Multiply.<br> (v-3)(v+7)<br> Simplify your answer.

Shelley is fresh out of college and looking for housing in Boston. She makes $37,000 a year and may have to move within two year

Aleonysh [2.5K]

Id go with option 4 or 1

5 0

3 years ago

Read 2 more answers

A land owner is planning to build a fenced-in, rectangular patio behind his garage, using his garage as one of the "walls." He w

GrogVix [38]

Answer: 800 feet²

Step-by-step explanation:

Lets remove the brackets from the function's expression

A(x) = -2x²+80x

So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max

As we know Xmax= (X1+X2)/2 , where X1 and X2 are the roots of the function A(x)

Lets find X1 and X2

x(80-2x)=0

x1=0 80-2*X2=0

x2=40

So Xmax= (0+40)/2=20

So Amax= A(20)= 20*(80-2*20)=20*40=800 feet²

3 0

3 years ago

A card is drawn from a standard deck of cards. What is the probability

Black_prince [1.1K]

The probality is 69 420

3 0

3 years ago

Convert the polar equation r = 2 secØ to a Cartesian equation.y = 2x = 2x^2 = 2

ss7ja [257]

Polar and cartesian equation<h2>Initial explanation</h2>

Let's analyze the relation between r and x and y:

We have that between the indicated value of r (of the polar coordinates) and x and y (of the cartesian coordinates) there is a relation because they form a triangle. If r changes, then the value of x and y will change.

<h2>STEP 1: given equation</h2>

Using the given equation

r = 2 secØ

we have that

$\begin{gathered} r=2secØ \\ \downarrow \\ \frac{r}{2}=secØ \end{gathered}$ <h2>STEP 2: secØ equation</h2>

Observing the image of the initial explanation we have a right triangle, we know that the equation of

secØ for any right triangle is given by:

$\sec Ø=\frac{\text{hypotenuse}}{\text{adjacent side}}$

In this case,

hypotenuse = r

adjacent side = x

then,

$\begin{gathered} \sec Ø=\frac{\text{hypotenuse}}{\text{adjacent side}}=\frac{r}{x} \\ \sec Ø=\frac{r}{x} \end{gathered}$ <h2>STEP 3: comparison between given equation and secØ equation</h2>

Then, we have that:

$\begin{gathered} \sec Ø=\frac{r}{x} \\ \sec Ø=\frac{r}{2} \end{gathered}$

This means that:

$\begin{gathered} \frac{r}{x}=\sec Ø=\frac{r}{2} \\ \downarrow \\ \frac{r}{x}=\frac{r}{2} \end{gathered}$

Then,

x = 2

The equation in cartesian coordinates is x=2.

Answer: x=2

6 0

1 year ago

At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 11 m. T

OLEGan [10]

Answer:

$\text{Exact area of the sidewalk}=40 \pi\text{ m}^2$

$\text{Approximate area of the sidewalk}=125.6\text{ m}^2$

Step-by-step explanation:

We have been given that at a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 11 m. The inner edge of the sidewalk is a circle with a radius of 9 m.

To find the area of the side walk we will subtract the area of inner edge of the side walk of lion pen from the area of the outer edge of the lion pen.

$\text{Area of circle}=\pi r^2$ , where r represents radius of the circle.