The function f(x) = −x2 + 60x − 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired. Determine the vertex, and explain what it means in the context of the problem. (30, 784); The vertex represents the maximum profit.
(30, 784); The vertex represents the minimum profit.
(2, 58); The vertex represents the maximum profit.
(2, 58); The vertex represents the minimum profit.

Answers

Answer 1

Answer:

Even tho the answer is not up there but its

(30, 784); The vertex represents the maximum profit.

Step-by-step explanation:

....

Answer 2

For the quadratic equation f(x) = -x^2 + 60x - 116, the vertex is (30, 784), and it is a maximum.

How to get the vertex?

For a general quadratic equation:

y = a*x^2 + b*x + c

The vertex is at the x-value:

h = -b/2a

To get the y-value, we evaluate the quadratic equation in h.

In our case, we have:

y = -x^2 + 60x - 116

Then:

h = -60/(2*-1) = 30

To get the y-value of the vertex, we evaluate in x = 30.

y = -(30)^2 + 60*30 - 116 = 784

And, as you can see, the leading coefficient of the quadratic equation is negative. This means that the arms open downwards, so the vertex is a maximum.

Then, concluding, the vertex is (30, 784), and it is a maximum.

If you want to learn more about quadratic equations, you can read:

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Related Questions

Devora tested two engines. As each engine's rotation got faster, its temperature increased at a constant rate.

The first engine's temperature (in degrees Celsius) as a function of its rotation speed (in cycles per second) is given by the following table of values:

The Table is for the first engine below
For the second engine, the graph is below

The temperature of which engine increased more for each increase of 1 cycles per second?

Choose 1 answer:


(Choice A)

A

The first engine


(Choice B)

B

The second engine


(Choice C)

C

The temperatures of both engines increased the same


Which engine was hotter when it rotated at 20 cycles per second?

Choose 1 answer:


(Choice A)

A

The first engine


(Choice B)

B

The second engine


(Choice C)

C

Both engines were equally hot

Answers

Final answer:

To compare the rates of temperature increase for the two engines, you can look at the slopes of their temperature vs. rotation speed graphs. To determine which engine was hotter at a rotation speed of 20 cycles per second, you can compare the corresponding temperature values on the graphs.

Explanation:

The question asks which engine's temperature increases more for each increase of 1 cycle per second. To determine this, we need to compare the rates of change of temperature for both engines. The rate of change of temperature for the first engine can be determined by finding the slope of the temperature vs. rotation speed graph. From the graph, it can be seen that the slope of the line connecting two points on the graph represents the rate of change of temperature per unit increase in rotation speed. By comparing the slopes of the two graphs, we can determine which engine's temperature increases more for each increase of 1 cycle per second.

To determine which engine was hotter when it rotated at 20 cycles per second, we can look at the corresponding temperature values on the graph. By finding the temperature value for each engine when the rotation speed is 20 cycles per second, we can compare the two temperatures to determine which engine was hotter.

Describe this scatter plot

Answers

Answer:

It is a negative correlation there is one outlier, it is going from the top left to the bottom right. a line could be drawn through it. it could be linear but i would  say non linear.

Step-by-step explanation:

Answer:

Negative correlation

Step-by-step explanation:

The trend shown by the data points appear to be downward sloping, indicating negative correlation between the variables

answer needed quick
is it
supplementary
vertical
complementary
adjacent

Answers

Hey!!

They are adjacent angles.

Both angles have common side and vertex.

Hope it will help u...

Adjacent
Explanation:adjacent angles are angle that have a common side and vertex

What are the soulutions to m^2-9=0

Answers

Answer:

m= 3, -3

Step-by-step explanation:

Hope this helps!

Answer : m=3 or m=-3

If c – 8 is an odd integer, which of the following could be the value of c?

Answers

Answer:

Since you didn't give me any choices I can tell you that c is ANY ODD NUMBER THAT EXISTS.

