Simplify the expression:<br> 3j

Solve the triangle. Round your answers to the nearest tenth. A. m∠A=43, m∠B=55, a=16 B. m∠A=48, m∠B=50, a=23 C. m∠A=48, m∠B=50,

alexgriva [62]

Answer:

D. m∠A=43, m∠B=55, a=20

Step-by-step explanation:

Given:

∆ABC,

m<C = 82°

AB = c = 29

AC = b = 24

Required:

m<A, m<C, and a (BC)

SOLUTION:

Find m<B using the law of sines:

$\frac{sin(B)}{b} = \frac{sin(C)}{c}$

$\frac{sin(B)}{24} = \frac{sin(82)}{29}$

$sin(B)*29 = sin(82)*24$

$\frac{sin(B)*29}{29} = \frac{sin(82)*24}{29}$

$sin(B) = \frac{sin(82)*24}{29}$

$sin(B) = 0.8195$

$B = sin^{-1}(0.8195)$

$B = 55.0$

m<B = 55°

Find m<A:

m<A = 180 - (82 + 55) => sum of angles in a triangle.

= 180 - 137

m<A = 43°

Find a using the law of sines:

$\frac{a}{sin(A)} = \frac{b}{sin(B)}$

$\frac{a}{sin(43)43} = \frac{24}{sin(55)}$

Cross multiply

$a*sin(55) = 25*sin(43)$

$a = \frac{25*sin(43)}{sin(53)}$

$a = 20$ (approximated)

8 0

2 years ago

One number is six times as large as a certain smaller number. Let x represent the smaller number. Write the larger number in ter

Svetach [21]

One number is six times as large as a certain smaller number.

i.e., Y = 6x

Answer is 6x

3 0

3 years ago

A trapezoid has an area of 30m^2. if all of its side lengths are tripled, what will its new area be

Norma-Jean [14]

Answer:

270

Step-by-step explanation:

Because we do not know what the side lengths are, as long as they multiply to 30m^2, it's fine

For this question, let's just say the base is 5, and the height is 6. If we triple 5, we get 15, and if we triple 6, we get 18. 15*18=270

Now what if, the sides are not 5 and 6. Will the area still be the same? Let's find out.

10*3=30 so we can say for this answer, the base is 3, and the height is 10.

10 tripled is 30, and 3 tripled is 9. 30*9=270

So as we look at these 2 answers. we can conclude that the new area, no matter the side lengths, will be 270

Hope this helpes!

5 0

3 years ago

Katherine and Crystal do landscaping. They recently earned $1472 for a project. If Katherine earned $5 for every $3 earned by Cr

Degger [83]

Answer:

Katherine: 920

Crystal: 552

Step-by-step explanation:

The total amount earned by each is 1472

The ratio of the earnings is Katherine / Crustal = 5/3

The total number of shares = 5 + 3 = 8

So the proportion for Katherine

5/8 = x / 1472 Cross multiply

8x = 5 * 1472

8x = 7360

x = 7360/8

x = 920

And the proportion for Crystal is

3/8 = x / 1472 Cross multiply

8x = 3 * 1472

8x = 4416

x = 4416 / 8

x = 552

4 0

3 years ago

1 pt) find the average rate of change of the function over the given intervals. h(t)=\cot (t);

blondinia [14]

$\text{Consider the function}\\
\\
h(t)=\cot(t) \text{ on the interval }\left [ \frac{\pi}{4}, \ \frac{3\pi}{4} \right ]\\
\\
\text{we know that the average rate of change of a funtion f(x) over the }\\
\text{interval [a, b] is given by}\\
\\
f_{avg}=\frac{f(b)-f(a)}{b-a}\\
\\
\text{so using this, the average rate of change of the given function is}$

$h_{avg}=\frac{h\left ( \frac{3\pi}{4} \right )-h\left ( \frac{\pi}{4} \right )}{\frac{3\pi}{4}-\frac{\pi}{4}}\\
\\
=\frac{\cot \left ( \frac{3\pi}{4} \right )-\cot \left ( \frac{\pi}{4} \right )}{\frac{3\pi-\pi}{4}}\\
\\
=\frac{(-1)-(1)}{\frac{2\pi}{4}}\\
\\
=\frac{-2}{\frac{\pi}{2}}\\
\\
\text{Average rate of change of function}=\frac{-4}{\pi}$

6 0

3 years ago

Simplify the expression: 3j–1+4