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raketka [301]
2 years ago
5

PLEASE SOLVE AND CHECK

Mathematics
1 answer:
Ymorist [56]2 years ago
3 0

Answer:

x^2=-10

Step-by-step explanation:

x squared equals to negative 10

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jasmine wants to build a 2 5/6 meter long garden path paved with square stones that measure 1/4 meter on each side there will be
patriot [66]
2 \frac{5}{6}*2= \frac{17}{6}* \frac{2}{1} = \frac{17}{3}= 5\frac{2}{3}

5 \frac{2}{3}: \frac{1}{4}=   \frac{17}{3}* \frac{4}{1}=  \frac{68}{3} =22 \frac{2}{3}

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3 years ago
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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.

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