F(x) = -(x+1)^2+4 What is the vertex

Mathematics

1 answer:

alexandr402 [8]2 years ago

5 0

4 is the vertex just to let you know that is the answer

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4x - 4 - 2x + 3 solve this problem

DENIUS [597]

Answer: 2x-1
combine like terms: 4x and -2x
-4 and 3

6 0

2 years ago

I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

7 0

3 years ago

Label the following graph as vertical or horizontal:

vfiekz [6]

The answer is vertical.

8 0

2 years ago

<img src="https://tex.z-dn.net/?f=z%5E%7B7%7D%3D128i" id="TexFormula1" title="z^{7}=128i" alt="z^{7}=128i" align="absmiddle" cla

abruzzese [7]

If z ⁷ = 128i, then there are 7 complex numbers z that satisfy this equation.

$z^7 = 128i = 2^7i = 2^7e^{i\frac\pi2}$