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2 years ago

Following the order of operations, exponents should be simplified after completing all multiplication and division.

Mathematics

1 answer:

xenn [34]2 years ago

6 0

False

Exponents should not be simplified.

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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

2 years ago

Read 2 more answers

In 2016, a billionaire's net worth was approximately $3.6 x 109. That same year, it

Alekssandra [29.7K]

Answer:

all you do is multiply 3.6 and 109 to see if its 45,000 per year

Step-by-step explanation:

3 0

3 years ago

At a school, 43% of students attend the homecoming football game. Only 23% of students go to the game and the homecoming dance.

Strike441 [17]

9.89%

You can get this number by multiplying the two together.

5 0

3 years ago

Select an expression that shows the sum of exactly two terms that is equivalent to 3(x + 7).

bixtya [17]

Answer:

3x + 21

Step-by-step explanation:

3(x + 7) Distribute

3x + 21

6 0

2 years ago

PLEASE HURRY -4 3/5 divid by 1 1/5

kaheart [24]

The answer is: -3 5/6

Hope this helped :3

4 0

2 years ago