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weqwewe [10]
2 years ago
7

1 Admission to the local movie theater is $3 for each child and $7 for each adult. A group of 12 people pay $64 admission. How m

any children are in this group?
Mathematics
1 answer:
Eduardwww [97]2 years ago
6 0

Given:

Admission to the local movie theater is $3 for each child and $7 for each adult.

A group of 12 people pay $64 admission.

To find:

The number of children in a group.

Solution:

Let the number of children be x and number of adults be y.

According to the question,

Total persons : x+y=12          ...(i)

Total cost : 3x+7y=64     ...(ii)

Multiply equation (i) by 7 and subtract the result from (ii).

3x+7y-7(x+y)=64-7(12)

3x+7y-7x-7y=64-84

-4x=-20

Divide both sides by -4.

x=5

Therefore, the number of children is 5.

You might be interested in
PLEASE HELPPP!!!
Tems11 [23]

Answer:

a) -16t^{2}+64t\geq40

b)[2-\frac{\sqrt{6}}{2} , 2+\frac{\sqrt{6}}{2}]

(see attached picture for the number line)

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) h_{max}=64ft

d) t=2s

Step-by-step explanation:

a)

Basically the ball will disappear when it is higher than 40 ft, so we can build the inequality like this:

-16t^{2}+64t\geq40

this is because the function represents it's height, so when the function is greater than or equal to 40, then the ball will disappear.

b) to solve the inequality, first we need to turn the ≥ symbol to an = symbol and solve for t, so we get:

-16t^{2}+64t =40

we can move the 40 to the other side of the equation so we get:

-16t^{2}+64t-40=0

we can factor the equation so it's easier to solve, so we get:

-8(2t^{2}-8t+5) =0

which simplifies to:

2t^{2}-8t+5=0

and we can use the quadratic formula to solve this equation, so we get:

t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}

so we get:

t=\frac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}

which yields:

2\pm \frac{\sqrt{6}}{2}

and next we need to test the posible intervals to see which one makes the inequality true, the possible intervals are:

(-\infty, 2-\frac{\sqrt{6}}{2}]  for a test value of 0

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}] for a test value of 1

[2+\frac{\sqrt{6}}{2},\infty) for a test value of 4

so next we test each of the values in the original inequality and see if the inequality is true:

(-\infty, 2-\frac{\sqrt{6}}{2}] for a test value of 0

-16(0)^{2}+64(0)\geq40

0\geq40 false

so this is not an answer.

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}] for a test value of 1

-16(1)^{2}+64(1)\geq40

48\geq40

true, so this is an answer.

[2+\frac{\sqrt{6}}{2}, \infty) for a test value of 4

-16(4)^{2}+64(4)\geq40

-16(16)+64(4)\geq40

-256+256\geq40

0\geq40

false, so this is no answer.

So the answer is the interval:

[2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}]

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) In order to find how high Penelope kick the football, we must find the vertex of the parabola which is gotten when graping the given function (see attached picture)

so we can use the following formula to find the t-value for this maximum height:

t=-\frac{b}{2a}

so we substitute the corresponding values:

t=-\frac{64}{2(-16)}

which yields:

t=2s

next, we can substitute this time into the original function to find the maximum height, so we get:

h=-16(2)^{2}+64(2)

which yields:

h=64 ft

d) We found the answer for d on the previous part where we got that t=2s

6 0
3 years ago
3. Find angle q.<br> A) 90 <br> B)116<br> C)123<br> D)130
Inga [223]

Answer:

C

Step-by-step explanation:

because 180 - 58

remember the quadrilateral is between the circumference

5 0
3 years ago
Which expression is equivalent to (2^3)^-5
Ostrovityanka [42]
Hi!

You didn't list the options, but I think I know the answer. Let me know if my answer isn't listed! :)

(x^{3} )^{-5}
We need to multiply the exponents.
3 · -5 = -15

The answer is 2^{-15}

Hope this helps! :)
3 0
3 years ago
Read 2 more answers
sam decides to build a square garden if the area of the other garden is 9x^2 -24x +16 square feet what is the length of one side
Yuri [45]
<span>9x^2 -24x +16 can be factored into (3x-4)</span>²
the length of each side is 3x-4
4 0
3 years ago
Simplify 4+(-3)-2 times (-6)
zloy xaker [14]
<span><span>4−3</span>−<span><span>(2)</span><span>(<span>−6</span>)</span></span></span><span>=<span>1−<span><span>(2)</span><span>(<span>−6</span>)</span></span></span></span><span>=<span>1−<span>(<span>−12</span>)</span></span></span><span>=<span>13</span></span>
6 0
3 years ago
Read 2 more answers
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