Amovie theater charges $4.50 for children and $8.00 for adults. on a certain day, 1200 people enter the theater and $8375 is collected. how many children and how many adults attended?

The number of adults who attended=850

The number of children who attended=350

Step-by-step explanation:

a). Determine first expression

Let the number of each group be as follows;

adults=a

children=c

total number of people=1200

This can be expressed as;

number of people=number of children+number of adults

replacing;

a+c=1200...equation 1

b). Determine the second expression

Let the total cost be expressed as shown;

total cost=(cost per child×number of children)+(cost per adult×number of adults)

where;

total cost=$8,375

cost per child=$4.5

number of children=c

cost per adult=$8

number of adults=a

replacing;

(8×a)+(4.5×c)=1,200

8 a+4.5 c=8,375...equation 2

c). Combine equation 1 and 2 and solve simultaneously

1(8 a+4.5 c=8,375)

4.5(a+c=1,200)=4.5 a+4.5 c=5,400

(8 a-4.5 a)+(4.5 c-4.5 c)=(8,375-5,400)=2,975

3.5 a=2,975

a=2,975/3.5

a=850

replacing the value for a in equation 1

850+c=1200

c=1200-850=350

The number of adults who attended=850

The number of children who attended=350

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

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cretdit to source

answer is 12345678900987654321234567890987654321

step-by-step explanation: