C) the function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles 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? part
b.determine the x-intercepts. what do these values mean in the context of the problem?

Answers

Answer 1

Given the function modeling the profit:
f(x)=-x^2+16x-60

a)a.determine the vertex. what does this calculation mean in the context of the problem?
The vertex form is given by y=(x-h)^2+k, where (h,k) is the vertex:
y=f(x)=-x^2+16x-60
y=x^2-16x+60
c=(-b/2a)^2
b=16
thus
c=(-16/2)^2=64
hence:
y=x^2-16x+64+60-64
y=(x-8)(x-8)-4
y=(x-8)^2-4
hence the vertex form will be:
y=(x-8)^2-4 the vertex is (8,-4)
The vertex represents the highest point of the graph which is the highest daily profits attained.

b] determine the x-intercepts. what do these values mean in the context of the problem?
let y=0 thus
0=−x2 + 16x − 60
factorizing the above we get:
0=x^2-16x+60
0=x^2-6x-10x+60
0=x(x-6)-10(x-6)
thus
x=6 and x=10
thus the x-intercepts are x=6 and x=10, they represent the breakeven point. The minimum number of units they can sell and not make any profit

Related Questions

I got 4/7s + 5/7 But I’m not sure if that’s correct

Answers

Hey there! :)

2/7(2s + 3)

Simplify by by using the rainbow tactic.

(2/7 × 2s) + (2/7 × 3)

Simplify.

**Remember : 2s is the same as 2/1s and 3 is the same as 3/1**

(2/7 × 2/1s) + (2/7 × 3/1)

Simplify.

4/7s + 6/7

~Hope I helped!~

The length of a rectangle is increase by 25%. to keep the area of the rectangle the same, by what percent must the width be decreased

Answers

are there any answer choices

Can someone answer this question for me as well.

The equation tan-1 (9.4/8.2) = x can be used to find the measure of angle LKJ. What is the measure of angler LKJ? Round to the nearest whole degree.

*KL = 7.7 cm, LJ = 8.9 cm*

Answers

This is most likely coming from a triangle where angle x has an opposite side of length 9.4, and an adjacent side of length 8.2, giving rise to the equation
tan(x) = 9.4/8.2
x = (tan^-1)(9.4/8.2)
Simplifying gives:
x = (tan^-1)(1.146)
x = 48.9 degrees.
This is approximately equal to 49 degrees.

the supplement of angle t is 4 times the measure of angle t

Answers

supplementary angles need to equal 180 degrees
one angle = t
the other angle = 4 x t or 4t
so we now have t + 4t = 180

4 + 4t = 5t

so we have 5t = 180

divide both sides by 5:
t = 180 /5
t = 36
so angle t = 36 degrees

the other angle = 4 x 36 = 144 degrees

The price of buying gasoline varies directly with the number of gallons bought.If five gallons of gas cost $17.50,what is the rate of change of this linear equation.

Answers

every 1 gallon is 3.5

Factor the trinomial below.

6x2 – 9x – 6

A. 3(2x + 1)(x – 6)
B. 3(2x + 2)(x – 1)
C. 3(2x + 1)(x – 2)
D. 3(2x + 6)(x – 1)

Answers

For this case we have the following trinomial:
6x2 - 9x - 6
Rewriting we have:
3 (2x2 - 3x - 2)
Factoring we have:
3 (2x + 1) (x-2)
Answer:
The factored expression for this case is given by:
C. 3 (2x + 1) (x - 2)

Answer:

C. 3(2x+1)(x-2)

Step-by-step explanation:

To factor the trinomial 6x² - 9x -6, we will follow the steps below;

First, 3 is common among the three numbers, so we will start by factoring out 3, so that the expression becomes;

3(2x² - 3x - 2)

We will now proceed to factorize; 2x² - 3x - 2

Find two numbers such that its product gives -4 and its sum gives -3.

Such number is -4 and 1

-4 × 1 = -4

-4 + 1 = -3

We will replace -3x by -4x + x in the above expression

2x² - 4x + x - 2

(2x² - 4x) (+x - 2)

In the first parenthesis, 2x is common, so we will factor out 2x while in the second parenthesis 1 is common, so we will factor out 1. Hence;

2x(x - 2) + 1(x-2)

(2x+1)(x-2)

3(2x² - 3x - 2) = 3(2x+1)(x-2)

6x² – 9x – 6 = 3(2x+1)(x-2)

Therefore the factorized form of 6x² – 9x – 6 is 3(2x+1)(x-2)

The surface area of a sphere is 200.96 square centimeters. What is the approximate volume of the sphere?

