To prepare for a triathlon, Amanda starts from position A and rides her bike along a straight road for 12 miles to reach position B. At B, she turns left and rides along another straight road for 15 miles to reach position C. At C, she turns left again and rides 20 miles along a straight road to return to A. In ΔABC, what are m∠A, m∠B, and m∠C, respectively?

Answers

Answer 1

Answer: The angles can solved by using the cosine law. Solving for the measure of angle A
15² = 20² + 12² - 2(20)(12) cos A
A = 48.35°

Angle B can solved by either also using the cosine law or by sine law. Let's use sine law:
20 / sin B = 15 / sin 48.35
B = 85.06°

The measure of angle C can just be solved by difference of the total angle of the triangle.
C = 180 - 48.35 - 85.06
C = 45.59°

Answer 2

Answer:

48.35°, 94.94°, 36.71°

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Give the coordinates for point A without using any new variables

Answers

$7.\nA(n+1;\ m)\n\n8.\nA(k;\ 0)$

Answer:

C-a, b

Step-by-step explanation:

A local mechanic charges customers a flat fee of $60 before any work is done and a rate of $85 per hour of labor which equation represents the relationship between the total charge of labor L in dollars and the number of hours worked H. A.) H=85L+6B.) L=145H
C.) L=60H+85
D.) L=85H+60

Answers

Answer:

L=85H+60

Step-by-step explanation:

i know

Answer:

L=85H+60

Step-by-step explanation:

A firefighter climbed up to the middle of a ladder to see if there was any fire on the second floor of a building and there was none; he then climbed up 10 more steps and saw some smoke so he came back down 14 steps and waited for 5 seconds to check his equipment. He then climbed 20 steps all the way to the top of the ladder and got off on the roof. How many steps are there on the ladder?

Answers

Answer:

Step-by-step explanation:

Let there be n number of steps on the ladder.

First, the firefighter climbed up to the middle of a ladder. so to reach the middle of the ladder he must have climbed $\frac n 2$ steps.

Then, after climbed 10 more steps, the total number of stairs from the ground he climbed $= \frac n 2 +10$ .

Then, he came back down 14 steps, so the total number of stairs from the ground he climbed $= \frac n 2 +10 -14=\frac n 2 -4$ .

Remaining steps $= n - \left(\frac n 2 -4 \right)=\frac n 2 +4$

Given that he climbed 20 steps all the way to the top of the ladder which is equal to the remaining steps. So,

$\frac n 2 +4 = 20$

$\Rightarrow \frac n 2 = 20-4=16$

$\Rightarrow n = 16 * 2 = 32.$

Hence, there are 32 steps on the ladder.

What number is 20% of 700

Answers

Answer:

140

Step-by-step explanation:

What is 20 percent (calculated percentage %) of number 700? Answer: 140.

6thh grade is harddd yall

Answers

Answer:

Step-by-step explanation:

i recommend using mathaway, type in "4,8,14"

For 4 the lcm is 2 for 8 the lcm is 4 and for 14 it is seven if I am not wrong

The area of the sector formed by the 110 degree central angle is 50 units squared. What is the radius of this circle??

Answers

Answer:

Area of the sector(A) is given by:

$A = \pi r^2 \cdot (\theta)/(360^(\circ))$

where,

r is the radius of the circle and $\theta$ is the central angle in degree.

As per the statement:

The area of the sector formed by the 110 degree central angle is 50 units squared.

⇒A = 50 units squared and $\theta = 110^(\circ)$

Substitute these in [1] and use 3.14 for pi we have;

$50 = 3.14 \cdot r^2 \cdot (110)/(360)$

⇒ $50 = 0.959444446r^2$

Divide both sides by 0.959444446 we get;

$r^2 = 52.1134915$

⇒ $r = √(52.1134915)$

Simplify:

r ≈ 7.22 units

Therefore, the radius of this circle is, 7.22 units

Hello,
Let make a rule of three.

For 360° area of the circle is π R²
For 1° ............of the sector .. πR²/360
For 110° ............................... πR²*110/360 =50(units squared)

R²=50*360/(110π)
==>R=6*√(50/(11π))≈7,217137....(units)

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