Please help me!! I have been stuck for hours

Please Help Me!! I Have Been Stuck For Hours

Answers

Answer 1

Answer:

The optimum price to sell the app is $2.55

Step-by-step explanation:

Modeling With Functions

The equation of the demand for the app store is given by

U=10000-2000P

Where U is the number of units sold and P is the price for each unit.

a.

The money from sales (Revenue) is U times the price of each unit, so

[tex]S=U.P[/tex]

Using the equation above

[tex]S=(10000-2000P).P=10000P-2000P^2[/tex]

b. The upfront costs function is given by

[tex]C=2000+0.1U[/tex]

Again, we use the equation for U

[tex]C=2000+0.1(10000-2000P)[/tex]

[tex]C=2000+1000-200P[/tex]

[tex]C=3000-200P[/tex]

c.

The profit is the sales minus the cost

[tex]Profic=S-C=10000P-2000P^2-(3000-200P)[/tex]

[tex]Profit=10000P-2000P^2-3000+200P[/tex]

[tex]Profit=-2000P^2+10200P-3000[/tex]

d.

The vertex of a quadratic function shown as

[tex]f(x)=ax^2+bx+c[/tex]

has an x-coordinate equal to

[tex]\displaystyle x=-\frac{b}{2a}[/tex]

The optimum price for selling the app can be found in the vertex of the above equation.

The P-coordinate of the vertex is given by

[tex]\displaystyle x=-\frac{10200}{-4000}=2.55[/tex]

The optimum price to sell the app is $2.55


Related Questions

What conclusion can you make based on the data/results you collect

Answers

Final answer:

To draw a conclusion from collected data, examine the hypothesis compared with the results observed. A careful analysis should lead to generalizations backed by evidence. Presenting and summarizing information thoroughly is vital for conclusions and future inquiries.

Explanation:

To draw a conclusion based on the data collected, one must first analyze the data carefully. For example, in an experiment assessing the number of deformed frogs in a non-polluted pond, the data should be compared to the initial hypothesis. If the data shows a significant number of deformed frogs in pristine conditions, this could imply other factors contributing to deformities besides pollution.

In language use among students, if the evidence suggests particular trends or patterns, you can make generalizations about these observations. If your findings are different from the initial answer in the 'Collect the Data' section, it might be due to various reasons such as experimental error or an incomplete hypothesis. When presenting your findings, it is critical to incorporate all the collected information which solidifies your conclusion.

Lastly, when summarizing information about a person's experience, it's necessary to incorporate all relevant data before settling on a conclusion. Afterward, forming a question for further research can open new avenues for exploration.

help me plzzzzzzzzzz

Answers

Answer:

Step-by-step explanation:

It is D and F because E is separating them. DF

PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!!

X= ___________

Answers

Answer: [tex]x=26[/tex]

Step-by-step explanation:

When parallel lines are cut by a transversal several angles are formed.

A pair of non-adjacent angles located outside the parallel lines and on opposite sides of the transversal are called  "Alternate Exterior angles".

By definition, they are congruent, which means that they have equal measure.

In this case, you can identify that [tex](5x+7)\°[/tex] and [tex](8x-71)\°[/tex] are Altermate Exterior angles.

Then, you can write the following equation:

[tex]5x+7=8x-71[/tex]

Finally, you must solve for "x" in order to find its value. This is:

[tex]7+71=8x-5x\\\\78=3x\\\\x=26[/tex]

crackers contain 12 calories each and cookies contain 52 calories each. if you eat 5 crackers and 2 cookies how many calories have u consumed in all?

Answers

Answer:

You have consumed 164 calories in total

Step-by-step explanation:

12 calories × 5 crackers = 60 calories

52 calories × 2 cookies = 104 calories

104 + 60 = 164 calories in total

12 x 5 is 60
52 x 2 is 104
Now you just add the two

I WILL GIVE BRAINLIEST PLEASE HELP!!!

