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4 years ago

Pls help ASAP I need it for tomarrow

Mathematics

1 answer:

kozerog [31]4 years ago

8 0

Answer:

The answer is 140 cars .

Step-by-step explanation:

$\frac{1}{5}$ × 300 = 60

$\frac{1}{3}$ × 300 = 100

100 + 60 = 160

300 - 160 = 140

TEXT:

One-fifth of 300 is 60. One-third of 300 is 100. If you add both vintage and race cars you get 160. the total, 300, minus the vintage and race cars, 160, is 140 cars.

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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

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Answer:

$\theta_{CAB}=128.316$

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$\theta_{BCA}=25.842$

Step-by-step explanation:

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

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

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

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

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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:

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

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

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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!

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

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

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

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