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3 years ago

Ma.clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?

Mathematics

2 answers:

k0ka [10]3 years ago

8 0

The answer to this question is 17

olga nikolaevna [1]3 years ago

6 0

In this question, we're trying to find how many science kits Ms. Clark bought.

We know that she spent a grand total of $89.85 on the science kits, this price also includes the tax she paid.

We know that she payed $4.85 in taxes

We also know that each kit cost $5 each

Lets first get rid of the tax in the final price.

89.85 - 4.85 = 85

Without tax, she spent $85

Since we know that each kit costs $5 each, we would divide 85 by 5 to see how many kits she bought.

85 ÷ 5 = 17

This means that she bought 17 science kits.

Answer:

17 science kits

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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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$\theta_{CAB}=128.316$

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Step-by-step explanation:

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

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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:

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

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

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

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

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

$\theta_{ABC}=25.842$

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

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$180$

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