All categories

4 years ago

Simplify completely quantity 5 x squared minus 21 x minus 20 all over quantity 5 x squared minus 16 x minus 16.

Mathematics

2 answers:

Morgarella [4.7K]4 years ago

8 0

(5x^2-21x-20)/(5x^2-16x-16)
((x-5)(5x+4))/((x-4)(5x+4))
(x-5)/(x-4)

SVEN [57.7K]4 years ago

3 0

Answer: Simplified form will be

$\frac{(x-5)}{(x-4)}$

Explanation:

Since we have given that

$\frac{5x^2-21x-20}{5x^2-16x-16}$

We need to simplify the expression, we get,

$\frac{5x^2-25x+4x-20}{5x^2-20x+4x-16}\\\\\text{We will split the middle terms}\\\\=\frac{5x(x-5)+4(x-5)}{5x(x-4)+4(x-4)}\\\\=\frac{(5x+4)(x-4)}{(5x+4)(x-4)}\\\\\text{ Cancel the common terms}\\\\=\frac{(x-5)}{(x-4)}$

Hence, simplified form will be

$\frac{(x-5)}{(x-4)}$

You might be interested in

An isosceles right triangle has a hypotenuse of length e. Select all that are true for the triangle.

____ [38]

<h3>2 Answers: </h3>

Choice C) Leg length = $\frac{e\sqrt{2}}{2}$
Choice E) Area = $\frac{e^2}{4}$

Note: if the formulas don't load properly, then you may need to refresh the page.

======================================================

Explanation:

For any 45-45-90 right triangle, the hypotenuse H is always sqrt(2) times the leg L

In terms of symbols, we can say

$H = L*\sqrt{2}$

We're told the hypotenuse is e, so H = e

Let's solve for L in terms of e

$H = L*\sqrt{2}\\\\e = L*\sqrt{2}\\\\L*\sqrt{2} = e\\\\L = \frac{e}{\sqrt{2}}\\\\$

Now let's multiply top and bottom by $\sqrt{2}$ to rationalize the denominator

$L = \frac{e}{\sqrt{2}}\\\\L = \frac{e\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\L = \frac{e\sqrt{2}}{\sqrt{2*2}}\\\\L = \frac{e\sqrt{2}}{\sqrt{4}}\\\\L = \frac{e\sqrt{2}}{2}\\\\$

If the hypotenuse is e, then the length of each leg is $\frac{e\sqrt{2}}{2}$

This matches with choice C, which is one of the two answers. This allows us to rule out choices A and B, as those expressions are not equivalent to the expression for choice C.

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

The two legs of any right triangle form the base and height. The order doesn't matter. The base is always perpendicular to the height. In a right triangle, the two legs are always perpendicular.

The base and height are $\frac{e\sqrt{2}}{2}$ each.

The area of the triangle is...

$\text{Area} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{Area} = \frac{1}{2}*\frac{e\sqrt{2}}{2}*\frac{e\sqrt{2}}{2}\\\\\text{Area} = \frac{e\sqrt{2}*e\sqrt{2}}{2*2*2}\\\\\text{Area} = \frac{e*e\sqrt{2*2}}{2*2*2}\\\\\text{Area} = \frac{e^2\sqrt{4}}{2*2*2}\\\\\text{Area} = \frac{e^2*2}{2*2*2}\\\\\text{Area} = \frac{e^2}{2*2}\\\\\text{Area} = \frac{e^2}{4}\\\\$

This matches with choice E, which is the other answer. Choices D and F are eliminated as they are not equivalent to the expression for choice E.

4 0

3 years ago

I need help asap<br> i need to know how to show work pls help

Alona [7]

Step-by-step explanation:

add all the freqency up which is 100

you have to use a customize spinner and put in all the colors that are all on the side...

Spin 150 times ( 250-100= 150) and put tally marks on the sheet of tallys.

Then count all you red and see.

Hope all that makes sense..

7 0

3 years ago

Functions can also be represented using a table of values. For the table shown in the figure, what kind of function does it corr

Sliva [168]

Answer:

This function s a linear relationship because this function increases about a consistent slope. The equation is 2x+5, where 2 is the slope.

Step-by-step explanation:

7 0

3 years ago

Will give BRAINLIEST!!!! Answer fast!!!

Snowcat [4.5K]

Divide the area by the length given. The area expression can be factored down. Here’s my work

6 0

3 years ago

The answer to this problem

Olenka [21]

Answer:

Step-by-step explanation:

I drew it out on a piece of paper. R is going up and down, through PQ, which is going left to right. If the ratio is 1:3, that means that for every 1 unit there is on one side, there are 3 units in the other. If R is -1 and P is -3, they are two numbers away from each other, which means that on the other side of R (to the right of R), there needs to be 6 numbers in between to make the 1:3 ratio. R is at -1, so then you would write the equation, -1+6=? The answer is 5.

-1+6=5 That is where Q would be

5 0

4 years ago