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Fed [463]
3 years ago
8

A total of 330 children and adults attended a school play. There were 21 times as many children in attendance as there were adul

ts.
This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children.

c = 21a

a + c = 330

How many children attended the play?
Mathematics
2 answers:
Pani-rosa [81]3 years ago
6 0

Answer:

15

Step-by-step explanation:

vovangra [49]3 years ago
5 0

Answer:

315 children

Step-by-step explanation:

a + 21a = 330 {substituted 21a, in for c, into second equation}

22a = 330 {combined like terms}

a = 15 {divided each side by 22}

15 adults attended

c = 21a {first original equation}

c = 21(15) {substituted 15,

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elena55 [62]
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An athlete took forward and backward steps of equal distance to warm up before his race. After taking 10 steps total, he was bac
snow_tiger [21]
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3 years ago
ABC was dilated to create A' B' C'. What is the center of dilation? And what is the scale factor of the dilation?
Virty [35]

Given:

In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).

The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).

To find:

The center of dilation and the scale factor.

Solution:

In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.

From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).

Therefore, the center of dilation is (0,0).

If a figure is dilated by factor k and the center of dilation is origin, then

(x,y)\to (kx,ky)

A(-2,2)\to A'(k(-2),k(2))

A(-2,2)\to A'(-2k,2k)

It is given that A'(-4,4). So,

(-2k,2k)=(-4,4)

On comparing both sides, we get

-2k=-4

2k=4

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4 0
3 years ago
What is the height of a right triangle if its other two sides are 30 centimeters and 10 centimeters long?​
Mila [183]

Answer:

Step-by-step explanation:

It depends on whether the 30 cm side is the hypotenuse, or one of the legs.

If the 30 cm side is the hypotenuse, then the third side is √(30^2-10^2) = √800 = 20√2 cm

If the 30 cm side is one of the legs, then the hypotenuse is √(30^2+10^2) = √1,000 = 10√10 cm

7 0
2 years ago
With a tailwind, a aircraft can fly 360 miles in 3 hrs. Against this same wind, the aircraft can fly the same distance in 4hrs.
Leona [35]

Answer:

15mph

Step-by-step explanation:

360 divide by 3 =  120

360 divide by 4 = 90

120 - 90 = 30

30 divide by 2 (cause boosting speed and drag) = 15

so let's check

120-15=105

105+15=120

105-15= 90

so the answer's 15.

3 0
3 years ago
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