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3 years ago

D.

Mathematics

1 answer:

Alex3 years ago

3 0

Answer:

Step-by-step explanation:

This is your correct answer if ur aim is simplification!

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What is the following quotient?

seropon [69]

Answer: Choice B) $\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\$

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Work Shown:

$\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\$

This shows why choice B is the answer.

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

Explanation:

In the second step, I multiplied top and bottom by $(\sqrt{11}+\sqrt{3})$
This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is $\sqrt{a}-\sqrt{b}$ and you want to rationalize the denominator, then you should multiply top and bottom by $\sqrt{a}+\sqrt{b}$ . The same applies in reverse as well.

This leads to the denominator becoming $(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b$

Keep in mind that $a \ge 0$ and $b \ge 0$

4 0

3 years ago

A quadrilateral has angles that measure 74°, 93°, and 117°.

Lana71 [14]

Answer:

Step-by-step explanation:

74 + 93 + 117= 284

360 - 284 = 76

3 0

3 years ago

Read 2 more answers

What is the value of z in the equation 2(4z − 3 − 1) = 166 − 46?

ZanzabumX [31]

In this equation z=16

7 0

3 years ago

in a class of 37 students,the number of students who like martial art only is double than the number of students who like athlet

yulyashka [42]

Answer:

number of students who like Athletics only = x = 10 students

number of students who like marshal arts only = 2x = 20 students

Step-by-step explanation:

In a class of 37 students, the number of students who like marshal arts only is

double than the number of students who like athletics only. If 3 students like both

and 4 like none of the games, find out how many students like:

i. Marshal arts

ii. Athletics

Total students in the class = 37

number of students who like Athletics only = x

number of students who like marshal arts only = 2x

Number of students who like both = 3

Number of students who like none = 4

Total = athletics + marshal art + both + none

37 = x + 2x + 3 + 4

37 = 3x + 7

37 - 7 = 3x

30 = 3x

x = 30/3

x = 10

number of students who like Athletics only = x = 10 students

number of students who like marshal arts only = 2x

= 2(10)

= 20 students

5 0

3 years ago

Christina also plans on leaving her $10,000 invested for 20 years. Write an equation representing her investment’s value, y, aft

kaheart [24]

The required equation is y = 10000(1.0.25)^2x. The value of Christina’s investment after 20 years is $30,773.14

Compound interest

The interest accrued on a sum of money is known as interest. The formula for calculating the compound interest is expressed as:

y = y0(1+r/n)^nx

where

x is the time taken

r is the rate in decimal

n is the compounding time

Given the following

x = 20 years

n 2(semi annually)

r = 5.7% = 0.057

Substitute

y = 10000(1+0.057/2)^2(20)
y = 10,000(1 + 0.0285)^40

y = 10000(1.0285)^40
y = 30,773.14

Hence the value of Christina’s investment after 20 years is $30,773.14

Learn more on compound interest here: brainly.com/question/24924853

4 0

2 years ago