All categories

3 years ago

The length of the hypotenuse of a 30°-60°-90° triangle is 12. Find the perimeter.

1 answer:

7 0

The answer is 18 + 6√3 or 18 + √108.

In a 30°-60°-90° triangle, the hypotenuse (c) is twice the length of the shorter leg (a):
c = 2a ⇒ a = c ÷ 2 = 12 ÷ 2 = 6

In a 30°-60°-90° triangle, the longer leg is equal to the shorter leg multiplied by √3:
b = √3a = √3 · 6

Now we have the length of all three sides:
a = 6
b = 6√3 = √6² · √3 = √36 · √3 = √(36 · 3) = √108
c = 12

So, the perimeter (P) of the triangle is:
P = a + b + c = 6 + 6√3 + 12 = 18 + 6√3 = 18 + √108

You might be interested in

8c + c = what please help me i am doing test and need answer right now. like 4rl

lianna [129]

Answer: 8c

Step-by-step explanation:

We do not know the value of c or the other c.

So, the answer to the question is 8c. Hope it helped.

8 0

3 years ago

Read 2 more answers

Ramauri is thinking of a mystery number. He cuts it in half then takes away 9. The result is -5. What is the mystery number

MaRussiya [10]

Answer:

Step-by-step explanation:

mystery number= x

he divdes x by 2 and then subtracts 9 and gets -5. reverse the order to find x.

-5+9 which is 4 times 2 which is 8. x is 8

7 0

3 years ago

a boat capsized and sank in the lake. based on an assumption of a mean weight of 143 lb, the boat was rated to carry 70 passenge

Alenkinab [10]

The final answer is the probability that the boat is overloaded because the mean weight of the 70 passengers is greater than 143lb is 1.0000.

A normal distribution is a continuous data distribution with a bell-shaped curve. The normally distributed random variable X has mean $\mu$ and standard deviation $\sigma$ .

In addition, the standard normal distribution represents a normal curve with a mean of zero and a standard deviation of one.

The number of standard deviations an element deviates from the mean is indicated by a standardized Z-score.

What is the theorem of the central limit?

If the sample size from the population is sufficiently large and has a finite variance, the mean of all samples taken will be approximately the same as the population mean. And the variance would be the population variance divided by the sample size. In addition, the sampling distribution would be roughly normal.
The formula for sampling distribution of the sample mean is $\mu_{\bar{x}}=\mu$
The formula for standard deviation of the sample mean is, $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$
Here, $\sigma$ is the population standard deviation and n is the sample size.
The formula for standard z-score is,

$z=\frac{\bar{x}-\mu_{x}}{\frac{\sigma}{\sqrt{n}}}$

From the given information,Population mean, $\mu=171$ ,Population standard deviation, $\sigma=37.7$ ,Sample size, n=70
Compute the probability that the boat is overloaded because the mean weight of the 70 passengers is greater than $143l \mathrm{~b}$ .

$\begin{aligned}P(\bar{X} > 143) &=P\left(\frac{\bar{X}-\mu}{\sigma / \sqrt{n}} > \frac{143-171}{37.7 / \sqrt{70}}\right) \\&=P(Z > -6.21) \\&=1-P(Z < -6.21) \text { (Use the Excel function NORMSDIST(-6.21)) } \\&=1-0.0000 \\&=1.0000\end{aligned}$

To learn more about standard deviation visit:

brainly.com/question/16555520?

#SP4

4 0

2 years ago

11. Find the sum of the arithmetic series. overset [22] underset{k=1}\huge{Sigma) (-4k - 13) =

sergiy2304 [10]

Answer:

okay, we need to add up for all k=1 till k=22

we could do it like this

(-4*1 -13) + (-4*2 -13) + (-4*3 -13) + ...

but this is long and boring, so we need another valid, yet vastly faster method to calculate this sum

we know that the "-13" part will occur 22 times, so let's write this component as "-13*22"

the -4k gents bigger with each step, k will take all the natural numbers from 1 to 22

so we could write

"-4 * (1+2+3+4+5+6+7...+21+22l

alot simpler and faster, but not fast enough

let's add up all numbers from 1 to 22 into one number

1 + 22 = 23

2 + 21 = 23

3 + 20 = 23

...

this works eleven times (bc we use up 2 numbers in each step), so the numbers from 1 to 22 added up are just

23*11= 230+23 = 252

now let's construct the final calculation

-4 * 252 -13*22 = -1294

there's your sum.

hope it helps you overall.

brainliest would be very kind ic some else leaves an answer, may it be just a greeting

4 0

3 years ago

QUESTION IS BELOW!!!!!!!!!!!!!!

insens350 [35]

Does Not Support
Does Support
Does Support

HOPE THIS HELPS!

7 0

3 years ago

Read 2 more answers