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3 years ago

Complete A,B and 6 for 13 points.

Mathematics

1 answer:

kicyunya [14]3 years ago

3 0

Answer:

a) 10

b) The $40+5 dollars for every ticket

c) See below

Step-by-step explanation:

1. Let t=number of tickets

2. Writing an equation

Breaking even means that you earn the same amount of money for both.

40 +5t=70+2t

3. Solving the equation

40 +5t=70+2t

5t-2t=70-40

3t=30

t=10

So the answer to a) is 10.

1. Using an equation

We already know that there are 2 equations for this problem. (40+5t, 70+2t)

So, we will substitute 20 for t.

40+5*20=40+100=140

70+2t=70+2*20=110

2. Comparing equations

140>110, so the first offer is better

The owner lets you choose how you get paid because one option will be better for you, as some days you might not sell many tickets (so you will go with the $70+2 tickets), or some days you might sell many tickets (you will choose the $40+5 dollars/ticket).

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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

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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.

Translating 11 units to the left:

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

Then translating 5 units down:

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

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

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

SECOND.

Translating 8 units to the right:

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

Then translating 1 unit down:

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

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

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

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madreJ [45]

Answer:

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Step-by-step explanation:

Find f( - 3) × g(4),

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and g(x) = x^½

g(4) = 4^½ = 2^2^½ = 2 ^1 = 2

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Data provided in the question:

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Step-by-step explanation:

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