Answers

The approximate volume of the sphere is 266.19 cubic centimeters.

To find the approximate volume of a sphere from its surface area, we will use the relationship between the surface area and radius of the sphere and then apply the formula for the volume. The surface area (A) of a sphere is given by the formula A = 4πr2, and the volume (V) is given by the formula V = (4/3)πr3. Given that the surface area of the sphere is 200.96 square centimeters, we can solve for the radius (r) first:

A = 4πr2
=> r2 = A / (4π)
=> r2 = 200.96 / (4π)
=> r = √(200.96 / (4π))
=> r ≈ 3.99 cm (after calculating using a calculator)

Now that we have the radius, we can find the volume:

V = (4/3)πr3
=> V = (4/3)π(3.99 cm)3
=> V ≈ 266.19 cm3 (after calculating using a calculator)

Therefore, the approximate volume of the sphere is 266.19 cubic centimeters.

I WAS ONLY ABLE TO SELECT 40 PTS THIS TIME, PLS ANSWER THIS ONE IT HAS THE PICTURE WITH IT.
In the figure, lines a and b are parallel.

Which statements are true?

Select each correct answer.
MORE THAN ONE ANSWER

m∠2=m∠1

m∠2=105°

m∠1=75°

m∠3=m∠1

Answers

Okay so the first one is right.
The second one is wrong.
the third one is right.
The forth one is wrong.

∠1 and 105° are supplementary angles. (supplementary = 180°)

180 - 105 = 75°

∠1 = 75°

∠1 and ∠2 are corresponding angles, and so there measurements will be the same

∠1 = ∠2
∠1 = 75°
∠2 = 75°

105° and ∠3 are same side, and are corresponding angles. Therefore, ∠3 = 105°

m∠1=75°

180° (the measurement of a straight angle).

Subtract the 105° (given) from the straight angle

180 - 105 = 75

m∠1=75°

hope this helps

Which equation in point-slope form contains the points (6, 2) and (2, 4)? A -4=-1/2(x-6) B y – 4 = –2(x – 2) C y-2=-1/2(x-6)

Answers

Hello!

The equation for point-slope form is

y - b = m(x - a)

m is the slope
(a, b) is a point the line passes through

We are looking for a equation that follows this

The answer is C because a point the line goes through is (6, 2)

The answer is C

Hope this helps!

I think that it is Y-2= -1/2 (x-6)

The English Alphabet has 20 letters more than one-fourth the number of letters in the Greek Alphabet. The English Alphabet has 26 letters. Which of the following equations would you use to find the number of letters, g, in the Greek Alphabet?

Answers

English Alphabet = e
Greek Alphabet = g

The English Alphabet has 20 letters more than one-fourth the numbers of letters in the greek alphabet: 1/4g + 20 = e

The English has 26 letters.

Plug in 26 for e

1/4g + 20 = 26

Isolate the g, do the opposite of PEMDAS. Note the equal sign. What you do to one side you do to the other.

Subtract 20 from both sides

1/4g + 20 (-20) = 26 (-20)

1/4g = 26 - 20

1/4g = 4

Multiply 4 to both sides to isolate the g

1/4(4)g = 4(4)

g = 4(4)

g = 16

The Greek Alphabet has 16 letters

hope this helps

What is the trigonometric ratio for cos D?

Answers

Hi there!

The definition of the cosine:
[tex] \cos( \alpha ) = \frac{adjecent}{hypotenuse} [/tex]

When we fill in this formula with the data from the picture, we get the following:
[tex] \cos(d) = \frac{21}{75} = \frac{7}{25} [/tex]

Therefore, the answer is 7 / 25

Assuming a truck container holds 24 cases, how many cases would 6 truck containers hold?

Answers

If you multiply 6 by 24 for you get 144 containers.
6 truck will hold 144 containers in total

Harry needs to paint a cereal box for a school project. What measure should he use to find the total amount of paint he needs to cover the cereal box with paint? area lateral area surface area volume.

