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2 years ago

Find the lengths of AC. Round your answer to the nearest whole number. C a 22.69 B 13 cm A

Mathematics

1 answer:

blondinia [14]2 years ago

5 0

The triangle ABC is a right triangle

The length of AC is 12.00 cm

<h3>How to determine the length of AC</h3>

From the figure, we have the following parameters:

Length AB = 13 cm

Angle A = 22.6 degrees

Represent the length AC with b.

So, we have the following cosine ratio

$\cos(A) = \frac{b}{AB}$

Substitute known values

$\cos(22.6) = \frac{b}{13}$

Make b the subject

$b = 13 * \cos(22.6)$

Evaluate the product

$b = 12.00$

Hence, the length of AC is 12.00 cm

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Factor the following polynomial completely.<br><br>y squared plus 5 zy plus 4 z squared<br><br>

sweet [91]

Answer:

(y + z)(y + 4z)

Step-by-step explanation:

${y}^{2} + 5zy + 4 {z}^{2} \\ = {y}^{2} + zy + 4zy + 4 {z}^{2} \\ = y(y + z) + 4z(y + z) \\ = (y + z)(y + 4z)$

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3 years ago

Use the substitution method to find the solution to the system of linear equations.

nataly862011 [7]

Answer: answer is d

Step-by-step explanation: input in calculator or set both equal to y and then set them equal to each other

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3 years ago

Find m 1 and m 2 in the diagram

Marysya12 [62]

Answers:
M for 1 is: 114
M for 2 is: 34

Why?
First you need to find out what the angle is for the corner to the left of angle 1 to do so

180-135 which equals 45

then to find on you take 180 (the sun of all interior angles in a triangle equal 180) and subtract all the angles give...
180-21-45= 114 (which makes since because angle one is obtuse and so is it)
Now for angle to you need to find the corner that is next to angle 1 to do so you do...

180-114 (because angle equals 114) this equals 66

Then you do 180-66-80 to get angle 2 which equals 34

Hope this helps :D

6 0

3 years ago

HELPPP!!!!!!

Furkat [3]

<h3>Answer: Choice D) 31.2 miles</h3>

This value is approximate.

============================================================

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

----------------

To sum things up so far, we have these known properties of triangle ABC

angle A = 107 degrees
side c = side AB = 24 miles
angle B = 42 degrees
angle C = 31 degrees

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

8 0

2 years ago

A credit union loaned out $50,000, part at an annual rate of 6% and the rest at an annual rate of 12% . The collected combined i

Natasha_Volkova [10]

Answer: the credit union loaned out $40000 at 6% and $10000 at 12%

Step-by-step explanation:

Let x represent the amount that the

credit union loaned out at the annual rate of 6%.

Let y represent the amount that the

credit union loaned out at the annual rate of 12%.

credit union loaned out $50,000, part at an annual rate of 6% and the rest at an annual rate of 12%. It means that

x + y = 50000

The interest on $x after 1 year would be

6/100 × x = 0.06x

The interest on $y after 1 year would be

12/100 × y = 0.12y

The collected combined interest was $3,600 that year. It means that

0.06x + 0.12y = 3600- - - - - - - - - 1

Substituting x = 50000 - y into equation 1, it becomes

0.06(50000 - y) + 0.12y = 3600

3000 - 0.06y + 0.12y = 3600

- 0.06y + 0.12y = 3600 - 3000

0.06y = 600

y = 600/0.06

y = $10000

x = 50000 - y = 50000 - 10000

x = $40000

5 0

2 years ago

Find the lengths of AC. Round your answer to the nearest whole number. C a 22.69 B 13 cm A​

Find the lengths of AC. Round your answer to the nearest whole number. C a 22.69 B 13 cm A