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3 years ago

I NEED HELP I WILL GIVE YOU 35 POINTS

Mathematics

1 answer:

Elena-2011 [213]3 years ago

6 0

The solution to this equation is x = 0 or x = 1

To find the solution, you use Desmos and enter x+2 in both one and 2^x+1 in box two. It will graph the lines for you and you take the x-coordinate of the two places where the lines overlap, and they overlap at (0,2) and (1,3).

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<img src="https://tex.z-dn.net/?f=%20%28%7B%20%7Bx%7D%5E%7B2%7D%20%20-%204%7D%29%5E%7B5%7D%20%28%20%7B4x%20-%205%7D%29%5E%7B4%7D

Makovka662 [10]

Let $u=x^2-4$ and $v=4x-5$ . By the product rule,

$\dfrac{\mathrm d(u^5v^4)}{\mathrm dx}=\dfrac{\mathrm d(u^5)}{\mathrm dx}v^4+u^5\dfrac{\mathrm d(v^4)}{\mathrm dx}$

By the power rule, we have $(u^5)'=5u^4$ and $(v^4)'=4v^3$ , but $u,v$ are functions of $x$ , so we also need to apply the chain rule:

$\dfrac{\mathrm d(u^5)}{\mathrm dx}=5u^4\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm d(v^4)}{\mathrm dx}=4v^3\dfrac{\mathrm dv}{\mathrm dx}$

and we have

$\dfrac{\mathrm du}{\mathrm dx}=2x$

$\dfrac{\mathrm dv}{\mathrm dx}=4$

So we end up with

$\dfrac{\mathrm d(u^5v^4)}{\mathrm dx}=10xu^4v^4+16u^5v^3$

Replace $u,v$ to get everything in terms of $x$ :

$\dfrac{\mathrm d((x^2-4)^5(4x-5)^4)}{\mathrm dx}=10x(x^2-4)^4(4x-5)^4+16(x^2-4)^5(4x-5)^3$

We can simplify this by factoring:

$10x(x^2-4)^4(4x-5)^4+16(x^2-4)^5(4x-5)^3=2(x^2-4)^4(4x-5)^3\bigg(5x(4x-5)+8(x^2-4)\bigg)$

$=2(x^2-4)^4(4x-5)^3(28x^2-57)$

7 0

3 years ago

A bag contains 6 black marbles and 4 white marbles. Sally takes out a black marble and does not put it back. What is the probabi

Neko [114]

Answer:

$\frac{5}{9}$

Step-by-step explanation:

$Total\ marbles=10\\\\Black=6\\\\White=4$

After removing one black marble:

$Total\ remaining\ marbles=9\\\\Remaining\ Black=5\\\\P(Black)=\frac{Remaining\ Black\ marbles}{Total\ remaining\ marbles}\\\\P(Black)=\frac{5}{9}$

6 0

3 years ago

A student studying for a vocabulary test knows the meanings of 16 words from a list of 26 words. If the test contains 10 words f

gayaneshka [121]

To get the probability that at least 8 of the words on the test are words that students know we need to do the following calculations.

<span>=[C(16,8)*C(10,2) + C(16,9)*C(10,1) + C(16,10)*C(10,0)] / C(26,10)
</span>
=0.132

4 0

3 years ago

Katlyn made 4 dresses with 7 yards of fabric. How many yards did she use on 1 dress?

Murrr4er [49]

Answer:

the answer would be 1.75 or 1 3/4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The marijority of the population in the United states _________.

Nadusha1986 [10]