5(2x-7)+42-3x=2 what is the answer

Suppose that the functions p and q are defined as follows.p(x) = -2x + 1q(x)=-x?Find the following.

MariettaO [177]

First let us find

$(q\mathrm{}p)(x)$ $\begin{gathered} q(p(x))=q(-2x+1) \\ =-(-2x+1)^2 \\ So\text{ } \\ (q\mathrm{}p)(5)=-(-2\times5+1)^2 \\ =-(9)^2 \\ =-81 \end{gathered}$

Now let;s solve the second part

$\begin{gathered} (p\mathrm{}q)(x)=p(q(x)) \\ =p(-x^2) \\ =-2(-x^2)+1 \\ =2x^2+1 \\ So\text{ (p.q)(5) will be } \\ (p\mathrm{}q)(5)=2(5)^2+1 \\ =51 \end{gathered}$

6 0

1 year ago

I bought a pear of pants that were $65 they had 25% off

CaHeK987 [17]

How much you need pay?
65x(1-25%)
=65x75%
=65x0.75
=48.75
Your answer should be $48.75.

8 0

3 years ago

Read 2 more answers

Help Please! Find The Area Of A Circle With D=8.2

astraxan [27]

Answer:

52.81

Step-by-step explanat

8 0

3 years ago

A homeowner plans to enclose a 200 square foot rectangular playground in his garden, with one side along the boundary of his pro

Anestetic [448]

Answer:

Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.

Step-by-step explanation:

Given that, a homeowner plans to enclose a 200 square foot rectangle playground.

Let the width of the playground be y and the length of the playground be x which is the side along the boundary.

The perimeter of the playground is = 2(length +width)

=2(x+y) foot

The material costs $1 per foot.

Therefore total cost to give boundary of the play ground

=$[ 2(x+y)×1]

=$[2(x+y)]

But the neighbor will play one third of the side x foot.

So the neighbor will play $=\$(\frac13x)$

Now homeowner's total cost for the material is

$=\$[ 2(x+y)-\frac13x]$

$=\$[2x+2y-\frac13x]$

$=\$[2y+x+x-\frac13x]$

$=\$[2y+x+\frac{3x-x}{3}]$

$=\$[2y+x+\frac{2}{3}x]$

$=\$[2y+\frac53x]$

$\therefore C(x)=2y+\frac53x$

where C(x) is total cost of material in $.

Given that the area of the playground is 200.

We know that,

The area of a rectangle is =length×width

=xy square foot

∴xy=200

$\Rightarrow y=\frac{200}{x}$

Putting the value of y in C(x)

$\therefore C(x)=2(\frac{200}{x})+\frac53x$

The domain of C is $(0,\infty )$ .

$\therefore C(x)=2(\frac{200}{x})+\frac53x$

Differentiating with respect to x

$C'(x)= - \frac{400}{x^2}+\frac53$

Again differentiating with respect to x

$C''(x) = \frac{800}{x^3}$

To find the critical point set C'(x)=0

$\therefore 0= - \frac{400}{x^2}+\frac53$

$\Rightarrow \frac{400}{x^2}=\frac{5}{3}$

$\Rightarrow x^2 =\frac{400\times 3}{5}$

$\Rightarrow x=\sqrt{240}$

$\Rightarrow x=15.49 \approx15.5$

Therefore

$\left C''(x) \right|_{x=15.5}=\frac{800}{15.5^3}>0$

Therefore at x= 15.5 , C(x) is minimum.

Putting the value of x in $y=\frac{200}{x}$ we get

$\therefore y=\frac{200}{15.5}$

=12.9

Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.

6 0

3 years ago

Each of the 8 cats in a pet store was weighed. Here are their weights (in pounds):

kow [346]

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

To find the mean of the data set shown here, let's begin by adding the numbers.

11 + 10 + 12 + 14 + 5 + 15 + 7 + 6 = 80

80 will now be divided by how many numbers are in the set which is 8.

80 ÷ 8 = 10

This means that the mean of the data set is 10.

___________________________________________________

Now, let's find the median of the data set. The median is the middle number in the data set when the data set is written from least to greatest.

Least to greatest ⇒ 5, 6, 7, 10, 11, 12, 14, 15

Since there are two numbers in the middle of the data set, we need to add the two numbers that are in the middle and divide the sum of the numbers by 2 since there are two numbers.

The two numbers in the middle are 10 and 11.

10 + 11 = 21

21 ÷ 2 = 11.5

Therefore, 11.5 the median of the data set.

5 0

3 years ago

5(2x-7)+42-3x=2 what is the answer ​

5(2x-7)+42-3x=2 what is the answer