Calculate the average rate of change of f(x) = 3x2
+ 2x + 1 for 2 ≤ x ≤ 4.

The vοlume οf the prism is 14 cubic feet.

A three-dimensiοnal structure having six rectangular faces is called a prism. It is alsο knοwn as a rectangular cubοid οr a rectangular parallelepiped.

The prism is cοmpletely filled with 1750 cubes that have an edge length οf 1/5 ft. This means that the vοlume οf each cube is \((1/5)^3 = 1/125\) cubic feet.

Tο find the vοlume οf the prism, we can divide the tοtal vοlume οf the cubes by the number οf cubes:

Vοlume οf prism = (Vοlume οf οne cube) x (Number οf cubes)

Vοlume οf prism = (1/125) x 1750

Vοlume οf prism = 14 cubic feet

Therefοre, the vοlume οf the prism is 14 cubic feet.

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Answer:

\( \frac{6}{x} = 7 - 2x \\ 6 = 7x - 2 {x}^{2} \\ 2{x}^{2} - 7x + 6 = 0\)

Answer:

100 ft

Step-by-step explanation:

1 yd = 3 ft

Gena: 12 yd= 36 ft

Alicia: 10 yd and 4 ft= 34 ft

Lyona: about 10 yd= 30 ft

36 + 34 + 30 = 100

Answer: Infinite many solutions

Step-by-step explanation:

Given

5x+3(x-1)=10x-2x-3

Expand Parenthesis

5x+3x-3=10x-2x-3

Combine like terms

8x-3=8x-3

Subtract 8x on both sides

8x-3-8x=8x-3-8x

-3=-3

Add 3 on both sides

-3+3=-3+3

0=0

Any number will work on both sides, therefore, there are infinite solutions

Hope this helps!!: )

Please let me know if you have any questions.

Brand A: 32 Diapers, $8.99: about 28 cents per diaper

Brand B: 50 Diapers, $12.49: about 24 cents per diaper

You divide the amount of diapers by the money.

For example, 32 diapers/$8.99 equals about 28 cents per diaper and 50 diapers/$12.49 equals about 24 cents per diaper.

Brand B is the better deal since you save about 4 cents more.

Answer:

He should have canceled x

Answer:

-4b^3 + 7b - 7

Step-by-step explanation:

We have to look at terms which look like each other, for example 1b and 6b.

We can add and subtract terms which have the same degree of b.

In this question, we can safely add -1 and -6, and also b and 6b,

which gives us (-4b^3 + b - 1 ) + 6b - 6) = -4b^3 + (1+6)b +( -1 - 6) = -4b^3 + 7b - 7

The three remaining terms all have different degrees of b's (respectively 3, 1, 0), so we can't add those up any further, which tells us that this is the right answer.

Answer:

Step-by-step explanation:

Answer: Do you need any help?

(I apologize because I didn’t see your full question before.$

Answer:

The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.

An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.

Answer:

11%

Step-by-step explanation:

the answer is 11 because you need to minus

Given:

We can use the calculator to find the value of the product :

The result will be = 5.623

Answer:

225 hamburgers

Step-by-step explanation:

system of equations:

h + c = 390

c = h-60

use Substitution:

h + h - 60 = 390

2h - 60 = 390

2h = 450

h = 225

Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

Answer:

I don't know "how many pounds total does his idea weights" but the stuff he purchased weights 10 pounds.

Answer:

x = 20

Step-by-step explanation:

-20 = -x

\(\frac{-20}{-1}\) = \(\frac{-x}{-1}\)

Simplify

x = 20

The profit function for a furniture company introducing a new line of lounge chairs is P(x) =\(-8.32x^2 + 1,248x - 36,400\), where x represents the number of chairs to be manufactured and sold.

The problem provides the revenue function and cost function for a furniture company introducing a new line of lounge chairs. To find the profit function, we need to subtract the cost function from the revenue function.

The revenue function R(x) is given as 1,248x - \(8.32x^2\), where x represents the number of chairs manufactured and sold. This function calculates the total revenue obtained by the company by multiplying the number of chairs sold (x) by the price of each chair (1,248 - 8.32x).

