The function f(x) = −x^2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games sold and f(x) is the amount of profit.Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answers

Answer 1

Answer: f(x) = −x^2 + 48x − 432

Part A

Find the zeros:

−x^2 + 48x − 432 = 0

x^2 - 48x + 432 = 0

Factor

(x - 36 ) (x - 12 )=0

Two solutions: x = 36 and x = 12

The vertex is in x = (36 +12 )/ 2 = 24

f(24) = -(24)^2 + 48(24) − 432 = 144

The vertex is (24, 144).

Given that the coefficient of x^2 is negative, the parabole opens downward, that mean that the vertex is a maximum value.

In the context of the problem that means that the maximum profit is 144 and is obtainded when the number of games sold is 24.

Part B.

The x-intercepts are the values of x when y=0. Which we calculated above.

They are x = 24 and x = 36.

Those values are the number of games for which the profit is zero.

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Solve for f is h=2f/m+1

Answers

h=2f/m+1
subtract one from both sides
h-1=2f/m
multiply m to both sides
m*h-1=2f
divide 2 both sides
mh-1/2=F
(the whole left side of the equation is divided by 2 i just cant do it on the computer)

Use the diagram to answer the question. Parallel lines a and b are crossed by transversal t to create 8 angles. Clockwise from top left, the angles are blank, blank, 2, 1; 3, 4, 6, 5. If m Angle1 = 45°, which other angles have a measure of 45°? Check all that apply.

Answers

Answer: angle 4 and angle 5

Answer:

Step-by-step explanation:

Which ratio forms a proportion with 16/20

Answers

Answer:

4/5 forms a proportion with 16/20.

Step-by-step explanation:

We are given an rational number as 16/20.

we have to find another rational number which is equivalent to it.

as both 16 and 20 are multiple of 4 we could also represent the ratio 16/20 as:

$(16)/(20)=(4 * 4)/(4*5)$

we cancel 4 on both the numerator and denominator to get $(4)/(5)$ .

Hence, the ratio $(4)/(5)$ is proportion with $(16)/(20)$ .

4/5 is equivalent to the fraction 16/20

I need help solving x^2+3xy-y^2=12 and x^2-y^2=-12

Answers

$substitute:x^2-y^2=-12\ to\ x^2+3xy-y^2=12\n\n3xy-12=12\n3xy=12+12\n3xy=24\ \ \ \ \ /:3\nxy=8\to x=(8)/(y)\n\nsubstitute\ to\ x^2-y^2=-12\n\n\left((8)/(y)\right)^2-y^2=-12\n\n(64)/(y^2)=y^2-12$

$(64)/(y^2)=(y^2-12)/(1)\n\ny^2(y^2-12)=64\n\ny^4-12y^2-64=0\n\nsubstitute:y^2=t > 0\n\nt^2-12t-64=0$

$a=1;\ b=-12;\ c=-64\n\Delta=b^2-4ac\to\Delta=(-12)^2-4\cdot1\cdot(-64)=144+256=400\n\nt_1=(-b-\sqrt\Delta)/(2a);\ t_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(400)=20\n\nt_1=(12-20)/(2\cdot1)=(-8)/(2)=-4 < 0;\ t_2=(12+20)/(2\cdot1)=(32)/(2)=16\n\ny^2=16\Rightarrow y=\pm√(16)\Rightarrow y=-4\ or\ y=4\n\nx=(8)/(-4)=-2\ or\ x=(8)/(4)=2\n\nSolution:x=-2\ and\ y=-4\ or\ x=2\ and\ y=4$

What mixed number is 3/8 of 100

Answers

3/8 0f 100
100 / 8 = 12.5
Now, let's multiply this by 3 to be able to get the value
=> 12.5 * 3 = 37.5 is the value of 3/8 of 100.
This is a mixed number because its a combination of whole and decimal numbers.

The mixed number that represents 3/8 of 100 is 37 1/2.

To find the mixed number that represents 3/8 of 100, we need to divide 100 by 8 and then multiply the result by 3. This will give us the fractionalpart of the mixed number.

First, let's calculate 100 divided by 8:

100 ÷ 8 = 12.5

Next, we multiply the result by 3 to find 3/8 of 100:

12.5 × 3 = 37.5

The fractional part of the mixed number is 3/8 of 100, which is 37.5.

Now, let's convert this fractional part into a mixed number. Since the fractional part is 37.5, we know that the whole number part of the mixed number is 37. The fractional part can be represented as 5/10 or 1/2 because 5 is half of 10.

Therefore, the mixed number that represents 3/8 of 100 is 37 1/2.

Learn more about mixed number click;

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(02.02 HC)Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week.

Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points)

Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points)

Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? (4 points)

Answers

A) 6x=W
B)(6 x 40) + 9y = s
240 + 9y = s
C) 240 +9y = 330
9y = 90
y=10

Andrew worked 40 hours plus 10 hours of overtime.
He worked a total of 50 hours

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