Step-by-step explanation:

im smart

Chris says that 3/4 is halfway between 0.5 and 100%. is he correct​

Answers

Answer:

Yes!

Step-by-step explanation:

0.5 is half, and 1.00 is whole so 3/4 would be correct because it is in between 0.5 and 1.00

Yes, Chris says that 3/4 is halfway between 0.5 and 100%.

What is an inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Chris says that 3/4 is halfway between 0.5 and 100%.

Midway of 0.5 and 1 is,

(1 + 0.5)/2 = 0.75

100% as a decimal is 1.0.

That means,

3/4 = 0.75.

0.5 < 0.75 < 1

Therefore, Chris is correct.

To learn more about the inequality;

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regina invests$12,600 in an account interest, 3,2% annual continuously .what is the value of the account after 12years ?

Answers

Answer: 4,838.40

Step-by-step explanation: 12,600* 3.2%*12

(PLEASE HELP FASTT I WILL MARK YOU BRAINLY ) Based on the information in the table, is the cost of the apples proportional to the
weight of apples?
ponds of apples:
2
3
4
5
cost of apples
$3.76
$5.64
$7.52
$9.40

yes or no?

Answers

Answer:

Yes

Step-by-step explanation:

Each apple costs 1.88

So 2 apples costs 3.76

And 3 apples costs 5.64, and so on

Answer:

i thank no cause see the price  should go down not up

Step-by-step explanation:

The retail price of red delicious apples was around 1.32 U.S. dollars per pound in the United States in 2017, up from about 0.82 U.S. dollars per pound in 2000.Jan 31, 2020

The probability that an egg on a production line is cracked is 0.01. Two eggs are selected at random from the production line. Find the probability that exactly one of the eggs is cracked. Write the entire decimal answer.

Answers

Answer:

Probability that exactly one of the eggs is cracked is 0.0198.

Step-by-step explanation:

We are given that the probability that an egg on a production line is cracked is 0.01.

Two eggs are selected at random from the production line.

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]

where, n = number trials (samples) taken = 2 eggs

           r = number of success = exactly one

           p = probability of success which in our question is probability that

                 an egg on a production line is cracked i.e; p = 0.01

Let X = Number of eggs on a production line that is cracked

So, X ~ Binom(n = 2, p = 0.01)

Now, probability that exactly one of the eggs is cracked is given by = P(X = 1)

                P(X = 1)  =  [tex]\binom{2}{1} \times 0.01^{1} \times (1-0.01)^{2-1}[/tex]

                               =  [tex]2 \times 0.01 \times (0.99)^{1}[/tex]

                               =  0.0198

Therefore, the probability that exactly one of the eggs is cracked is 0.0198.

A 128-ounce jug of milk costs $3.20, and a 64-ounce jug of milk costs $2.24. What is the difference in cost per ounce between the larger and the smaller jugs of milk?

brainiest

Answers

Answer:

The 64 ounce jug of milk costs $0.010 more per ounce than the 128 ounce jug of milk/

Step-by-step explanation:

3.20/128=$0.025 per ounce jug of milk

2.24/64=$0.035 per ounce jug of milk

0.035 - 0.025 = .010

What is the y-intercept of y= -3x

Answers

Answer:

there is no y intercept. if there was it would be at the end of -3x

The y intercept would be -3x that is what y equals

1) find x -------> 3x-8

2) find y -------> (7y+6)

3) find z -------->5z+9

PLEASE HELP ME!!

Answers

Answer: x=4

y=2

z=-11

Step-by-step explanation:

find like terms

A circle has the equation x2+12y+22x+y2−167=0.
What is the equation of the circle in standard form?

(x−11)2+(y−6)2=324

(x+11)2+(y+6)2=184

(x−11)2+(y−6)2=184

(x+11)2+(y+6)2=324

Answers

Answer:

[tex](x + 11)2 + (y + 6)2 = 184[/tex]

Answer: The answer would be (x+11)2+(y+6)2=324

Step-by-step explanation: I just got it right on my test :)

HELP I WILL GIVE U A FREE HUG!!!!!!

