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2 years ago

What is the greatest common factor of the numerator of ?

Mathematics

1 answer:

Annette [7]2 years ago

4 0

The greatest common factor of the numerator and denominator of the rational expression is x - 4

<h3>How to determine the greatest common factor?</h3>

The fraction expression is given as:

$\frac{5x-20}{x^2-2x-8}$

Factorize the numerator and the denominator

$\frac{5x-20}{x^2-2x-8} = \frac{5(x-4)}{(x- 4)(x + 2)}$

Cancel out the common factor

$\frac{5x-20}{x^2-2x-8} = \frac{5}{(x + 2)}$

The common factor that was canceled out is x - 4

Hence, the greatest common factor of the numerator and denominator of the rational expression is x - 4

Read more about greatest common factors at:

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.002 is 1/10 of what

amid [387]

Let the unknown number be x. Then (1/10)x = 0.002. To solve for x, multiply both sides by 1000 to remove the decimal fraction 0.002.

Then 1000(1/10)x = 1000(0.002), or 100x = 2. Dividing both sides by x returns

x=100/2, or x= 50 (answer)

5 0

3 years ago

Which linear inequality is represented by the graph?

Tamiku [17]

Answer:

Option (4)

Step-by-step explanation:

From the graph attached,

A dotted line passes through two points (3, 1) and (-3, -3)

Let the equation of the given line is,

y = mx + b

where 'm' = slope of the line

b = y-intercept

Slope of a line passing through $(x_1, y_1)$ and $(x_2,y_2)$ is,

m = $\frac{y_2-y_1}{x_2-x_1}$

For the given points,

m = $\frac{1+3}{3+3}$

m = $\frac{2}{3}$

y-intercept 'b' = -1

Therefore, equation of the given line will be,

$y=\frac{2}{3}x-1$

Since graphed line is a dotted line so it's representing an inequality(having < or > sign)

And the shaded part is below the dotted line,

Inequality will be,

y < $\frac{2}{3}x-1$

Therefore, Option (4) will be the answer.

7 0

3 years ago

What is the distance in units from (2, -12) to (-11, -12)<br> 20 POINTSSS <br> HURRY PLEASEEEE

sweet [91]

Answer:

d= (-11-2)^2 + (-12--12)^2

d= (-13)^2 + (0)^2

d=169

square root the 169

answer is 13

that's the distance from (2, -12) (-11, -12)

hope that helps

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A circular swimming pool has a diameter of 40 meters. The depth of the pool is constant along west-east lines and increases line

Nataliya [291]

Answer:

Volume is $2000\pi\ m^{3}$

Solution:

As per the question:

Diameter, d = 40 m

Radius, r = 20 m

Now,

From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:

iff

h(y) = cy + d

Then

when y = 1 m

h(- 20) = 1 m

1 = c.(- 20) + d = - 20c + d (1)

when y = 9 m

h(20) = 9 m

9 = c.20 + d = 20c + d (2)

Adding eqn (1) and (2)

d = 5 m

Using d = 5 in eqn (2), we get:

$c = \frac{1}{5}$

Therefore,

$h(y) = \frac{1}{5}y + 5$

Now, the Volume of the pool is given by:

$V = \int h(y)dA$

where

A = $r\theta$

$A = rdr\ d\theta$

Thus

$V = \int (\frac{1}{5}y + 5)dA$

$V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}rsin\theta + 5) rdr\ d\theta$

$V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}r^{2}sin\theta + 5r}) dr\ d\theta$

$V = \int_{0}^{2\pi} (\frac{1}{15}20^{3}sin\theta + 1000) d\theta$

$V = [- 533.33cos\theta + 1000\theta]_{0}^{2\pi}$

$V = 0 + 2\pi \times 1000 = 2000\pi\ m^{3}$

7 0

3 years ago

Simplify the radical expression 5√7+2√175

yanalaym [24]

$5\sqrt{7} + 2\sqrt{175}=5\sqrt{7}+2\sqrt{25 \cdot 7}=5\sqrt{7}+ 2 \cdot \sqrt{25} \cdot \sqrt{7}= \\ \\ = 5\sqrt{7}+2 \cdot 5 \cdot \sqrt{7}=5\sqrt{7}+10\sqrt{7}=\boxed{15\sqrt{7}} \approx 39.69$

remember about formula $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$

5 0

3 years ago