Juan must purchase car insurance. He needs to earn at least $50.00 a week to cover the payments.

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

The order pairs (1, 2), (2, 5), (3, 10), (4, 17), and (5, 26) represent a function. what is a rule that could represent this fun

LenaWriter [7]

The X which is the first number in each () in called the input
There is only one input for every number
Meaning all the first numbers mystery br DIFFERENT

6 0

3 years ago

HELP PLEASE <br> solve the right triangle

aleksandrvk [35]

Answer:

Part 1) $FG=4.4\ units$

Part 2) $EF=3.9\ units$

Part 3) $m\angle G=63^o$

Step-by-step explanation:

step 1

Find the measure of length side FG

In the right triangle EFG

we know that

$sin(27^o)=\frac{GE}{FG}$ ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

$sin(27^o)=\frac{2}{FG}$

$FG=\frac{2}{sin(27^o)}=4.4\ units$

step 2

Find the measure of length side EF

In the right triangle EFG

we know that

$cos(27^o)=\frac{EF}{FG}$ ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

$cos(27^o)=\frac{EF}{4.4}$

$EF=cos(27^o)(4.4)=3.9\ units$

step 3

Find the measure of angle G

we know that

$m\angle G+27^o=90^o$ ---> by complementary angles in a right triangle

$m\angle G=90^o-27^o=63^o$

7 0

3 years ago

Translate the following word sentence into a numerical expression: When you square five times a number, you get three more than

8090 [49]

“Square five times a number” with “a number” being x is the same as saying:

5x²

“three more than the number” is the same as saying:

3 + x

Therefore the sentence “When you square five times a number, you get three more than the number.” is the same as:

5x² = 3 + x

Hope this helps, have a great day! :)

4 0

3 years ago

Read 2 more answers

Kara did a survey to determine to study the types of pets that students in her school had. She surveyed 300 students and found t

julsineya [31]

Answer:

(C)81

Step-by-step explanation:

Total Number of Students =300

Percentage who had cats, n(C) = 40%

Percentage who had both cats and dogs , $n(C \cap D)$ = 12%