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snow_tiger [21]
3 years ago
13

The cost of printing T-shirts is defined by the equation C = 250+5.5n, where C represents the total

Mathematics
1 answer:
tatuchka [14]3 years ago
7 0

Answer:

<em>The school paid for printing 130 T-shirts</em>

Step-by-step explanation:

<u>Function Models</u>

We are given the cost of printing n T-shirts as the equation:

C=250+5.5n

For example, if 10 T-shirts were printed, the school would pay:

C=250+5.5(10)=250+55=\$305

We know the school paid $965 and are required to find the number of T-shirts that were printed. If we use the equation with C=965, we can solve it for n:

965=250+5.5n

965-250=5.5n \Rightarrow 5.5n=715

Solving:

n=715/5.5=130

The school paid for printing 130 T-shirts

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GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola:  y=3x^2-4

Step-by-step explanation:

Given:

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  • parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola:  y=a(x-h)^2+k

(where (h, k) is the vertex and a is some constant)

Substitute point (0, -4) into the equation:

\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}

Substitute point (-2, 8) and ah^2+k=-4 into the equation:

\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}

Substitute point (1, -1) and ah^2+k=-4 into the equation:

\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}

Equate to find h:

\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}

Substitute found value of h into one of the equations to find a:

\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}

Substitute found values of h and a to find k:

\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}

Therefore, the equation of the parabola in vertex form is:

\implies y=3(x-0)^2-4=3x^2-4

So the vertex of the parabola is (0, -4)

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