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3 years ago

Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x^2 - y^2 and 2xy.

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

3 0

By pythagorean theorem,

$h^2=(2x^2-y^2)^2+(2xy)^2$

First simplify RHS,

$h^2=4x^4-4x^2y^2+y^4+4x^2y^2$

$h^2=4x^4+y^4$

Take square root of both sides,

$h=\sqrt{4x^4+y^4}$

So the answer is A.

Hope this helps :)

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Eastside middle school has 1,500 students. Thirty-two percent of them are in sixth grade. How many sixth-grade students are the

hichkok12 [17]

480 six graders
1,500*0.32 = 480

6 0

3 years ago

Does anybody know anything about simplifying rational expressions? 4x/11x

babunello [35]

All you have to do is cancel the x 4/11

7 0

3 years ago

A number of fiction books at a library was 3/4 of the total number of books. After 592 fiction books were donated to the library

Zielflug [23.3K]

There approximately 7133 books in the library;

Data;

Let the number of total books = x
Number of fictional books = 3/4x

<h3>Word Problem</h3>

To solve this problem, we simply need to use an equation to explain the word problem into mathematical statements.

Let the total number of books be represented by x

The number of fictional books = 3/4x

After 592 fictional books were donated;

$\frac{3x}{4} + 592 = \frac{5}{6}x$

Let collect like terms and solve

$\frac{3x}{4} +592 = \frac{5}{6} x\\\frac{5}{6}x - \frac{3x}{4} = 592\\ 0.083x=592\\x = 592/0.083\\x = 7132.53$

There approximately 7133 books in the library;

Learn more on word problems here;

brainly.com/question/13818690

4 0

2 years ago

How do i find y in y=mx+c if m=8 and (5,3)

Ganezh [65]

Answer:

y = 8x-37

Step-by-step explanation:

y=mx+c

We know the slope m

y=8x+c

We know a point on the line (5,3). Substitute this in for x and y

3 = 8(5) +c

3 = 40+c

3-40 = 40+c-40

-37 =c

y = 8x-37

8 0

3 years ago

Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answ

gulaghasi [49]

Answer:

Part a ) The degrees of freedom for the given two sample non-pooled t test is 24

Part b ) The degrees of freedom for the given two sample non-pooled t test is 30

Part c ) The degrees of freedom for the given two sample non-pooled t test is 30

Part d ) The degrees of freedom for the given two sample non-pooled t test is 25

Step-by-step explanation:

Degrees of freedom for a non-pooled two sample t-test is given by;

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Now given the information;

a) :- m = 12, n = 15, s₁ = 4.0, s₂ = 6.0

we substitute

Δf = {[ 4²/12 + 6²/15 ]²} / {[( 4²/12)²/12-1] + [(6²/15)²/15-1]}

Δf = 30184 / 1241

Δf = 24.3223 ≈ 24 (down to the nearest whole number)

b) :- m = 12, n = 21, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/12 + 6²/21 ]²} / {[( 4²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 56320 / 1871

Δf = 30.1015 ≈ 30 (down to the nearest whole number)

c) :- m = 12, n = 21, s₁ = 3.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 3²/12 + 6²/21 ]²} / {[( 3²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 29095 / 949

Δf = 30.6585 ≈ 30 (down to the nearest whole number)

d) :- m = 10, n = 24, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/10 + 6²/24 ]²} / {[( 4²/10)²/10-1] + [(6²/24)²/24-1]}

Δf = 1044 / 41

Δf = 25.4634 ≈ 25 (down to the nearest whole number).

6 0

3 years ago