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3 years ago

Solve for x in the diagram.

Mathematics

2 answers:

BARSIC [14]3 years ago

8 0

Answer:

x = 20

Step-by-step explanation:

x° + 2x° + (x+10)° = 90°

3x° + x° + 10° = 90°

4x° + 10° = 90°

4x° = 90°-10°

4x° = 80°

x = 80/4

x = 20

olga nikolaevna [1]3 years ago

4 0

Answer:

20°

Step-by-step explanation:

The sum of all three angles combined is 90°. You can see this by the square at the corner. This means that you have to add all of the angles together and set it equal to 90° to solve for x.

x° + 2x° + (x + 10)° = 90°

3x° + (x + 10)° = 90°

4x° + 10° = 90°

4x° = 80°

x = 20°

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A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.

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Answer:

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Step-by-step explanation:

Given

Let:

$C = Children; S = Students; A = Adults$

For the capacity, we have:

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For the tickets sold, we have:

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Half as many as adults are children implies that:

$A = \frac{C}{2}$

Required

Solve for A, C and S

The equations to solve are:

$C + S + A = 329$ -- (1)

$5C + 7S + 12A = 2388$ -- (2)

$A = \frac{C}{2}$ -- (3)

Make C the subject in (3)

$C = 2A$

Substitute $C = 2A$ in (1) and (2)

$C + S + A = 329$ -- (1)

$2A + S + A = 329$

$3A + S = 329$

Make S the subject

$S = 329 - 3A$

$5C + 7S + 12A = 2388$ -- (2)

$5*2A + 7S + 12A = 2388$

$10A + 7S + 12A = 2388$

$7S + 22A = 2388$

Substitute $S = 329 - 3A$

$7(329 - 3A) + 22A = 2388$

$2303 - 21A + 22A = 2388$

$2303 +A = 2388$

Solve for A

$A = 2388 - 2303$

$A = 85$

Recall that: $C = 2A$

$C = 2 * 85$

$C = 170$

Recall that: $S = 329 - 3A$

$S = 329 - 3 * 85$

$S = 329 - 255$

$S = 74$

Hence, the result is:

$C = 170$

$S = 74$

$A = 85$

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