Answers

A. side AB = 38/3 units B.m∠VYX =77°

Step-by-step explanation:

A.A rhombus has its four sides equal. This means side AB=side CD

Given that AB=5x+1 and CD=2x+8  equate the two sides to find value of x as;

5x+1=2x+8

collect like terms

5x-2x=8-1

3x=7

x=7/3

side AB = 5x+1

AB= 5*7/3 +1

AB=35/3 +1

AB=35/3 +3/3 = 38/3

B.

The diagonals of a rhombus intersect to form 90°

Hence

(3n²-0.75)°=90°

3n²=90°+ 0.75°

3n² =90.75° -----dividing by 3 both sides

n² =90.75°/3 =30.25°

n²=30.25°

n=√30.25°

n=5.5°

so angle Z =90°

and angle ZVW =(9n+2)°

∠ZVW = (9*5.5 +2 )° =51.5°

In a rhombus all four sides are equal, thus side VY = YX.This means triangle VYX is an isosceles triangle.

Hence angle ∠YVZ=∠WVZ =51.5°, and because VYX is an isosceles triangle then ∠YXV =51.5° so

∠VYX= 180°-(51.5°+51.5°)

          =180°-103°=77°

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The two triangles are similar. Solve for x.

Answers

Answer:

Here Two triangles BDE and BAC are similar as mentioned

So, According to Similarity of triangles theorem

BE/BC = DE/AC

4/16= x/20

1/4 = x/20

x= 20/4

x=5

plz help me quick.....................................................

Answers

Answer:

-2

Step-by-step explanation:

The equation is -12/c=6

by solving for c you get,

-12/c=6

Then multiply both sides by the LCM c to get, -12=6c

Divide both sides by 6 to get,

-12/6=6c/6

-2=c

Verification:

-12/-2=6 since when a negative number divides a negative number the answer is a positive value

Sam saves 76 tickets every time he goes to the arcade. He needs a total of 4712 tickets to receive a stuffed bear for his girlfriend. So far, he has earned 456 tickets. How many more times will Sam have to go to the arcade to earn the additional points he needs?

Answers

Answer:

Sam has to 56 times more to the arcade to earn additional points he need.

Step-by-step explanation:

Given:

Number of tickets already earned = 456

Number of tickets saved each time visit at arcade = 76

Total Number of tickets required to buy Stuffed bear = 4712

We need to find number of times he need to go to arcade to earn the additional points.

Solution:

Let Number of times he need to visit arcade be 'x'.

Now we know;

Number of tickets already earned plus Number of tickets saved each time visit at arcade multiplied by Number of times he need to visit arcade equals to Total Number of tickets required.

Framing in equation form we get;

[tex]456+76x = 4712[/tex]

Now Solving the equation we get;

Subtracting both side by 456 we get;

[tex]456+76x=4712-456\\\\76x= 4256[/tex]

Now Dividing both side by 76 we get;

[tex]\frac{76x}{76} = \frac{4256}{76} \\\\x=56[/tex]

Hence, Sam has to 56 times more to the arcade to earn additional points he need.

Mia listed five rational numbers. Then she drew a number line to display and compare them. a. Plot the numbers on the number line -0.5, 7/4, 1.25, 0.75, -9/4

Answers

Answer:

-9.4, -0.5, 0.75, 1.25, 7/4

Step-by-step explanation:

These are the values of all the numbers in order.

Have a good day!!!

Final answer:

To plot the given numbers -0.5, 7/4, 1.25, 0.75, -9/4 on a number line, convert them into decimal form and mark these points on a line between appropriate integers. Hence, the points are -2.25 (between -2 and -3), -0.5 (between 0 and -1), 0.75 (between 0 and 1), and 1.25 and 1.75 (between 1 and 2).

Explanation:

To plot the given numbers -0.5, 7/4, 1.25, 0.75, -9/4 on a number line, we first need to convert them all into the same form. Converting everything into decimals, we have -0.5, 1.75 (which is 7/4), 1.25, 0.75, and -2.25 (which is -9/4).

