V = lwh
2x³ + 17x² + 46x + 40 = l(x + 4)(x + 2)
2x³ + 12x² + 16x + 5x² + 30x + 40 = l(x + 4)(x + 2)
2x(x²) + 2x(6x) + 2x(8) + 5(x²) + 5(6x) + 5(8) = l(x + 4)(x + 2)
2x(x² + 6x + 8) + 5(x² + 6x + 8) = l(x + 4)(x + 2)
(2x + 5)(x² + 6x + 8) = l(x + 2)(x + 4)
(2x + 5)(x² + 2x + 4x + 8) = l(x + 4)(x + 2)
(2x + 5)(x(x) + x(2) + 4(x) + 4(2)) = l(x + 4)(x + 2)
(2x + 5)(x(x + 2) + 4(x + 2)) = l(x + 4)(x + 2)
(2x + 5)(x + 4)(x + 2) = l(x + 4)(x + 2)
(x + 4)(x + 2) (x + 4)(x + 2)
2x + 5 = l
Let us assume the number of children attending the movie = x
Let us also assume the number of adults attending the movie = y
Cost of admission for a children in the movie = $8
Cost of admission of an adult in the movie = $12
Number of people going to the movie on a certain day = 3200
Total amount collected from the movie theater = $33040
Then
x + y = 3200
And
8x + 12y = 33040
2x + 3y = 8260
Let us first take the equation
x + y = 3200
x = 3200 - y
Now we will put the value of x in the equation
2x + 3y = 8260
2(3200 - y) + 3y = 8260
6400 - 2y + 3y = 8260
y = 8260 - 6400
= 1860
Now we will put the value of y from the above deduction in the equation
x + y = 3200
x + 1860 = 3200
x = 3200 - 1860
= 1340
So the number of children going to the movie theater is 1340 and the number of adults going to the movie theater is 1860.
The lengths of each of the segments connected by the given pairs of points are:
1. AB = 10 units
2. CD = 17 units
3. EF = 3 units
<h3>How to Find the Length of Segments Connected by Two Points?</h3>
To find the length of a segment connected by two coordinate points, the distance formula is applied, which is:
d = 
.
1. Find the length of segment AB:
A(5,-3)
B(-3,3)
AB = √[(−3−5)² + (3−(−3))²]
AB = √[(−8)² + (6)²]
AB = √100
AB = 10 units
2. Find the length of segment CD:
C(-2, -7)
D(6, 8)
CD = √[(6−(−2))² + (8−(−7))²]
CD = √(64 + 225)
CD = 17 units
3. Find the length of segment EF:
E(5,6)
F(5,3)
EF = √[(5−5)² + (3−6)²[
EF = √(0 + 9)
EF = √9
EF = 3 units
Learn more about lengths of segments on:
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