Ask question

Ask question

All categories

3 years ago

8

A basketball court is in the shape of a rectangle. It has a length of (x − 7) meters and a width of (x + 3) meters. The expressi

on below represents the area of the court in square meters:
(x − 7)(x + 3)

Which of the following simplified expressions represents the area of the basketball court in square meters?

− 6x + 3
x^2 − 21
x^2 − 4x − 21
x^2 − 7x + 3

1 answer:

Step2247 [10]3 years ago

5 0

X^2 -3x+7x-21

so simplified is:

x^2 - 4x - 21

You might be interested in

3y''-6y'+6y=e*x sexcx

Simora [160]

From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

$3r^2-6r+6=0\iff r^2-2r+2=0$

which has roots at $r=1\pm i$ . This admits the two fundamental solutions

$y_1=e^x\cos x$
$y_2=e^x\sin x$

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

and so

$u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx$
$u_1=\dfrac13\ln|\cos x|$

$u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx$
$u_2=\dfrac13x$

Therefore the particular solution is

$y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

so that the general solution to the ODE is

$y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

7 0

2 years ago

Which of the following can prove that figure ABCD is a square?

Klio2033 [76]

Answer:

A

Step-by-step explanation:

all sides of square is 90degrees

Since AC and BD is the same, when you join the lines together, it will definitely be a square

7 0

3 years ago

Porter uses 2 pints of stain on each table that he makes. How many tables can he paint with

Nitella [24]

<h3>Answer: 4 tables</h3>

Explanatioin

1 table needs 2 pints

There are 8 pints in a gallon, so he can paint 8/2 = 4 tables.

6 0

2 years ago

Read 2 more answers

At one gas station, gas costs $2.75 per gallon. Complete the equation that relates the total cost, C, to the number of gallons o

dolphi86 [110]

Answer:

C = 2.75

Step-by-step explanation:

it does not tell how much there for it is 1 gallon

6 0

2 years ago

A family buys a studio apartment for $240,000. They pay a down payment of $60,000.

stealth61 [152]

Answer:

Part A: 25%
Part B: 40%

Step-by-step explanation:

Given the following questions:

$240000 for a studio apartment
$60000 as a down payment.

In order to find the answer, we use the formula to calculate the percentage for the total cost of the studio apartment and the down payment.

<u>Part A:</u>
$\frac{c\times n}{100}$
$\frac{25\times240000}{100} =25\times240000=60000$
$=60000$

<u>Part B:</u>
$\frac{c\times n}{100}$
$\frac{40\times240000}{100} =40\times240000=9600000\div100=96000$
$=96000$

The percent of a down payment of $60,000 for a $240,000 studio apartment is "25%." While the percent of a $96,000 dollar down payment for a $240,000 studio apartment is "40%."

Hope this helps.

8 0

2 years ago