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liubo4ka [24]
3 years ago
11

In triangle ABC, a=31 , b=22 , c=18. Identify m∠A rounded to the nearest degree.

Mathematics
1 answer:
Veronika [31]3 years ago
8 0

Answer:

101

Step-by-step explanation:

According to the Law of Cosines, for any △ABC with side lengths a, b, and c, a2=b2+c2−2bccosA; b2=a2+c2−2accosB; and c2=a2+b2−2abcosC

.

The Law of Cosines can be used because all three side lentghs are known.

Set up the equation for the Law of Cosines:

a2=b2+c2−2bccosA

Substitute the known values into the Law of Cosines:

312=222+182−2(22)(18)cosA

Square the values and multiply:

961=484+324−792cosA

Add:

961=808−792cosA

Subtract 808

from both sides:

153=−792cosA

Divide both sides by −792

:

153−792=cosA

According to this equation m∠A

is equal to the inverse cosine function of −153792

. Write this:

m∠A=cos−1(−153792)

Calculate the value of the inverse cosine −153792

on a calculator:

m∠A≈101°

Therefore, m∠A≈101°

.

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After a storm damages the community center, Shanika and her friends hold fundraising
Inessa [10]

Answer:

The total amount of money Shanika and her friends want to raise is <u>$2400</u>.

Step-by-step explanation:

Given:

After a storm damages the community center, Shanika and her friends hold fundraising.

After the first event, they raise $240, which is 10% of the  total amount that they want to raise.

Now, to find the total amount of money that Shanika and her friends want to raise.

Let the total amount of money that Shanika and her friends want to raise be x.

As given 10% of fundraise is $240.

So, according to question:

10\%\ of\ x=\$240.

\frac{10}{100}\times x=240

\frac{10x}{100}=240.

<em>Multiplying both sides by 100 we get:</em>

10x=24000.

<em>Dividing both sides by 10 we get:</em>

x=\$2400.

Therefore, the total amount of money Shanika and her friends want to raise is $2400.

3 0
3 years ago
Please help right now!!!!! Solve the system of equations below. x + y = 7 2x + 3y = 16
motikmotik

Answer:

x=5 and y=2.

Step-by-step explanation:

We have been given a system of equations. We are asked to solve our given system.

x+y=7...(1)

2x+3y=16...(2)

From equation (1), we will get:

x=7-y

Upon substituting this value in equation (2), we will get:

2(7-y)+3y=16

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Now, we will substitute y=2 in equation (1).

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In the given figure we can determine the coordinate of point M from the graph, we get:

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Now, to determine the length of segment MN, we need to subtract the x-coordinate of M from the coordinates of N, we get:

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