Start by drawing a straight horizontal line and mark the points for integers. For example, if the numbers range from -3 to +2, mark these integers on your line. Next, find the points that correspond to the decimal numbers. Suppose you've marked the numbers from -3 to 2, your plot would look like the following:

-2.25 (or -9/4; is located between -2 and -3)-0.5 (is located between 0 and -1)0.75 (is located between 0 and 1)1.25 and 1.75 (or 7/4; both are located between 1 and 2)

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write an equation of a line parallel to y = 5x + 4 that passes through (-1, 2)

Answers

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

Step-by-step explanation:

The parallel lines have:

Same slopesDifferent y-intercepts

The form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y = 5x + 4

∴ m = 5 and b = 4

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = 5

- Substitute the value of the slope in the form of the equation

∴ y = 5x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ The parallel line passes through point (-1 , 2)

∴ x = -1 and y = 2

∵ 2 = 5(-1) + b

∴ 2 = -5 + b

- Add 5 to both sides

∴ 7 = b

- Substitute the value of b in the equation

∴ y = 5x + 7

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

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the coordinates of endpoint D in CD are at D (5,5).if the midpoint of the segment is at M(1,_1)what are the coordinates of point C?​

Answers

Answer:

The required points of the given line segment  are ( - 3, - 7 ).

Step-by-step explanation:

Given that the line segment CD whose midpoint M is ( 1, - 1 ) and point D is ( 5, 5 ), then we have to find point C of the line segment CD-

As we know that-

If a line segment AB is with endpoints ([tex]x_{1}, y_{1}[/tex] ) and  ([tex]x_{2}, y_{2}[/tex]  then the mid points C are-  

C = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )

Here,

Let C ( x, y ), D ( 5, 5 ) with midpoint M ( 1, -1 )-

then by the midpoint formula-

( 1, -1 )  = ( [tex]\frac{x+ 5}{2}[/tex] , [tex]\frac{y + 5}{2}[/tex] 

On comparing x coordinate and y coordinate -

We get,

( [tex]\frac{x+ 5}{2}[/tex] = 1  , [tex]\frac{y + 5}{2}[/tex] = -1 )

( x + 5 = 2, y + 5 = - 2 )

( x = 2 - 5,  y = -2 - 5 )

( x = - 3,  y = -7 )

Hence the required points  C are (- 3, - 7 ).

We can also verify by putting these points into Midpoint formula.

im confused for what the question is asking me,can someone explain for me please or help me out in answering the question

Answers

Answer:

It's asking for simplifying expression with the given value.

Step-by-step explanation:

3x^4 - x + 4; x = 3

3(3)^4 - (3) + 4

3(81) - 3 + 4

243 - 3 + 4

243 + 1

244

Answer:

Step-by-step explanation:

2) 3x⁴ - 25x³ + 27 =   3(2)⁴ - 25(2)³ + 27  = 3*16 - 25*8  +27 = 48 - 200 + 27

= -125

3) 20s⁴ + 24s³ + 4s = 20(1)⁴ + 24(1)³ + 4(1)

= 20 + 24 + 4 = 48

4) 6m⁴ - 4m +20 =  6(4)⁴ - 4(4) +20

= 6*256 - 16 + 20= 1536 - 16 + 20

=1540

5) - 7p⁴ - p + 9 = -7(-2)⁴ - (-2) +9 = -7*16 + 2 +9 = -112 + 2 + 9 = - 101

6) 6a⁷ - a³ + a = 6(-1)⁷ - (-1)³ + (-1) = 6*(-1) - (-1) - 1 = -6 + 1 - 1 = -6

Justin has a rectangular garden measuring 10ft by 16ft that he wants to split diagonally from corner to corner using a fence. How long should the fence be? Round your answer to the tenth

Answers

Answer:

The fence is 18.9 ft long.

Step-by-step explanation:

If you were to create a diagonal line from corner to corner with a square that is 10x16ft, you would have a triangle with 2 known sides and an unknown value. In this case, because you are making a 90° triangle, you can use Pythagorean Theorem:

a^{2} + b^{2} = c^{2}

by plugging in the two values given (10 and 16):

10^{2} + 16^{2} = c^{2}

solve

100 + 256 = c^{2}

356 = c^{2}

√356 = c

18.9 = c

The length of the fence that Justin needs to split the garden diagonally is approximately 18.9 feet (rounded to the tenth of a foot).

