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3 years ago

Dpf-sdzm-tdo = common girls

Mathematics

1 answer:

arlik [135]3 years ago

6 0

Answer: I don’t understand

Step-by-step explanation:

Next time actually ask something about college math

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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

What best describes the end behavior of the graph of f(x)=-x^4+5x-5

Neko [114]

Answer:

It describes multiplication

Step-by-step explanation:

As you can see its 5x-5 (the x is say "by" or "of), So when you look at it you can clearly see it's multiplication.

8 0

3 years ago

Over the past ten years, the town's population doubled in size. The population is currently 12,000. What was the population ten

Sidana [21]

I think the answer is <span>2P = 12,000 but I might be wrong

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8 0

3 years ago

Which set of graphs can be used to find the solution set to 3 log2(x + 4) < 6?

alexgriva [62]

Answer:

It's graph D

Step-by-step explanation:

5 0

3 years ago

Given that f(x)=6x+2 and g(x)= 2x+4/5 solve for g(f(1))

kolbaska11 [484]

Note that f(1) = 6(1)+2 = 8. Next, evaluate g(x) at x=8: g(f(1)) = g(8) = 2(8) + 4/5, or 16 4/5.

3 0

3 years ago

Dpf-sdzm-tdo = common girls​

Dpf-sdzm-tdo = common girls