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CaHeK987 [17]
3 years ago
11

Which of the following is always true about Vertical Angles?

Mathematics
1 answer:
Paul [167]3 years ago
7 0
Vertical angle are always congruent
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Find the radian measure of the angle with the given degree measure. Round your answer to three decimal places.
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Answer:

-0.663

Step-by-step explanation:

-38/180 × pi = -0.6632251158

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A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. At a certain screening
-BARSIC- [3]

Answer:

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving  a system of linear equations.

First we write the system equations :

C+S+A=750

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

3C+5S+7A=3450

This equation represents the totaled receipts.

The system :

C+S+A=750\\3C+5S+7A=3450

has the following associated matrix :

\left[\begin{array}{cccc}1&1&1&750\\3&5&7&3450\end{array}\right]

By performing elementary matrix operations we find that the matrix is equivalent to

\left[\begin{array}{cccc}1&0&-1&150\\0&1&2&600\\\end{array}\right]

The new system :

C-A=150\\S+2A=600

Working with the equations :

C = 150 + A\\S = 600-2A

Our solution vector is :

\left[\begin{array}{c}C&S&A\end{array}\right] =\left[\begin{array}{c}150+A&600-2A&A\end{array}\right]

For example :

If 0 adults attended ⇒ A = 0

C = 150 + 0 \\C = 150\\S = 600 - 2A\\S = 600

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S = 600 -2A

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

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3 years ago
A cube has a surface area of 3/2. What's the volume?
Cloud [144]

Answer:

C

Step-by-step explanation:

Assume the surface area = 6x²

6 is the number of faces and x is the length of the cube

so 3/2 = 6x²

Divide by 6

1/4 = x²

Square root both sides

1/2 = x

Volume is : l×w×h

so 1/2 × 1/2 × 1/2 = 1/8

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Find the maximum power of 5 which can divide 49!
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Answer:

10

Step-by-step explanation:

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