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3 years ago

Geometry Help!!!

Mathematics

1 answer:

dem82 [27]3 years ago

4 0

<h3>Answer: Choice A) 24.0</h3>

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Explanation:

Let's say we had a triangle with side lengths a,b,c.

If we know that a = 12.25 and b = 12.25, then the third side c has its length restricted in such a way that

b-a < c < b+a

This is a variation of the triangle inequality theorem.

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So,

b - a < c < b + a

12.25 - 12.25 < c < 12.25 + 12.25

0 < c < 24.5

which means the third side c is between 0 inches and 24.5 inches.

The value of c cannot be 0, and it cannot be 24.5 either.

Among the answer choices given, we see that only 24.0 is the only valid option here. The other two choices are too large.

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Side Note: If your teacher gave you two angles (instead of two sides) to be 12.25 degrees, and wanted the third missing angle of the triangle, then you would be correct in having 12.25+12.25+x = 180 as your first step.

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Find the exact values of sin θ/2 and cos θ/2 for sin θ = 3/4 on the interval 0° ≤ θ ≤ 90°

timofeeve [1]

Answer:

Step-by-step explanation:

If our interval is between 0 and 90 degrees, that means that our angles are first quadrant angles. Since the formulas for the half angles of sin and cos consider both the positive and negative roots, knowing that we are in QI leaves us using only the principle, or positive, root.

Also, if we know that the sin of angle is 3/4, we can set up a right triangle in QI and find the missing side of that triangle using Pythagorean's Theorem. Sin of an angle is the ratio opposite side/hypotenuse. That means that, according to Pythagorean's Theorem,

$4^2=3^2+b^2$ and

$16-9=b^2$ and

$b=\sqrt{7}$

Now for the forula for the sin of a half-angle:

$sin(\frac{\theta}{2})=\sqrt{\frac{1-cos\theta}{2} }$

Referring to the right triangle we created and found the missing side for, we see that the cosine of that same triangle is $\frac{\sqrt{7} }{4}$

Filling in the formula then:

$sin(\frac{\theta}{2})=\sqrt{\frac{1-\frac{\sqrt{7} }{4} }{2} }$

Get a common denominator on the upper fraction:

$sin(\frac{\theta}{2})=\sqrt{\frac{\frac{4-\sqrt{7} }{4} }{2} }$

Bring up the 2 as 1/2 to multiply and get:

$sin(\frac{\theta}{2})=\sqrt{\frac{4-\sqrt{7} }{8} }$

When you do the exact same thing to find the cos of the half angle, you are using a + sign instead of a - sign under the radical. That gives you as your exact value:

$cos(\frac{\theta}{2})=\sqrt{\frac{4+\sqrt{7} }{8} }$

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3 years ago

At a student art fair, 100 projects were on display. Of all the

Daniel [21]

Answer: 90 projects in all 1/5 were photographs 1/5 of 90=90/5=18

Step-by-step explanation: done :)

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3 years ago

Read 2 more answers

Tom has some marbles in two bags. In one bag he has 3 yellow, 2 green and 1 red marble. In the other bag he has 3 yellow, 3 gree

shutvik [7]

Answer:

1 / 3

Step-by-step explanation:

Bag 1 :

Yellow = 3

Green = 2

Red = 1

Total = 3 + 2 +1 = 6

Bag 2 :

Yellow = 3

Green = 3

Red = 3

Total = 3 + 3 + 3 = 9

P(not yellow from bag 1) = (green + red) / total = 3 /6 = 1/2

P(not yellow from bag 2) = (green + red) / total = 6/9 = 2 /3

P(neither is yellow) = 1/2 * 2/3 = 2 / 6 = 1/3

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3 years ago

From the expressions below, select the one that results in a negative difference.

balu736 [363]

uhm..

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3 years ago

A town has a population of 13,000 and grows at 5% every year what will the population be after 11 years to the nearest whole num

scoray [572]

This question is based on the concept of
amount of interest. Therefore, 22,234 would be
the population after 11 years, to the nearest
whole number.
Given:
A town has a population of 13000 and grows at
5% every year.
We need to determined the population after 11
years, to the nearest whole number.
We know that,
Formula =A = P(1+ r)
Where, p be the population. r is the rate and t is
the time.
P= 13000,
r= 5%
†= 11
Now put all these values in formula.
We get,
5
A = 13000(1 +
A
= 13000(1 + 0.05)11
A
= 1300022, 234.41(0.95)

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2 years ago