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3 years ago

What is the equation of the quadratic function graphed below?

Mathematics

1 answer:

Hitman42 [59]3 years ago

5 0

Answer:

y = -3(x + 1)² + 9

Step-by-step explanation:

y = a(x - h)² + k, where (h, k) is the vertex

The vertex of the quadratic function is (-1, 9)

The only equation listed that has a vertex at (-1, 9) is:

y = -3(x + 1)² + 9

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Find exact values for sin θ, cos θ and tan θ if csc θ = 3/2 and cos θ < 0.

kumpel [21]

Answer:

Part 1) $sin(\theta)=\frac{2}{3}$

Par 2) $cos(\theta)=-\frac{\sqrt{5}}{3}$

Part 3) $tan(\theta)=-\frac{2\sqrt{5}}{5}$

Step-by-step explanation:

step 1

Find the $sin(\theta)$

we have

$csc(\theta)=\frac{3}{2}$

Remember that

$csc(\theta)=\frac{1}{sin(\theta)}$

therefore

$sin(\theta)=\frac{2}{3}$

step 2

Find the $cos(\theta)$

we know that

$sin^{2}(\theta) +cos^{2}(\theta)=1$

we have

$sin(\theta)=\frac{2}{3}$

substitute

$(\frac{2}{3})^{2} +cos^{2}(\theta)=1$

$\frac{4}{9} +cos^{2}(\theta)=1$

$cos^{2}(\theta)=1-\frac{4}{9}$

$cos^{2}(\theta)=\frac{5}{9}$

square root both sides

$cos(\theta)=\pm\frac{\sqrt{5}}{3}$

we have that

$cos(\theta) < 0$ ---> given problem

$cos(\theta)=-\frac{\sqrt{5}}{3}$

step 3

Find the $tan(\theta)$

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=\frac{2}{3}$

$cos(\theta)=-\frac{\sqrt{5}}{3}$

substitute

$tan(\theta)=\frac{2}{3}:-\frac{\sqrt{5}}{3}=-\frac{2}{\sqrt{5}}$

Simplify

$tan(\theta)=-\frac{2\sqrt{5}}{5}$

6 0

2 years ago

How do you write 287% as a fraction or mixed number in simplest form? Submit

Anna007 [38]

As a fraction: 287/100

As a mixed number: 2 87/100

_____
Remember, "%" means exactly the same thing as "/100".

3 0

3 years ago

What would a piece 430 feet 3 inches cost if you get a 10% discount for the larger volume? A piece of wire cable 180 ½ feet long

alexgriva [62]

To get the answer to this question you would have to multiply these numbers.
The normal price appears to be 65.95 for 180.5 feet.
First we could divide 430.25 by 180.5
This divides out to become 2.39027778.
We would then multiply This by our normal price for 180.5 feet, which is 65.95.
This gives us 157.63882.
We would next need to take the 10 percent off. The easiest way to do this is to multiply our price by .90
This would give us 141.484938.

3 0

3 years ago

A 3” x 5” photo is enlarged so that the length of the new photo is 7 inches. Find the width of the new photo.. a. 4.20 inches. c

Andrej [43]

As far as the old dimensions of the photo are concerned,
Width of the photo = 3"
Length of the photo = 5"
New length of the photo = 7 inches
Let us assume the new width of the photo = x inches
Then
3/5 = x/7
5x = 7 * 3
5x = 21
x = 21/5
= 4.20 inches
So the correct option among all the options that are given in the question is the first option. I hope that the answer has come to your help.

3 0

2 years ago

Which representation has a constant of variation of -2.5

Neporo4naja [7]

Answer:

See explanation

Step-by-step explanation:

The constant of variation is found using the slope formula:

$\frac{y_2-y_1}{x_2-x_1}$

The given relation is

X : -2 , -3, -4, -5

Y : -5, -7.5,-10,-12.5

We can use any two ordered pair to find the constant of variation.

Using (-2,-5) and (-3,-7.5), we have

$m=\frac{-7.5--5}{-3--2} =\frac{-2.5}{-1} =2.5$

The constant of variation is 2.5

We need to repeat this for all the options to identify the one with -2.5 as slope.

unfortunately, you did not provide the remaining options.

6 0

3 years ago

Read 2 more answers