Factor the sum of terms as a product of the gcf and sum. 60 + 72

10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x

ddd [48]

Rationalizing the denominator, simply means "getting rid of that pesky root at the bottom", and we do so by simply multiplying it by something to take it out, of course, we multiply the bottom, we have to also multiply the top,

$\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}$

$\bf \cfrac{4\sqrt{28350x}}{189x}\qquad 
\begin{cases}
28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\
\qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\
\qquad 2\cdot (45)^2\cdot 7\\
\qquad 14\cdot 45^2
\end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x}
\\\\\\
\cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}$

4 0

3 years ago

A certain unsavory bar for poker-playing dogs is attended by only two types of dogs: "good dogs" and "bad dogs." For a randomly

SVETLANKA909090 [29]

Answer: The required probability is 0.1923.

Step-by-step explanation:

Since we have given that

Probability that it's a good dog = 0.4

Probability that it's a bad dog = 1-0.4 = 0.6

Probability that the dog smokes given that its a bad dog = 0.7

Probability that it smokes given that its a good dog = 0.25

According to question, probability of smoking pipe would be

P(good).P(Smoking pipe|good)+P(bad).P(smoking pipe|bad)

$0.4\times 0.25+0.6\times 0.7\\\\=0.1+0.42\\\\=0.52$

So, Probability of getting a good dog given that it is smoking pipe is given by

$\dfrac{P(good).P(smoking\ pipe|good)}{P(smoking\ pipe)}\\\\=\dfrac{0.4\times 0.25}{0.52}\\\\=\dfrac{0.1}{0.52}\\\\=0.1923$

Hence, the required probability is 0.1923.

3 0

3 years ago

Read 2 more answers

The slipe of the line passing through the points (7, 5) and (21, 15) is

SOVA2 [1]

Answer:

5/7

Step-by-step explanation:

You find a slope by using the equation y2-y1/x2-x1.

In this case: 15-5/21-7

10/14

5/7

6 0

3 years ago

Find a in the figure below and place the value in the empty box

AleksAgata [21]

Answer:

a = 12m

Step-by-step explanation:

In order to solve this problem we will need to know the Pythagoras theorem that states that in a right angled triangle the square of the hypotenuse (the side opposite to the right angel) is equal to the sum of the squares of the other two sides. This theorem can be written as an equation....

$c^{2} = a^{2} + b^{2}$