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My name is Ann [436]
3 years ago
12

Determine the measure of an angle whose measure is 14 times that of its complement

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
8 0

Answer:

84°

Step-by-step explanation:

Let the two complementary angles be x and y.

If the measure of an angle is 14 times the other, then x = 14y...... 1

Since the two angles are complementary, their sum will be 90° i.e x+y = 90° ...... 2

Substitute equation 1 into 2

14y+y = 90

15y = 90

y = 90/15

y = 6

Since the angle is x = 14y

x = 14(6)

x = 84°

Hence the measure of the angle is 84°

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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
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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

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This equation represents the totaled receipts.

The system :

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

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\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

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600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

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Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

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