [55]

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Which ordered pair is a solution of the equation? y=-2x+5y=−2x+5 (Choice A) A Only (2,-9)(2,−9) (Choice B) B Only (-2,9)(−2,9) (

Firdavs [7]

Answer:

Choice B: Only (-2, 9)

Step-by-step explanation: