MATHEMATICS HIGH SCHOOL

What is the vertex of g(x)=8x^2 - 48x + 65?(-3,-7)
(3,-7)
(24, -7)
(-24, -7)

Answers

Answer 1
Answer:

\textit{vertex of a vertical parabola, using coefficients} \n\n g(x)=\stackrel{\stackrel{\textit{\small a}}{\downarrow }}{8}x^2\stackrel{\stackrel{\textit{\small b}}{\downarrow }}{-48}x\stackrel{\stackrel{\textit{\small c}}{\downarrow }}{+65} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)

\left(-\cfrac{ -48}{2(8)}~~~~ ,~~~~ 65-\cfrac{ (-48)^2}{4(8)}\right) \implies\left( - \cfrac{ -48 }{ 16 }~~,~~65 - \cfrac{ 2304 }{ 32 } \right) \n\n\n \left( \cfrac{ 48 }{ 16 }~~,~~65 - \cfrac{ 2304 }{ 32 } \right)\implies \left( \cfrac{ 48 }{ 16 }~~,~~65 - 72 \right)\implies (~3~~,~~ -7~)

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: Sergio wants to fence in a circular portion of his backyard for a play space for his dog. Determine the area of the largest portion of the yard he can enclose with 72 feet of fencing. Use 3.14 for π.

Answers

For this case we have to:

If Sergio has 72 feet of fence then we have that the circumference of the fence (whose space is circular) is 72.

By definition, the circumference of a circle is given by:

C = \pi * d

Where:

d: It is the diameter of the circumference

So:

72 = \pi * d\nd = \frac {72} {\pi}\nd = \frac {72} {3.14}\nd = 22.93 \ ft

Then, the radius will be given by: r = 11.45 \ ft

Thus, the area of the circular portion will be:

A = \pi * r ^ 2\nA = 3.14 * (11.45) ^ 2\nA = 3.14 * 131.1025\nA = 411.66 \ ft ^ 2

Thus, the area of the playing space is:A = 411.66 \ ft ^ 2

Answer:

A = 411.66 \ ft ^ 2

Josh purchased 8 cans of tennis balls. The cans came with 3 balls in each can. How many balls did Josh purchase?

Answers

Answer:

8 x 3 = 24 balls

Step-by-step explanation:

Multiplication.
Answer 24
Just multiply

How many real solutions does the equation below have?3x^2 − x + 5 = 0


PLEASE HELP ME ASAP

Answers