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krok68 [10]
3 years ago
11

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

Mathematics
1 answer:
liraira [26]3 years ago
4 0
60+72=(12x5) +(12x6)=12(5+6)

          60=12x5
          72=12x6
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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}

Now we can see that we can easily find the missing value by using this theorem. We just have to substitute the values. And we get the following

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

a^{2} = c^{2} - b^{2}

a^{2} = 15^{2} - 9^{2}

a^{2} = 225 - 81

a^{2} = 144

a = \sqrt{144}

a = 12

7 0
3 years ago
Help ............. ​
NARA [144]

What kinda of math is this so i can answer..

:)

5 0
3 years ago
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