What is the distance between (2,-6) and (-4,3)

Make x the subject of the formula 6x+a=5(x+t)

Mademuasel [1]

1. Expand
6x + a = 5x + 5t
2. Get x on one side
6x - 5x = 5t - a
3. Simplify
x = 5t - a (I think)

5 0

3 years ago

For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

alexira [117]

Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

$\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

3 0

4 years ago

sherry had $125.05 in her checking account She made deposit of $28.35 and $78.88 how much money was in sherry account after the

Doss [256]

Answer:

$17.82

Step-by-step explanation:

$125.05 - 28.35 = 96.7 \\ 96.7 - 78.88 = 17.82$

4 0

4 years ago

Read 2 more answers

HELPPP

alexdok [17]

Answer:

7 boxes

Step-by-step explanation:

The area of a rectangular prism is given by the formula ...

A = 2(LW +H(L+W))

The amount of wallpaper Carmen needs for one box is found by computing the area of the box.

__

A = 2(5·6 +7(5+6)) = 2(30 +7·11) = 2(107) = 214 . . . square feet

<h3>All boxes</h3>

Carmen will be using a total of 214x square feet of wallpaper to cover x boxes. She has 1498 ft² available, so can cover ...

1498 ft²/(214 ft²/box) = 7 boxes

Carmen has enough wallpaper to cover 7 storage boxes.

7 0

2 years ago

An entertainment firm offer serveral DJ choices and light shows that range in price based on the rental time period. The DJs cos

Fantom [35]

Answer:

$378\le x\le 678.$

Step-by-step explanation:

If you are booking both a DJ and a light show and the DJs cost between $219 and $369 per night and the light shows cost between $159 and $309 per night, then the possible total amount you would pay x must be between $(219+159)=$378 (the least price) and $(369+309)=$678 (the greatest price).

A compound inequality will take look

$378\le x\le 678.$

3 0

3 years ago