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Alex777 [14]
2 years ago
10

Use the function f(x) to answer the questions.

Mathematics
1 answer:
PIT_PIT [208]2 years ago
3 0

Answer:

See below

Step-by-step explanation:

<u>Part A</u>

Remember that x-intercepts are located where y=0:

<u />

<u />f(x)=-16x^2+60x+16<u />

<u />0=-16x^2+60x+16<u />

<u />0=x^2+60x-256<u />

<u />0=(x+64)(x-4)<u />

<u />0=(x-4)(-16x-4)<u />

<u />x=4 and x=-\frac{1}{4}

<u>Part B</u>

Since the leading coefficient, -16, is negative, the parabola will open downward, making the vertex a maximum. We can determine the x-coordinate of the vertex using x=-\frac{b}{2a} and plug it into the function to find the y-coordinate:

x=-\frac{b}{2a}

x=-\frac{60}{2(-16)}

x=-\frac{60}{-32}

x=\frac{60}{32}

x=\frac{15}{8}

Now we find the y-coordinate given the x-coordinate:

f(x)=-16x^2+60x+16

f(\frac{15}{8})=-16(\frac{15}{8})^2+60(\frac{15}{8})+16

f(\frac{15}{8})=-16(\frac{225}{64})+\frac{900}{8}+16

f(\frac{15}{8})=\frac{-3600}{64}+\frac{225}{2}+16

f(\frac{15}{8})=\frac{-225}{4}+\frac{225}{2}+16

f(\frac{15}{8})=\frac{-225}{4}+\frac{450}{4}+\frac{64}{4}

f(\frac{15}{8})=\frac{289}{4}

Therefore, the coordinates of the vertex are (\frac{15}{8},\frac{289}{4}).

<u>Part C:</u>

Notable points of a quadratic function include its x-intercepts, y-intercept, and vertex. Plotting these points on a graph help to visualize what the resulting graph of the function looks like. I've attached a graph with the function and the notable points for you to see.

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Freddy’s savings account went from $520 to $321 after he purchased a new bike. What was the percent decrease? *
ruslelena [56]

If my calculations are correct, the percentage decrease faced here is roughly 38.2%. Based on the calculations, the bicycle costs 199$ and when the cost is subtracted from 520, you would create the percentage of 38.2%.

6 0
2 years ago
(a) Work out the reciprocal of 1.25
Oxana [17]

Answer:

0.8 OR \frac{4}{5}

Step-by-step explanation:

The reciprocal of any number is the number that it multiplies by to equal 1.

The reciprocal can be found by simply converting the number into a fraction and then 'flipping' the fraction as any number multiplied by its reciprocal is 1.

E.g.

No. X/Y * Y/X (its reciprocal) = 1

\frac{x}{y} *\frac{y}{x} =\frac{xy}{xy} =1

So, to find the reciprocal of 1.25,we should first convert 1.25 to a fraction.

1.25 = 125/100

\frac{125/25}{100/25}=\frac{5}{4}

Now we just flip 5/4 to get our reciprocal:

\frac{4}{5} = 0.8

Test: 0.8 * 1.25 = 1

The reciprocal of 1.25 (\frac{5}{4}) is 0.8 (\frac{4}{5}).

Hope this helped!

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2 years ago
Can anyone help solve this equation?
koban [17]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
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Answer:

V = 6079.04 ft³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

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Whenever a,x,y are positive integers, which of the following expressions is equivalent to x^ay^a
lilavasa [31]

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Step-by-step explanation:

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Hope I get your question~

3 0
2 years ago
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