Answers

Answer:

the screen it very tight( squished together)

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2x²-12x-32

=2(x²-6x+9-9)-32

=2(x-3)²-18-32

=2(x-3)²-50

so vertex is (3,-50)

again 2x²-12x-32=0

or  x²-6x-16=0

or x²-8x+2x-16=0

or x(x-8)+2(x-8)=0

(x-8)(x+2)=0

x=8,-2

8>-2

d=8

e=-2

f=3

The radius of the circle F is 19cm.
What is the length of it's diameter?

A) 9.5cm
B) 19cm
C) 21cm
D) 38cm

Answers

Answer:

38.(D)

Step-by-step explanation:

Diameter=2R

Which gives u 19+19= 38

Answer:

38

Step-by-step explanation:

A circle's diameter is 2x the radius. (2r=d)

2x19=38

Please rate thanks and mark brainliest ! hope this helps :)

Help me out please..

Answers

Answer:

[tex]g(x) = \frac{3}{4} {x}^{2} [/tex]

There are 1000 tickets. Of these, 75 are winning tickets. How likely are you to win the lottery if you take one ticket?

Answers

Answer:

7.5%

Step-by-step explanation:

75 is 7.5% of 1000

Hope this helps!

Consider the following sets: U = {points on the coordinate plane} A = {solutions to the equation y = 2x + 5} B = {points on the line y = mx} For what value of m does A ∩ B = ∅?

Answers

Answer:

m=2

Step-by-step explanation:

4x^2+16x-4=?

A. 2x(2x^2+8x-2)
B. 2(2x^2+8-2)
C. 4x(x^2+4x-1)
D. 4(x^2+4x-1)

Answers

Answer:

What was the most important thing you learned during AlcoholEdu?

Step-by-step explanation:

How many seconds are in 35 minutes

Answers

Answer:

2100 seconds

Step-by-step explanation:

60x35=2100

Answer:

2100 seconds.

Step-by-step explanation:

There are 60 seconds in 1 minute.

Multiply 60 with 35:

60 x 35 = 2100

2100 seconds is your answer.

~

Help please? It due today and I don’t understand

Answers

Answer:

times it

Step-by-step explanation:

So you just have to twice it

the product of 4 and 1/6 is _

Answers

Answer:

2/3

Step-by-step explanation:

The answer is 252 I don’t even know the acc answer I jus wana say that

Julius needs to determine how much information needs to be given about an isosceles triangle to be able to draw an isosceles triangle. He is looking at six different cases and is trying to determine if that amount of detail will allow him to construct just one isosceles triangle or if it allows for more than one isosceles triangle.

Answers

Final answer:

To uniquely construct an isosceles triangle, you would either need the lengths of two sides and the angle between them, two sides and the angle opposite to one of them, or two angles and any side.

Explanation:

Julius is examining the principles of constructions in geometry. To construct a unique isosceles triangle, certain specific information is needed. An isosceles triangle is a triangle with two sides of equal length, and the angles opposite these sides are of equal measure too.

In general, there are three common cases in which the information given would be enough to construct only one unique isosceles triangle:

Two side lengths and the angle between them (SAS)Two sides and the angle opposite to one of them (SSA)Two angles and any side (AAS)

If other information is given, it may or may not be possible to construct a unique isosceles triangle. For example, given only the lengths of two sides, multiple different isosceles triangles can be made, depending on the size of the included angle.

Learn more about Triangle Constructions here:

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I WILL GIVE BRAINLIEST
Solve the inequality:
8 + 4x ≥ 12

A. x ≥ 1
B. x ≥ 5
C. x ≤ 5
D. x ≤ 1

Answers

Answer:

x ≥ 1

Step-by-step explanation:

8 + 4x ≥ 12

Subtract 8 from each side

8-8 + 4x ≥ 12-8

4x ≥ 4

Divide by 4

4x/4 ≥ 4/4

x ≥ 1

The solution to the inequality 8 + 4x ≥ 12 is x ≥ 1. Therefore, the correct answer is A. x ≥ 1.

