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3 years ago

The function f(x)=(25)x is shown on the coordinate plane. Which statement is true?

Mathematics

1 answer:

aivan3 [116]3 years ago

3 0

Answer: In the right end, as x increases without bound, the graph of f(x) decreases.

In the left end, as x decreases without bound, the graph of f(x) increases.

Step-by-step explanation:

According to the graph, the end behaviour of the function in the image is decreasing without bound. When we graph a function, with put an arrow to indicate when a function increases or decreases without bound, that's why in this case we can say the decreases without bound, the function extends without limit.

Therefore, as the x increases, f(x) decreases. If you carefully pay attention to the graph, x is constantly increasing in the right end, and f(x) is more and more close to the x-axis.

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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac

Fed [463]

Answer:

$\theta=k\pi, \hspace{3}k\in Z\\\\ or\\\theta =2\pi k \pm arccos(\frac{1 }{8} ), \hspace{3}k\in Z\\$

Step-by-step explanation:

Factor constant terms:

$-2(-4sin(2\theta)+sin(\theta))=0$

Divide both sides by -2:

$sin(\theta)-4sin(2 \theta)=0$

Expand trigonometric functions using the fact:

$sin(2 \theta) =2 sin(\theta) cos(\theta)$

So:

$sin(\theta) -8sin(\theta)cos(\theta)=0$

Factor sin(x) and constant terms and multiply both sides by -1:

$sin(\theta) (8cos(\theta)-1)=0$

Split into two equations:

$(1)=8cos(\theta)-1=0\\\\(2)=sin(\theta)=0$

For (1)

Add 1 to both sides and divide both sides by 8:

$cos(\theta)=\frac{1}{8}$

Take the inverse cosine of both sides:

$\theta =2\pi k \pm arccos(\frac{1 }{8} ), \hspace{3}k\in Z$

For (2)

Simply take the inverse sine of both sides

$\theta = k \pi, \hspace{3}k\in Z$

Therefore, the solutions are given by:

$\theta=k\pi, \hspace{3}k\in Z\\\\ or\\ \theta =2\pi k \pm arccos(\frac{1 }{8} ), \hspace{3}k\in Z\\$

8 0

3 years ago

Determine all intervals on which f(x) > 0.

8_murik_8 [283]

Answer: [-7, -4]u[0, 3]

4 0

3 years ago

How to find the discounted price example $25.00 is the original price and the discount is 15%

Alexandra [31]

Since the price is now 15% less you would first find what 15% of 25 is by using 25*.15 and get 3.25 then you subtract that from 25 and get 25-3.25= $21.75

3 0

3 years ago

What’s the answer to this?

Vanyuwa [196]

Answer:

answer c

Step-by-step explanation:

the two x-intercepts are (-4,0) and (2,0) so the factors of the equation are (x-2) and (x+4). if you multiply the factors it gives you the equation of the graph whic is x^2+2x-8 so c= -8 and b= 2

8 0

3 years ago

Amanda teaches the art of quilling to four students these students each teach the art of quilling to four other students if this

il63 [147K]

Answer:

341

Step-by-step explanation:

The number of people who know the art of quilting in each successive generation is

1, 4, 16, …

These numbers represent a geometric sequence where each term has the form

aₙ = a₁rⁿ⁻¹

In your sequence, a₁ = 1 and r = 4.

Then, the formula for your sequence is

aₙ = 4ⁿ⁻¹

Sum over five generations

The formula for the sum of the first n terms of a geometric series is

Sum = a₁[(1 - rⁿ)/(1 - r)]

Sum = 1[(1 - 4⁵)/(1 - 4)

= (1 - 1024)/(-3)

= -1023/-3

= 341

If the process continues for five generations, 341 people will know the art of quilting.

4 0

3 years ago

Read 2 more answers