To split the rectangular garden diagonally using a fence, you would be creating two right triangles with the fence as the hypotenuse. You can use the Pythagorean Theorem to find the length of the fence.

The Pythagorean Theorem states: [tex]\(c^2 = a^2 + b^2\)[/tex], where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

In this case, the rectangular garden has dimensions of 10 feet and 16 feet, so a = 10 and b = 16. Let c be the length of the fence.

Now, use the Pythagorean Theorem to find c:

[tex]\[c^2 = 10^2 + 16^2\][/tex]

[tex]\[c^2 = 100 + 256\][/tex]

[tex]\[c^2 = 356\][/tex]

Now, take the square root of both sides to find c:

[tex]\[c = \sqrt{356} \approx 18.9\text{ feet}\][/tex]

So, the length of the fence that Justin needs to split the garden diagonally is approximately 18.9 feet (rounded to the tenth of a foot).

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Ben, Tim, and Sam have to do a certain job. Ben can finish the job in 5 hours. Tim can finish the job in 6 hours. Sam can finish the job in x hours. The three of them can finish the job in 2 hours if they work together. Find x.

Answers

x is 7.5 hours

Step-by-step explanation:

Ben, Tim, and Sam have to do a certain job

Ben can finish the job in 5 hoursTim can finish the job in 6 hoursSam can finish the job in x hoursThe three of them can finish the job in 2 hours if they work together

We need to find x

∵ Ben can finish the job in 5 hours

∴ The rate of Ben = [tex]\frac{1}{5}[/tex]

∵ Tim can finish the job in 6 hours

∴ The rate of Tim = [tex]\frac{1}{6}[/tex]

∵ Sam can finish the job in x hours

∴ The rate of Sam = [tex]\frac{1}{x}[/tex]

They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2

∵ They can finish the job in 2 hours if they work together

∴ [tex]\frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}[/tex]

To add the fractions find the LCM for all denominators to make all fractions with same denominators

∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,

- Divide it by each denominator to find the new numerators

∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30

- Change all the denominators to 30 x and then write the new

   numerators of each fraction

∴ [tex]\frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}[/tex]

Add the numerators and put the sum over 30 x

∵ [tex]\frac{11x+30}{30x}=\frac{1}{2}[/tex]

- By using cross multiplication

∴ 2(11 x + 30) = 1(30 x)

- Simplify the both sides

∴ 22 x + 60 = 30 x

- Subtract 22 x from both sides

∴ 60 = 8 x

- Divide both sides by 8

∴ 7.5 = x

∴ The value of x is 7.5 hours

x is 7.5 hours

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Plz help: You have asked your parents if you can have some money to decorate your bedroom for Christmas. You want to put up a little Christmas tree and some ornaments and some lights. They give you $10. You go to the store and find an incredible deal. You buy a tiny fake tree, some lights and a box of ornaments. You pay with the 10$ your parents gave you and the cashier gives you back three bills of the same denomination and two coins in change. (you receive no dollar coins and no half-dollars). How much did you spend? There are 10 possible answers

1. amount spent:____________ Change given (bills/coins):_________

Answers

Answer: ALL THE AMOUNT SPEND ARE 3 1$ bills

1. Amount spent: 6.98

Change:  2- penny

2. Amount Spent: 6.94

Change:   Penny  Nickel

3. Amount Spent: 6.9

Change: 2 Nickels

4. Amount Spent: 6.89

Change: Penny, Dime

5. Amount Spent: 6.85

Change: Nickel Dime

6. Amount Spent: 6.74

Change: Penny Quarter

7. Amount Spent: 6.50

Change: 2 Quarters

8. Amount Spent: 6.80

Change: Nickel Nickel

9. Amount Spent: 6.70

Change: Quarter Dime

10. Amount Spent: 6.65

Change: Quarter Nickel

Step-by-step explanation:

Pweeeese gimme brainliest answer

Final answer:

To find out how much you spent, subtract the change given from the amount your parents gave you.

Explanation:

To find out how much you spent, you need to subtract the change given from the amount your parents gave you. Since the cashier gave you three bills and two coins as change, the total value of the change given is equal to the amount you spent. Since you received no dollar coins and no half-dollars, the change given consists of only bills and coins of smaller denominations. Therefore, the amount you spent is equal to the value of the change given.