Correct option is A.

To solve the inequality 8 + 4x ≥ 12, we need to isolate x. Here's how we do it step by step:Start with the given inequality: 8 + 4x ≥ 12.First, subtract 8 from both sides of the inequality to isolate the term with the variable:8 + 4x - 8 ≥ 12 - 8.Simplify both sides:4x ≥ 4.Now, divide both sides by 4 to solve for x:(4x)/4 ≥ 4/4,x ≥ 1.So, the solution to the inequality is:x ≥ 1.Now, let's match this solution to the given answer choices:A. x ≥ 1 - This matches our solution.B. x ≥ 5 - This is not correct.C. x ≤ 5 - This is not correct.D. x ≤ 1 - This is not correct.The correct answer is A. x ≥ 1.

For more questions on inequality -

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Saturn is 8.867 × 10^8 miles away from the Sun. Uranus is 1.787 × 10^9 miles away from the Sun. Approximately how many times farther is Uranus from the Sun than Saturn is?

Answers

Answer: 0.2 times

Step-by-step explanation:

Is triangle ABC=DCB? Complete the table to prove or disprove this statement

Answers

Answer:

ABC ≅ DCB by SAS

Step-by-step explanation:

1. Segment DB ≅ segment AC because it was given

2. Angle C ≅ angle B because it was given

3. Segment CB ≅ segment CB because of Reflexive Property

4. Triangle ABC ≅ DCB because of SAS (side-angle-side postulate)

Hope I helped and please give me brainliest!

Two different websites offer the same watch for sale. The watch costs $45 on both sites. The site, Watches for Less charges a shipping fee of 4% of the cost of the watch. The site, Tick Tock charges 2.5% of the cost of the watch for shipping. How much less will the total cost of the watch be if purchased from Tick Tock?
Round your answer to the hundredths place.

Answers

Final answer:

The total cost of the watch will be $0.67 less if purchased from Tick Tock.

Explanation:

To find out how much less the total cost of the watch will be if purchased from Tick Tock, we need to calculate the shipping fee for both websites and subtract that amount from the total cost.

For Watches for Less, the shipping fee is 4% of $45, which is $1.80.

For Tick Tock, the shipping fee is 2.5% of $45, which is $1.13.

Therefore, the total cost of the watch from Tick Tock will be $45 - $1.13 = $43.87. The total cost from Watches for Less will be $45 - $1.80 = $43.20.

The difference in the total cost is $43.87 - $43.20 = $0.67.

Therefore, the total cost of the watch will be $0.67 less if purchased from Tick Tock.

Examine the diagram.


Parallel lines a and b are crossed by transversal t to create 8 angles. Clockwise from top left, the angles are blank, 60.75 degrees, blank, blank; 2, 1, blank, blank.


What are the measures of angle 1 and angle 2?


The m Angle1 is degrees.

The m Angle2 is degrees

Answers

Answer:

[tex]m\angle 1 =60.75^\circ \\m\angle 2 =119.25^\circ[/tex]

Step-by-step explanation:

From the diagram:

[tex]m\angle 1 =60.75^\circ $(Corresponding Angles)\\[/tex]

Now Angle 1 and Angle 2 are on a straight line, therefore:

[tex]m\angle 1 +m\angle 2 =180^\circ $(Linear Postulate)\\Since m\angle 1=60.75^\circ\\60.75^\circ +m\angle 2 =180^\circ\\m\angle 2=180^\circ-60.75^\circ\\m\angle 2 =119.25^\circ[/tex]

Answer:   60.75    

               119.25

Step-by-step explanation:

Which statement is true about point Y?

Answers

Answer:C

Step-by-step explanation:


Will mark right answer brainlliest

Answers

-9 19/22 that’s in a mixed number
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