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3 years ago

How do you calculate the Hypotenuse?

1 answer:

4 0

Formula:
a^2+b^2=c^2

c^2: Is the hypotenuse.

For a^2 and b^2, you have to multiply both it by its self.

Then, add both.

Next, you square root it.

Example:

a^2+b^2=c^2

14^2+7^2=c^2

196+49=c^2

245=c^2

15.64=c^2

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To three decimal places, find the average value of f(x) = 2x2 + 3 on the interval [0, 2].

salantis [7]

The formula for the average value of a function is $\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx$ where b is the upper bound and a is the lower. For us, this formula will be filled in accordingly. $\frac{1}{2} \int\limits^2_0 {(2x^2+3)} \, dx$ . We will integrate that now: $\frac{1}{2}[ \frac{2x^3}{3}+3x]$ from 0 to 2. Filling in our upper and lower bounds we have $\frac{1}{2}[( \frac{2(2^3)}{3}+3(2))-0]$ which simplifies to $\frac{1}{2}( \frac{16}{3}+6)$ and $\frac{1}{2}( \frac{16}{3}+ \frac{18}{3})= \frac{1}{2}( \frac{34}{3})$ which is 17/3 or 5.667

7 0

3 years ago

Write the eqauation of a line that has the slope pf 6 passes through (-3,5)

Darina [25.2K]

Y = mx + b
slope(m) = 6
(-3,5)...x = -3 and y = 5
now we sub and find b, the y int
5 = 6(-3) + b
5 = -18 + b
5 + 18 = b
23 = b

so ur equation is : y = 6x + 23

6 0

2 years ago

The sum of two numbers is thirteen, and the sum of<br> their squares is 89. Find the two number

Murljashka [212]

Answer:

$Suppose~that~the~two~numbers~are~x~and~y.\\According~to~question,\\Sum~of~the~numbers = 13\\or, x+y=13........(1)\\or, y = 13-x.......(2)\\Again,\\Sum~of~their~squares=89\\or, x^2+y^2=89\\or, (x+y)^2-2xy=89\\From~eq^n(1)~and~(2),\\13^2-2x(13-x)=89\\or, 169-26x+2x^2=89\\or, 2x^2-26x+169-89=0\\or, 2x^2-26x+80=0\\or, x^2-13x+40=0\\or, x^2-8x-5x+40=0\\or, x(x-8)-5(x-8)=0\\or, (x-5)(x-8)=0\\i.e. x=5~or~8\\When~x=5,~y=13-x=13-5=8\\When~x=8,~y=13-x=13-8=5\\So,~the~two~numbers~are~5~and~8.$

8 0

2 years ago

Solve for b at the top <br> And x at the bottom <br> I’ll give 17 points

slavikrds [6]

Answer:

b = -1

x = 1

Step-by-step explanation:

8 - (b - 2) = 11

subtract 8 from both sides

- (b - 2) = 3

distribute

-b + 2 = 3

subtract 2 from both sides

-b = 1

now, to make the b positive, we make the other side negative by multiplying.

b = -1

-2x+ 4 = 5 -3x

subtract 4 from both sides

-2x = 1 -3x

add 3x to both sides

1x = 1

divide by 1

x = 1

(hopefully this helps?)

6 0

3 years ago

Which expression is equivalent to 1/4 (8-6x+12)

Dovator [93]

So:

Let us simply the parenthesis first.

So we have $\sf{(8-6x+12)}$

We can rearrange the terms and get:

$\sf{(8+12-6x)}$

Which is equal to

$\sf{(20-6x)}$

So now we have to complete it by multiplying it all by 1/4 which is basically dividing it by 4.

So:

$\sf{\frac{20-6x}{4}}$

Simplifying that, we get:

$\sf{5-\frac{6}{4}x}$

And reducing that farther we finally get:

$\sf{5-\frac{3}{2}x}$

Which is your final answer :)

6 0

2 years ago