Explain how to use the distributive property to create an expression that is equivalent to 2b + 5b

13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.

aev [14]

Answer:

$y=4sin(\frac{\pi}{2} x+\pi)-2$

Step-by-step explanation:

The equation of a periodic function is in the form:

y = Asin(Bx + C) + D

Where A = amplitude, B = 2π / period, D = vertical shift, phase shift = -C / B.

Given that:

amplitude: 4, period 4 phase shift = vertical shift = -2

Hence:

A = amplitude = 4, B = 2π / period = 2π / 4 = π / 2, D = vertical shift = -2.

Phase shift = -C / B

C = -phase shift * B = - * -2 * π / 2 = π.

Therefore substituting gives:

$y=4sin(\frac{\pi}{2} x+\pi)-2$

8 0

3 years ago

To prepare for a bake-off, Travis used 630 grams of flour each day for 3 weeks. How many kilograms did Travis use in those 3 wee

Diano4ka-milaya [45]

Answer:

hahahahhahahahahahahahahq

6 0

3 years ago

Please help ASAP!!! I will mark the Brainliest!!

Svetlanka [38]

To answer this question, you need to know that a scale factor is the relationship between one dimension of the shape.

Because the information given to us is a two-dimensional measurement, you will need to consider that when getting the answer.

The ratios of the areas of the triangles is 3/5 x 3/5 or 9/25.

To determine the area of the larger triangle, you will solve the following equation using the information you know. x is the area of the larger triangle.

9/25x = 576; solve for x by dividing both sides by 9/25
x = 1600 square inches

The area of the larger triangle is 1600 square inches.

6 0

3 years ago

A square with unknown side length x has one side extended by 3 inches and the other side extended by 4 inches as shown. The area

natulia [17]

Answer:

(x + 3)(x + 4) = 110

or x² + 7x + 12 = 110

Step-by-step explanation:

4 0

3 years ago

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

As

$3^{\frac{1}{8}\cdot \:24}=3^3$

So

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

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6 0

3 years ago