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3 years ago

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An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 7100 dollars. If she earns a total of 90400

dollars per year, what is her monthly salary in dollars

1 answer:

photoshop1234 [79]3 years ago

5 0

90,400-7,100=83,300

83,300/12=6,941.66667

Monthly Salary Rounded: 6,941.67

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Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

Find the arc length of the partial circle.

nalin [4]

Answer:

1/2 pi

Step-by-step explanation:

This is 1/4 of a circle

Find the circumference and multiply by 1/4

1/4 C

1/4 ( 2*pi*r) where r is the radius

The radius is 1

1/2 pi*1

1/2 pi

7 0

3 years ago

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Isnt this skewed left since majority of the data is on the right side.

forsale [732]

Answer:

I'm only here because I'm dumb and I use brainly

5 0

2 years ago

When Vince does 14 push-ups and 12 sit-ups, it takes a total of 52 seconds. In comparison, he needs 48 seconds to do 12 push-ups

marshall27 [118]

Answer:

it takes 2 seconds to do one situp

it takes 2 seconds to do one pushup

to do 14 pushups, it takes 28 seconds.

to do 12 situps it takes 24 seconds

to do 12 pushups, it takes 24 seconds

BRAINLIEST PLEASE!

hope this helps :)

Step-by-step explanation:

14x + 12y = 52

12x + 12y = 48

^^^ this is an inequality that we can make.

x stands for pushups

y stands for situps

if we subtract the second equation from the first, we get

2x = 4

x = 2

now we can place x in one of the equations to solve for y

12(2)+12y=48

24 + 12y = 48

12y = 24

y = 2

5 0

2 years ago

Need help fast please

castortr0y [4]

Answer:

The answer for the first one is 1/f3

the second one is b-5 i think

third one is 8k^5/m4

last one is -9

hope this helped

Step-by-step explanation:

6 0

2 years ago

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