1. area
2. lateral area
3. surface area
4. volume

Answers

For this case, the first thing we should do is observe that Harry needs to paint the entire box.
Therefore, he must paint:
Base and roof.
Left and right side.
Front and back side.
The measure you need to know therefore is:
Surface area of the box.
Answer:
He should use to find the total amount of paint I need to cover the cereal box with paint:
3. surface area

Answer: C

Step-by-step explanation:

Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs are: utilities = $100, salary = $2,000, advertising = $0, insurance = $0, interest = $0, rent (cart) = $600, depreciation = $0. what are carla's fixed costs?

Answers

Carla's fixed cot will be given by:
Cost=(cost of beverages)+(salaries)+(utilities)+(rent)
cost=800+2000+100+600
cost=$3500
Thus the total fixed cost was $3500

It is 3500

$2,400 principal earning 2%, compounded annually, after 7 years

Answers

equation i think is 2,400(1+[\[tex] \frac{2}{100} [/tex])nt

so i think the answer is 14 lol i could be wrong i did this so long ago...

Answer:

The answer is 2,765.85 dollars. Thanks.

Step-by-step explanation:

A car wash machine cleaned 20 cars in 50 minuets at this rate how many minutes will it take the machine to clean 1 car

Answers

For this case what we should do is define variables:
x: time in minutes
y: number of clean cars
We then have the following equation:
y = (20/50) x
For 1 car we have:
1 = (20/50) x
Clearing x:
x = 50/20
x = 2.5 minutes
Answer:
It will take the machine to clean 1 car about:
x = 2.5 minutes

Final answer:

The machine will take 2.5 minutes to clean 1 car.

Explanation:

To find the number of minutes it will take the machine to clean 1 car, we can use the concept of ratios. If the machine cleaned 20 cars in 50 minutes, we can set up a ratio:

20 cars / 50 minutes = 1 car / x minutes

Using cross-multiplication, we can solve for x:

20x = 50

x = 50 / 20 = 2.5 minutes

Therefore, it will take the machine 2.5 minutes to clean 1 car.

Calculate the length b to two decimal places A) 890.68 B) 36.99 C) 36 D) 29.84

Answers

the picture in the attached figure
we know that
the law of cosines established that
b² = a² + c² − 2ac cos(B)

in this problem
a=22 units
c=14 units
B=110°

b² = 22² + 14² − 2*22*14*cos(110°)----> b²=890.68------> b=29.84 units

the answer is the option
D) 29.84

There are 9 red gum balls, 5 green gum balls, 8 yellow gum balls, and 8 blue gum balls in a machine. find p(green, then yellow).
a. start fraction 40 over 900 end fraction
b. the term shows 5 over 30.
c. the term shows 8 over 30.
d. start fraction 40 over 870 end fraction

Answers

The correct answer is choice D. To find this you will find the probability of each event happening and then multiply them together.

Green: 5/30
Yellow: 8/29 (you subtract one from the denominator because you already picked a green the first time)

5/30 x 8/29 = 40/870

The correct option is d. [tex]$ \frac{40}{870} $[/tex]

To find the probability of selecting a green gum ball followed by a yellow gum ball, we first calculate the total number of gum balls and then determine the number of ways to select a green gum ball followed by a yellow gum ball.

[tex]\text{Total number of gum balls} = 9 (red) + 5 (green) + 8 (yellow) + 8 (blue) = 30[/tex]

Number of ways to select a green gum ball followed by a yellow gum ball:

There are [tex]5[/tex] green gum balls and [tex]8[/tex] yellow gum balls.

Therefore, the number of ways to select a green gum ball followed by a yellow gum ball is [tex]$5 \times 8 = 40$[/tex]

The probability of selecting a green gum ball followed by a yellow gum ball is the number of ways to select them divided by the total number of gum balls:

[tex]\[ P(\text{green, then yellow}) = \frac{40}{30 \times 29} \][/tex]

[tex]\[ P(\text{green, then yellow}) = \frac{40}{870} \][/tex]

PLease dont answer if you dont know...
Use the Law of Sines to find side "b" of the triangle.

