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2 years ago

Solve for A Exact (no rounding, no calculator needed) 0 = A^2 + 13A + 36

Mathematics

1 answer:

marysya [2.9K]2 years ago

3 0

Answer:

-4 or -9

Step-by-step explanation:

-a^2-13a-36=0

(-a-4)(a+9)=0

-a-4=0

a+9=0

a= -4, -9

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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.

kipiarov [429]

Answer:

170 children

74 students

85 adults

Step-by-step explanation:

Given

Let:

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

For the capacity, we have:

$C + S + A = 329$

For the tickets sold, we have:

$5C + 7S + 12A = 2388$

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:

$C = 170$

$S = 74$

$A = 85$

8 0

3 years ago

Find the equation of the line through point (2,2) and parallel to y=x+4. Use a forward slash (i.e.”/“) for fractions (e.g. 1/2 f

aleksandr82 [10.1K]

Answer:

The equation of the line is, y = x

Step-by-step explanation:

The constraints of the required linear equation are;

The point through which the line passes = (2, 2)

The line to which the required line is parallel = y = x + 4

Two lines are parallel if they have the same slope, therefore, we have;

The slope of the line, y = x + 4 is m = 1

Therefore, the slope of the required line = 1

The equation of the required lime in point and slope form becomes;

y - 2 = 1 × (x - 2)

∴ y = x - 2 + 2 = x

The equation of the required line is therefore, y = x

5 0

3 years ago

A certain class has 25 students. If 8 students play football and, 10 plays baseball and 6 plays both, how many students play nei

NNADVOKAT [17]

Answer:1

Step-by-step explanation:

8+10=18 18+6=24 25-24=1

6 0

2 years ago

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Can someone please help me factor this 48m^12-16

Damm [24]

Factor 16 out of 48m^12 -16

Your answer
16(3m^12 - 1)

7 0

3 years ago

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To make copies of blueprints, Vantage Reprographics charges a $5 setup fee plus $3 per copy. Myra can spend no more than $59

Butoxors [25]

Answer:

Myra can make 18 or fewer copies

Step-by-step explanation:

Let n be the no. of copies

The cost:

5 + 3n《59

3n《54

n《18

3 0

3 years ago

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