Harris is building a deck around his pool. His contractor charges $525 for labor plus an additional $4.75 per square foot for materials. Formulate a function that can be used to determine the cost, in dollars, for a deck with an area of x square feet.

Answers

Answer: 4.75x + 525

Step-by-step explanation:

4.75 times x (the square feet) plus 525

I need help !!!!!! Please

Answers

Answer:

See explanation

Step-by-step explanation:

         Statement                Reason

1. [tex]\angle M\cong \angle X[/tex]      - Given

2. [tex]\angle N\cong \angle Y[/tex]      - Given

3. [tex]\overline{YO}\cong \overline{NZ}[/tex]    -  Given

4. [tex]\overline{OZ}\cong \overline{OZ}[/tex]    -  Reflexive property

5. [tex]YO=ZN[/tex]     - Definition of congruent segments

6. [tex]YZ=YO+OZ[/tex]    - Segment addition postulate

7. [tex]ON=ZN+OZ[/tex]    - Segment addition postulate

8. [tex]YZ=ZN+OZ[/tex]     - Substitution property

9. [tex]YZ=ON[/tex]     - Substitution property

10. [tex]\triangle MNO\cong \triangle XYZ[/tex]     - AAS postulate

Answer:

What is your gram?

Step-by-step explanation:

38)
A math teacher wants to make a test containing 50 easy questions and 20 hard questions. Each easy question is allowed 30
seconds and each hard question is allowed 1 minute 30 seconds to complete. How many minutes should the teacher allow for the
whole test?

Answers

Answer:

Maximum time the teacher should allow for the whole test should be = 55 minutes

Step-by-step explanation:

Number of easy questions in the test = 50

Number of hard questions in the test = 20

Time for each easy question = 30 seconds = [tex]30\ sec\times\frac{1\ min}{60 sec}=0.5\ min[/tex]    

[As 1 minute = 60 seconds]

Time for each hard question = 1 minute 30 seconds = [tex]1\ min+(30\ sec\times\frac{1\ min}{60 sec})=1\ min+0.5\ min=1.5\ min[/tex]

Using unitary method to find duration of whole test.

If 1 easy question takes = 0.5 minutes

Then, 50 easy questions will take = [tex]50\times 0.5\ min[/tex] = 25 minutes

If 1 hard question takes = 1.5 minutes

Then, 20 hard questions will take = [tex]20\times 1.5\ min[/tex] = 30 minutes

Total time for the test will be = [tex]25\ min+30\ min[/tex] = 55 minutes

Alex is going to the carnival with his friends. His mom gave him $45 to spend, If admission to the fair was
$7, and each ride costs $1.50, write an inequality to show how many rides he can ride. What is the
maximum number of rides he can go on?
Solution Set:
Max # of Rides:

Answers

Maximum number of rides Alex can go is 23

Solution:

Given that Alex mom gave him $ 45 to spend

Admission to the fair was  $ 7, and each ride costs $1.50

From given question,

The amount of money spent on admission to the fair and on a number of rides which each cost $ 1.50, must be at most $ 45

"At most $ 45" means $ 45 exactly or less

Let "x" be the number of rides Alex takes up

[tex]7 + 1.50 (x) \leq 45[/tex]

[tex]1.50x + 7 \leq 45[/tex]

This is the required inequality

To find the maximum number of possible rides, solve for  x

[tex]1.50x + 7 \leq 45\\\\1.50x\leq 45 - 7\\\\1.50x\leq 38\\\\x \leq 25.33[/tex]

Thus maximum number of rides he can go is 23

What is 12% of 95? I keep getting 11.4

Answers

Hey!

I'm also getting 11.4, do you think you're wrong or is it saying so? I have also calculated the answer 11.4.

I believe you aren't wrong, but we will make sure.

12 Divided by 100 times 95, you get 11.4, I believe you're correct!

Please give me any updates and let me know if you need any extra help.