Answers

Using the law of sins:

side a / sin (angle A) = side b / sin(Angle B)

Side a is opposite angle A, so from the picture we know side a = 50, angle A is 58 degrees and angle B is 48 degrees.

replace those values in the formula we get:

50 / sin(58) = b/ sin(48)

so now we can cross multiply the 2 fractions to get:

50 * sin(48) = b*sin(58)

to get b by itself, divide both sides by sin(58) to get:

b = (50*sin(48)) / sin(58)

b = 43.82

You may need to round the answer as needed.

The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. What are the coordinates of the point P on the line segment such that P is the length of the line segment from G?

Answers

The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. Hence the required coordinate point is (9/4, 11/4).

What is the coordinate of the point which divides a line segment in a specified ratio?

Suppose that there is a line segment [tex]\overline{AB}[/tex] such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

where we have:

the coordinate of A is[tex](x_1, y_1)[/tex]

and the coordinate of B is [tex](x_2, y_2)[/tex]

The coordinate point between two points P and G divided between ratios a and b is expressed as;

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

Given the coordinate points F(3, 5) and G(0, –4) divided within the ratio 1:3

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{1(0) + 3(3)}{1+3} , \dfrac{1(-4)+ 3(5)}{1+3} \right)\\\\(x,y) = \left( \dfrac{9}{4} , \dfrac{11}{4} \right)[/tex]

Hence the required coordinate point is (9/4, 11/4).

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For the function y = -2x + 20, what is the output when the input is 50.

Answers

y=-2x+20
Input 50
Y=-2(50)+20
Y=-100+20
y=-80

I hope this helps :) feel free to ask if you need anything cleared up

PLSSSSS HELP :(

Determine whether the following pair of lines are parallel, perpendicular, or neither.

3x + 4y = 7 y = −2 − 34x

Answers

convert each one to slope-intercept form

y = -34x - 2

4y = -3x + 7

y = (-3/4)x + 7/4

if the first equation is meant to b -3/4x - 2 then they are parallel

Explain why the graph shown may be misleading.

Answers

there are 40 compact cars, 4 of 10 each.

there are 30 mid-size, 3 of 10 each.

and there are 20 trucks,

however, in the graph, they all seem to have the same start point and end point, and the mid-size are elongated more than the compacts, and the trucks are much larger than the others above it, almost suggesting the amounts for all are equal somehow for that period.

the amounts must correlate horizontally as they're laid, thus the compacts should be longer than the rest, the mid-size behind it and the trucks half-way of the compacts.

If you don't see the legend, you may think that a truck means more than a compact which, in fact is false. 2 trucks = 20 vehicles, just as 4 compacts = 40 vehicles. Each icon = 10 vehicles no matter what they represent.

WILL GIVE BRAINLIEST
FIND VOLUME
60 is the area of the base

Answers

Hey so yeah this can be a challenging problem, Vol (V) is much easier to solve than surface area (SA), but I'll show you how it's done, my friend.
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3

So now for the hard part... how to calculate the SA of this prism

IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]

means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??

This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).

Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38

Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
.
.
.

now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft

NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2

Answer:

300 ft³

Step-by-step explanation:

Volume = Area of base × height

Volume = 60ft² × 5ft

Volume = 300 ft³

A hyperbola centered at the origin has a vertex at (9, 0) and a focus at (−15, 0).
Which are the equations of the asymptotes?

Answers

Hyperbola equation opening horizontally:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Asymptotes:
[tex]y = \pm \frac{b}{a} x[/tex]

'a' is distance vertex is from center --> a = 9
'c' is distance focus is from center --> c = 15
[tex]a^2 + b^2 = c^2 \\ \\ b^2 = 15^2 - 9^2 = 144 \\ \\ b = 12[/tex]

Asymptotes are:
[tex]y = \pm \frac{12}{9} x = \pm \frac{4}{3} x[/tex]

Answer:

Step-by-step explanation:

A square can be changed into a rectangle by increasing the length of the square by 5 units and increasing the width by 3 units. which expression represents the area of the rectangle in square units?

Answers

Final answer:

The area of the rectangle that was transformed from a square by increasing the length by 5 units and the width by 3 units is given by the expression (a + 5)(a + 3), or when expanded a² + 8a + 15.

