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Usimov [2.4K]
3 years ago
13

Simplify into lowest terms. 20r + 10 over 30r +15

Mathematics
1 answer:
Tanya [424]3 years ago
5 0
Factor out common thing

\frac{20r+10}{30r+15}= \frac{5(4r+2)}{5(6r+3)}= (\frac{5}{5} )( \frac{4r+2}{6r+3})=
(1)( \frac{4r+2}{6r+3})=\frac{4r+2}{6r+3}
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Help I will be marking brainliest!!!
Keith_Richards [23]
<h3>Answer:  A.  18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

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

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

4 0
3 years ago
Identify the coefficient of -z
harina [27]

Answer:

-1

Step-by-step explanation:

Your welcome back to the inputs is

6 0
3 years ago
For each part, use the Distributive Property to write an equivalent expression
iren2701 [21]

Answer:

The answer is -3x.

Step-by-step explanation:

Combine like terms.

Hope this helps :)

6 0
3 years ago
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Calculate the effective annual interest rate if the annual interest rate, i, is 9%.
jeyben [28]
B. ) Unless you're missing some data.
4 0
3 years ago
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According to this diagram, what is tan 62 degrees ?
sammy [17]
Check the picture below

in case you want to know how to get who's the adjacent or opposite, notice in the picture, if you put your eye on the angle itself, what you'd be facing is the opposite side, the adjacent is the side touching the angle.

3 0
4 years ago
Read 2 more answers
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