A student is solving a system of equations by substitution and comes up with the solution 3=3. Assuming that he solved the problem correctly, which of the following can be said about this system of equations?

A) The system has exactly 1 solution.
B) The system has exactly 2 solutions.
C) The system has infinitely many solutions.
D) The system has no solution.

HELLP MEEEEE PLZZZZ

Answers

Answer:

a

Step-by-step explanation:

• Solve using the quadratic formula
2x2 + 11x +15= 0

Answers

Answer:

x=-5/2, -3

Step-by-step explanation:

2x^2+11x+15=0

factor out the trinomial

(2x+5)(x+3)=0

zero property,

2x+5=0, x+3=0

2x=0-5=-5, x=-5/2

x=0-3=-3

How you can identify a Linear A linear non proportional relationship from a table

Answers

Answer:

Step-by-step explanation:

Put the equation in the form y = mx + b.

Plot the y-intercept, (0,b).

Use the slope to find another point on the line.

Connect the two points in a straight line.

a film canister in the shape of a cylinder has a height of 8 centimeters and a volume of the film canister. write an equation for the volume of the film canister.

Answers

Answer:

Part a) The equation for the volume of the film canister is

[tex]32\pi=\pi r^{2}(8)[/tex]

Part b) The radius of the film canister is [tex]2\ cm[/tex]

Step-by-step explanation:

The complete question is

A film canister in the shape of a cylinder has a height of  8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius of the circular base

h is the height of the cylinder

we have

[tex]V=32\pi\ cm^3[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

[tex]32\pi=\pi r^{2}(8)[/tex]

[tex]32\pi=8\pi r^{2}[/tex]

Simplify

Divide by 8π both sides

[tex]4=r^{2}[/tex]

square root both sides

[tex]r=2\ cm[/tex]

The equation for the volume of the film canister is V = 3.142 × r² × 8.

Use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height.

Substitute the given values into the formula to calculate the volume.

For a given height of 8 centimetres, the volume formula becomes V = 3.142 × r² × 8.

3a²b ÷ 2ab what is the result ?​

Answers

Answer:3/2a

Step-by-step explanation:

Answer:

3 a /2

Step-by-step explanation:

3 a² b ÷ 2 a b

3 a / 2

The function A(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 12.579
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the othef base?

Answers

Answer:

[tex]B(a)=\frac{a}{6}-9[/tex]

Step-by-step explanation:

see the attached figure , to better understand the problem

we have

[tex]A(b)=12(\frac{b+9}{2})[/tex]

where

A(b) ---> is the trapezoid's area

b ---> is the other base value

Solve the equation for b

That means ----> isolate the variable b

Divide 12 by 2 right side

[tex]A=6(b+9)[/tex]

Divide by 6 both sides

[tex]\frac{A}{6}=b+9[/tex]

subtract 9 both sides

[tex]\frac{A}{6}-9=b[/tex]

Rewrite

[tex]b=\frac{A}{6}-9[/tex]

Convert to function notation

[tex]B(a)=\frac{a}{6}-9[/tex]

Final answer:

The inverse function for the area of a trapezoid with one base of 9 and height of 12 is B(a) = a/6 - 9, which gives the length of the other base when provided with the area of the trapezoid.

Explanation:

The question revolves around finding the inverse function for the function that represents the area of a trapezoid. Given the area function A(b) = 12.579 for a trapezoid with a height of 12 and one base of length 9, we seek the function B(a) which provides the length of the other base when given the trapezoid's area. To derive this, recall that the area of a trapezoid with bases b and c and height h is given by A = (1/2)(b+c)h. Here, b is 9 and h is 12. Hence, A(b) = (1/2)(9+b)(12) = (9+b)(6).

To find B(a), we express b in terms of A: (9+b)(6) = A → b = A/6 - 9. The inverse function is B(a) = a/6 - 9.

