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Marta_Voda [28]

2 years ago

10

You paint four walls. Each wall is a rectangle with a length of 18 feet and a height of 12 feet. One gallon of paint covers abou

t 320 square feet. How many gallons of paint do you need in order to cover the walls?

1 answer:

Agata [3.3K]2 years ago

3 0

Answer:

you will need exactly 2.7 gallons of paint but if rounded you'll need 3 gallons

Step-by-step explanation:

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Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.

ycow [4]

The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: $y = k \times f(x)$

Horizontal stretch by a factor k: $y = f\left(\dfrac{x}{k}\right)$

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

Learn more about Transforming functions:

brainly.com/question/17006186

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5 0

2 years ago

You have decided to invest $1000 in a savings bond that pays 4% interest, compounded semi-annually. What will the bond be worth

Evgen [1.6K]

Answer:

$2191.12

Step-by-step explanation:

We are asked to find the value of a bond after 10 years, if you invest $1000 in a savings bond that pays 4% interest, compounded semi-annually.

$FV=C_0\times (1+r)^n$ , where,

$C_0=\text{Initial amount}$ ,

r = Rate of return in decimal form.

n = Number of periods.

Since interest is compounded semi-annually, so 'n' will be 2 times 10 that is 20.

$4\%=\frac{4}{100}=0.04$

$FV=\$1,000\times (1+0.04)^{20}$

$FV=\$1,000\times (1.04)^{20}$

$FV=\$1,000\times 2.1911231430334194$

$FV=\$2191.1231430334194$

$FV\approx \$2191.12$

Therefore, the bond would be $2191.12 worth in 10 years.

3 0

3 years ago

Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter

Vaselesa [24]

We have been given a function $f(x)=2x^3+3x^2-336x$ . We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

$f'(x)=2(3)x^{2}+3(2)x^1-336$

$f'(x)=6x^{2}+6x-336$

$6x^{2}+6x-336=0$

$x^{2}+x-56=0$

$x^{2}+8x-7x-56=0$

$(x+8)-7(x+8)=0$

$(x+8)(x-7)=0$

$x=-8,x=7$

So $x=-8,7$ are critical points and these will divide our function in 3 intervals $(-\infty,-8)U(-8,7)U(7,\infty)$ .

Now we will find derivative over each interval as:

$f'(x)=(x+8)(x-7)$

$f'(-9)=(-9+8)(-9-7)=(-1)(-16)=16$

Since $f'(9)>0$ , therefore, function is increasing on interval $(-\infty,-8)$ .

$f'(x)=(x+8)(x-7)$

$f'(1)=(1+8)(1-7)=(9)(-6)=-54$

Since $f'(1)$ , therefore, function is decreasing on interval $(-8,7)$ .

Let us check for the derivative at $x=8$ .

$f'(x)=(x+8)(x-7)$

$f'(8)=(8+8)(8-7)=(16)(1)=16$

Since $f'(8)>0$ , therefore, function is increasing on interval $(7,\infty)$ .

(b) Since $x=-8,7$ are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

$f(-8)=2(-8)^3+3(-8)^2-336(-8)$

$f(-8)=1856$

$f(7)=2(7)^3+3(7)^2-336(7)$

$f(7)=-1519$

Therefore, $(-8,1856)$ is a local maximum and $(7,-1519)$ is a local minimum.

(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

$f''(x)=6(2)x^{1}+6$

$f''(x)=12x+6$

$12x+6=0$

$12x=-6$

$\frac{12x}{12}=-\frac{6}{12}$

$x=-\frac{1}{2}$

Therefore, $x=-\frac{1}{2}$ is an inflection point of given function.

3 0

2 years ago

What could the measure of the acute angles in a right triangle be?

Aleksandr [31]

25 and 65 because 90 and 90 makes a square

7 0

3 years ago

Read 2 more answers

Which of the following are the subset of ,B={1,2,3,4,5,6,7,8,9,10}.

Verdich [7]

Answer:

A, C, T

Step-by-step explanation:

A subset simply means a set of which all of its elements are contained in a larger set :

To obtain the subsets of B={1,2,3,4,5,6,7,8,9,10}.

We observe the smaller sets whose entire elements can be found in B

D={0,2,4,6,8,10,12} = not a subset of B ; B does not contain 0

A={5,6,7} = subset of B, all elements Cann be found in B

C={2} = subsets of B, 2 can be found in B

T={1,2,3,4,5,...,8} = subset of B; all elements can be found in B

4 0

2 years ago