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alexandr402 [8]
3 years ago
14

Adult tickets are $16 and child tickets are $6. The theater sold a total of 137 tickets for a total of $1772. How many adult tic

kets did the theater sell
Mathematics
1 answer:
GenaCL600 [577]3 years ago
5 0

Answer:

95

Step-by-step explanation:

Let x represent the cost of adult tickets for $16

Let y represent the cost of children tickets for $6

x + y = 137...........equation 1

16x +6y = 1772............equation 2

Multiply equation 1 by 16 and equation 2 by 1

16x + 16y= 2192

-

16x + 6y = 1772

10y = 420

y= 420/10

y= 42

Substitute 42 for y in equation 1

x + y = 137

x + 42= 137

x = 137-42

x= 95

Hence 95 adult tickets were sold for $16 and 42 children tickets were sold for $6

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Aleksandr-060686 [28]

√52-√13+√117

sqrt (4*13) - sqrt (13) + sqrt (13*9)

sqrt(4)sqrt(13) -sqrt(13)+sqrt(13)sqrt(9)

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3 years ago
If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f
nikklg [1K]

The quadratic function given by:


f(x)=a(x-h)^2+k, \ \ \ a\neq 0


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To translate the graph of a function to the right, left, upward or downward we have:

For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)


By knowing this things, we can solve our problem as follows:


FIRST.

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g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2


  • Then translating<em> 5 units down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5


Since the new function is fatter, the factor we need to multiply the term (x+11)^2 <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.


<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>


SECOND.

  • Translating <em>8 units to the right:</em>

g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2


  • Then translating<em> 1 unit down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1


As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.


<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

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