Explanation:

Given that the original shape was a square, the length and width of the square are the same. Let's denote this common length as 'a'. When transformed into a rectangle, the length was increased by 5 units and the width increased by 3 units. Therefore, the new length and width of the rectangle are 'a + 5' and 'a + 3' respectively.

The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the rectangle in square units is represented by the expression (a + 5)(a + 3), which when expanded gives a² + 8a + 15.

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Final answer:

The area of a new rectangle formed from a square by increasing the length by 5 units and the width by 3 units is represented by the mathematical expression (side+5) * (side+3) in square units. This equation stems from the basic geometric formula of calculating the area by multiplying the length by the width.

Explanation:

The area of a shape, such as a square or rectangle, is calculated by multiplying its length by its width. In the case of a square, where all sides are equal, the formula for area can be represented as side² or side * side. If we know the side of the square, and it is increased in length by 5 units and width by 3 units, we are essentially creating a rectangle now. The formula for the rectangle area changes to (side+5) * (side+3). So, if you have a square and you increase the length by 5 units and the width by 3 units, the expression that represents the area of the new rectangle in square units would be (side+5) * (side+3). For example, if side of the square was 5 units originally, upon modification, length of rectangle will be [tex]5+5 = 10[/tex] and width will be [tex]5+3 = 8[/tex]. So, area of rectangle becomes [tex]10*8 = 80[/tex] square units.

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Find k if 64 ÷ k = 4

Answers

Hi there! The answer is k = 16.

Let's solve this problem step by step!
[tex]64 \div k = 4[/tex]

Multiply both sides by k.
[tex]64 = 4k[/tex]

Switch sides.
[tex]4k = 64[/tex]

Divide both sides by 4.
[tex]k = \frac{64}{4} = 16[/tex]

~ Hope this helps you!

The circumference of a roll of party streamers is 9 inches. The circumference decreases by 2 inches after you use the streamers to decorate for a graduation party. Find the diameter of the roll after the decrease. Round your answer to the nearest hundredth.

Answers

For that case the new circumference is:
C = 9 - 2
C = 7 inches
By definition, the circumference is:
C = 2 * pi * r
Where,
r: radio
Substituting values:
7 = 2 * pi * r
Clearing the radio:
r = 7 / (2 * pi)
Then, the diameter is:
d = 2 * r
Substituting:
d = 2 * (7 / (2 * pi))
d = 2.228169203
Round to the hundredth:
d = 2.23 inches
Answer:
The diameter of the roll after the decrease is:
d = 2.23 inches

The diameter of the roll of streamers after the circumference decreases to 7 inches is approximately 2.23 inches.

To find the diameter after the circumference decreases, we can use the formula for the circumference of a circle, which is C = πd, where C is the circumference and d is the diameter.

Initial circumference, C₁ = 9 inches.After using some streamers, the new circumference, C₂ = 9 inches - 2 inches = 7 inches.Using the formula C₂ = πd₂, we solve for d₂:
d₂ = C₂ / π
d₂ = 7 / ππ (pi) approximately equals 3.14159.
So, d₂ = 7 / 3.14159 ≈ 2.23 inches.

Therefore, the diameter after the decrease is approximately 2.23 inches.

During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. if the first caller has a chance to win $100, which equation finds the amount the 10th caller receives, if the 10th is the first to answer the question correctly?

Answers

To solve this problem you must apply the proccedure shown below:

1. You have that $50 is added to the prize money each time a caller answers the contest question incorrectly and the first caller has a chance to win $100.

2. Therefore, the amount the 10th caller receives, if the this caller answers the question correctly, is:

x: the amount the 10th caller receives.
y: the number of caller

x=100+50(y-1)

As y=10 (the 10th caller), you have:

x=100+50(10-1)
x=100+50(9)
x=100+450
x=$550

Answer:

a is correct on edege

Step-by-step explanation:

sally is comparing the prices of two window cleaning companies. company A charges $7 per window and ajbadditional $12 as service charges. company B charges $5 per window and an additional $15 as service charges. Part A: write an equation to represent each company’s total charges for cleaning a certain number of windows, for both equations (one for company A and one for company B), define the variable used . Part b: how much would company A AND company B each charge for cleaning 8 windows ?

Very quick please

Answers

part a : company A : 7w+12
Company B: 5w+15

Part B:::
company a would charge $68
and company B would charge $55

Other Questions

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