The cost function C(x) is given as 36,400 - 83.2x. This function calculates the total cost incurred by the company to manufacture x chairs, which includes both fixed and variable costs.

To find the profit function for the furniture company, we need to subtract the cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x) = (1,248x - \(8.32x^2\)) - (36,400 - 83.2x)

Simplifying this expression, we get:

P(x) =\(-8.32x^2\) + 1,248x - 36,400

Therefore, the profit function for the furniture company is P(x) = \(-8.32x^2\) \(+ 1,248x - 36,400\).

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Answer:

The parabola opens upward because the vertex is pointing down.

The x-intercepts are -4 and 8.

The y-intercept is -8.

The equation of the axis of symmetry is 2.

Step-by-step explanation:

Answer:

The parabola opens upward because the vertex is pointing down.

The x-intercepts are -4 and 8.

The y-intercept is -8.

The equation of the axis of symmetry is 2.

Step-by-step explanation:

Answer: We can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events.

In this case, we want to find the probability that a randomly selected senior is a varsity athlete or on the honor roll. We can define the events as follows:

A = the event that a senior is a varsity athlete

B = the event that a senior is on the honor roll

From the problem statement, we know:

P(A and B) = 10/200 = 1/20

P(A) = 70/200 = 7/20

P(B) = 68/200 = 17/50

Plugging these values into the formula:

P(A or B) = P(A) + P(B) - P(A and B)

= 7/20 + 17/50 - 1/20

= 21/50

Therefore, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 21/50.

Answer:

395, 396, 397, 398, 399

Step-by-step explanation:

Answer:

1. 358

2. 363

3.401

4.447

5.439

A small family is a family with parents and up to two children. Because of their small size, they are also called nuclear families. Living in small families is good because resources are better managed. In the essay, we will understand some of the norms of small families.

Living in a small family is a good thing because even average resources effectively support the needs of the whole family. If the number of people in the family is reduced, there will be fewer things to spend and save, and the family will be financially stable. Small families are common today due to mass migration to cities and metropolitan areas. A working parent with one or two children has become the norm.

A small family can take better care of their children's education health and entertainment than a large family. Children from small families get the best education, go to the best schools, and enjoy festivals and other events. There are some standards set by the government regarding small families. In this regard, the main norm for small families is that they should have a maximum of four members including parents and their children.

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deduct one whole number from the other number

Answer:

volume of sphere=4/3πr³=4/3×3.14×6²=164.16cm³

He should have divided both sides by -10.

The system of equations:

5x + 10y = 30

4x + 8y = 36

Has no solutions, the correct option is C.

Here we have the system of equations:

5x + 10y = 30

4x + 8y = 36

We want to use the substitution method, then we need to isolate one of the variables. Let's work with the second equation:

4x + 8y = 36

Divide by 4:

x + 2y = 9

x = 9 - 2y

Now replace that in the other equation to get:

5*(9 - 2y) + 10y = 30

45 - 10y + 10y = 30

45 = 30

This is a false equation, thus, the system has no solutions.

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20.49 trillion is 412.25% larger than 4.00 trillion.

To calculate the percentage increase of a value from an initial value to a final value, you can use the following formula:

increase in percentage = ((final value - initial value) / initial value) x 100%

Percentage increase is useful in a variety of contexts, including: Finance, Sales, Economics, Science, Education. Percentage increase is a useful tool for measuring growth or change over time and comparing different values.

To find the percentage increase, we first need to calculate the difference between the two numbers:

20.49 trillion - 4.00 trillion = 16.49 trillion

Next, we can divide the difference by the original amount (4.00 trillion) and multiply by 100 to get the percentage increase:

(16.49 trillion / 4.00 trillion) * 100 = 412.25%

Therefore, 20.49 trillion is 412.25% larger than 4.00 trillion.

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Answer:

£150 saved; £240 spent.

Step-by-step explanation:

If the ratio of savings to spending is 5:8, we find the fractions representing the amount saved and the amount spent by adding up 5 and 8 and then forming fractions:

savings:  5/13

spending:  8/13

(5/13) of £390 is £150; this is the amount saved.

(8/13) of £390 is £240; this is the amount spent.

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The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.