100 POINTS PLEASE HELP (x^3 − 11x^2+ 22x + 40) ÷ (x − 5) Please solve this equation using the synthetic division method and show all steps

Answers

Answer:

[tex](x^3-11x^2+ 22x + 40)\div (x-5)=(x^2-6x-8)[/tex]

Step-by-step explanation:

When dividing [tex](x^3-11x^2+ 22x + 40)[/tex] by [tex](x-5),[/tex]

1. Multiply [tex](x-5)[/tex] by [tex]x^2[/tex] and subtract the result from [tex](x^3-11x^2+ 22x + 40)[/tex] to eliminate [tex]x^3:[/tex]

[tex](x^3-11x^2+ 22x + 40)-x^2(x-5)\\ \\=x^3-11x^2+22x+40-x^2+5x^2\\ \\=-6x^2+22x+40[/tex]

2. Multiply [tex](x-5)[/tex] by [tex]-6x[/tex] and subtract the result from [tex]-6x^2+22x+40[/tex] to eliminate [tex]-6x^2:[/tex]

[tex]-6x^2+22x+40-(-6x)(x-5)\\ \\=-6x^2+22x+40+6x^2-30x\\ \\=-8x+40[/tex]

3. Multiply [tex](x-5)[/tex] by [tex]-8[/tex] and subtract the result from [tex]-8x+40[/tex] to eliminate [tex]-8x:[/tex]

[tex]-8x+40-(-8)(x-5)\\ \\=-8x+40+8x-40\\ \\=0[/tex]

So,

[tex](x^3-11x^2+ 22x + 40)\div (x-5)=(x^2-6x-8)[/tex]

factor 3x squared -12x -36

Answers

Answer:

3x² - 12x - 36

= 3(x - 6)(x + 2)

Step-by-step explanation:

3x² - 12x - 36      Find any common factor. All terms are divisible by 3.

= 3(x² - 4x - 12)    Find two numbers that sum to -4 and whose product is -12. Replace -4 with these two numbers.

= 3(x² - 6x + 2x - 12)   Group the terms splitting from the middle

= 3( (x² - 6x) + (2x - 12) )   Find the common factor in each group.

= 3( x(x - 6) + 2(x - 6) )      The groups have a common factor (x - 6).

= 3( (x - 6)(x + 2) )           Remove the extra brackets

= 3(x - 6)(x + 2)             Fully factored

Quaker Oatmeal is a very popular breakfast cereal. If Susan wrapped the entire container without any overlapping paper, what is the minimum amount of paper she will need to wrap the entire container

11cm tall
with a width of 6cm

Answers

263.76 cm is the minimum amount of paper she will need to wrap the entire container.

Step-by-step explanation:

As we know that the equation for surface area of a cylinder,

Surface area of cylinder =  [tex]2\pi r^{2}+2 \pi r h[/tex]

Where,

r - the radius of the cylinder. Here given diameter (D) as 6. So,

          [tex]r=\frac{D}{2}=\frac{6}{2}=3 \mathrm{cm}[/tex]

h - the height of the cylinder (given as 11 cm). The value for pi = 3.14. Now, calculate the surface area of the cylinder as

                     [tex]A=2(3.14)(3)^{2}+2(3.14)(3)(11)[/tex]

                            A = 56.52+ 207.24 = 263.76 cm

What is
[tex] |x - 4| - 5 = 3(x - 1)[/tex]

Answers

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x-4|=\left\{\begin{array}{ccc}x-4&for&x-4\geq0\to x\geq4\\-(x-4)&for&x<4\end{array}\right[/tex]

[tex](1)\ x<4\\\\-(x-4)-5=3(x-1)\qquad\text{use the distributivep property}\\\\-x-(-4)-5=3x+(3)(-1)\\\\-x+4-5=3x-3\qquad\text{combine like terms}\\\\-x+(4-5)=3x-3\\\\-x-1=3x-3\qquad\text{add 1 to both sides}\\\\-x-1+1=3x-3+1\\\\-x=3x-2\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-2\\\\-4x=-2\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-2}{-4}\\\\x=\dfrac{1}{2}\in(1)[/tex]

[tex](2)\ x\geq4\\\\x-4-5=3(x-1)\\\\x+(-4-5)=3x-3\\\\x-9=3x-3\qquad\text{add 9 to both sides}\\\\x-9+9=3x-3+9\\\\x=3x+6\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\x-3x=3x-3x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3\notin(2)[/tex]

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