1457 divided by 12<br> Using long division to solve the following question

Determine what must be multiplied so that the expression below will have a common denominator. Use the backslash / to type in a

Mashutka [201]

Answer:

Multiply the first fraction by $\frac{x+4}{x+4}$

Multiply the second fraction by $\frac{x-4}{x-4}$

Step-by-step explanation:

Given

$\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}$

Required

Make the denominator equal

$\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}$

Factorize the denominator

$\frac{4}{x^2 - 4^2} + \frac{3}{x^2 + 4x + 4x+ 16}$

$\frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)}$

Multiply the first fraction by $\frac{x+4}{x+4}$

Multiply the second fraction by $\frac{x-4}{x-4}$

$\frac{x+4}{x+4} * \frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)} * \frac{x-4}{x-4}$

$\frac{4(x + 4)}{(x - 4)(x + 4)(x + 4)} + \frac{3(x - 4)}{(x+ 4)(x + 4)(x - 4))}$

$\frac{4(x + 4)}{(x^2 - 16)(x + 4)} + \frac{3(x - 4)}{(x^2 - 16)(x + 4))}$

<em>The expression now have the same denominator</em>

7 0

3 years ago

-2x+15y=-24<br> 2x+9y=24

BARSIC [14]

Answer:

x = 12 and y = 0

Step-by-step explanation:

Use elimination by adding the equations together.

-2x + 15y =-24

2x + 9y = 24

---------------

24y = 0

y=0

Then substitute y = 0 into one equation to find x.

-2x + 15(0) = -24

-2x + 0 = -24

-2x = -24

x = 12

3 0

3 years ago

The length of a rectangle is 5 times larger than x. The width is 4 cm less than the length. The perimeter is at least 96 cm. Wha

Ede4ka [16]

We know that the perimeter of a rectangle = 2(l + w)

l = length

w = width

In our problem,

l = 5x

w = 5x - 4

Let's create an inequality to help us solve this problem.

2(5x + (5x - 4)) ≥ 96

Let's start off by simplifying the terms inside the parentheses.

2(10x - 4) ≥ 96

Distribute the 2

20x - 8 ≥ 96

Add 8 to both sides.

20x ≥ 104

Divide both sides by 20

x ≥ 5.2

Let's plug 5.2 into x for our length and width.

Length = 5x = 5(5.2) = 26 cm

Width = 5x - 4 = 5(5.2) - 4 = 26 - 4 = 22 cm

The smallest possible dimensions for the rectangle are, length = 26 cm and width = 22 cm

6 0

3 years ago

Read 2 more answers

Aaron is constructing a circle circumscribed about a triangle. He has partially completed the construction as shown below. What

Anastasy [175]

The correct answer to this question is letter b.There are only three steps in constructing a circle circumscribed by a triangle. He is done with the first step. Use the compass to find the perpendicular bisector for side DF. I hope I have helped you.

6 0

3 years ago

Read 2 more answers

Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her

Ratling [72]

Answer:

0.0677 = 6.77% probability that they will all be nonfiction

Step-by-step explanation:

The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$