21x^3 + 6x^2 - 28x - 8 factor this expression with work please?

Answers

Answer 1

Answer: $21x^3 + 6x^2 - 28x - 8 \n \n 3x^2 (7x + 2) - 4(7x + 2) \n \n (7x + 2)(3x^2 - 4) \n \n$

The final result is: (7x + 2)(3x² - 4).

Answer 2

Answer: 21x^3+6x^2-28x-8
(21x^3+6x^2)-(28X+8)
3x^2(7x+2)-4(7x+2)
3x^2-4=0 and 7x+2=0

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Josh spent $30 at the movies. 1/5 was spent on a drink, 45% on a ticket and the rest on food. How much did he spend on food?

Answers

Answer:

$10.5

Step-by-step explanation:

Given data

Total amount=$30

Drink = 1/5*30= $6

Ticket= 45% of 30

=45/100*30

=0.45*30

=$13.5

The remainder is for food

=30-6-13.5

=$10.5

Which of the following integrals cannot be evaluated using a simple substitution? (4 points) Select one: a. the integral of the square root of the quantity x minus 1, dx
b. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
c. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
d. the integral of x times the square root of the quantity x squared minus 1, dx

Answers

Answer:

B. and C.

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Integration

Integrals
Indefinite Integrals
Integration Constant C

U-Substitution

Step-by-step explanation:

*Note:

It seems like B and C are both the same answer.

Let's define our answer choices:

a. $\displaystyle \int {√(x - 1)} \, dx$

b. $\displaystyle \int {(1)/(√(1 - x^2))} \, dx$

c. $\displaystyle \int {(1)/(√(1 - x^2))} \, dx$

d. $\displaystyle \int {x√(x^2 - 1)} \, dx$

Let's run u-substitution through each of the answer choices:

a. $\displaystyle u = x - 1 \rightarrow du = dx \ \checkmark$

∴ answer choice A can be evaluated with a simple substitution.

b. $\displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx$

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice B cannot be evaluated using a simple substitution.

C. $\displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx$

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice C cannot be evaluated using a simple substitution.

D. $\displaystyle u = x^2 - 1 \rightarrow du = 2x \ dx \ \checkmark$

Using a little rewriting and integration properties, this integral can be evaluated using a simple substitution.

∴ answer choice D can be evaluated using a simple substitution.

Out of all the choices, we see that B and C cannot be evaluated using a simple substitution.

∴ our answer choices should be B and C.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

How is 4.3 x 10^-3 the answer to this question? A sample of air from a home is found to contain 6.2 ppm of carbon monoxide. This means that if the total pressure is 695 torr, then the partial pressure of CO is..................4.3 x 10^-3.

Answers

The partial pressure of CO2 is equal to the total pressure * molar fraction of CO2.

To give 4.3 * 10^-3, they are using molar fraction = 6.2 * 10^ - 6

Because, 695 * 6.2-10^-6 = 0.004309 = 4.309 * 10^-3 = 4.3 * 10^-3.

Then the new question is why the molar fraction is consideres to be the same ppm concentration. This is because ppm means parts per million, and in this case, they are considering that the parts are moles (usually it is grams, but it is not the case, given the result).

6.2 ppm = 6.2 / 1,000,000 = 6.2*10^-6, which is the number used above to multiply the total pressure and get the partial pressure of CO2.

If you had not told me that the result was 4.3 * 10^-3, I had assumedthat 6.2 was referred to grams and not moles and I had made a conversionusing the molar masses of the air and the CO2 but, again, this is not the case.

Final answer:

The partial pressure of CO in a home with air containing 6.2 ppm CO, when the total air pressure is 695 torr, can be calculated by (6.2 ÷ 1,000,000) x 695, which equals 4.3 x 10^-3 torr.

Explanation:

The partial pressure of a gas is the individual pressure contribution a single type of gas makes to the overall pressure of a gas mixture. In this case, a sample of air from a home was found to contain 6.2 parts per million (ppm) of carbon monoxide (CO). To calculate the actual pressure of CO in the room, we can use the fact that 1 ppm = 1 part of the substance per 1,000,000 parts of air.

To do so, we need to multiply thetotal pressure of the air, which is 695 torr, by the ratio of the CO to the total volume of the air. That would be: (6.2 ÷ 1,000,000) x 695 = 4.3 x 10-3 torr. Hence, that is how 4.3 x 10-3 is derived as the partial pressure of CO in this context.

Learn more about Partial Pressure here:

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Neveah goes out to dinner at a restaurant. The bill for dinner is $57.25, and Neveah gives the server a 20% tip. What is the total cost for dinner? Need answer please :(

Answers

The total cost he paid is $68.7

What is percentage?

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part;

Given:

Bill for dinner is $57.25

20% tip was given

So, 20% on 57.25 is

=0.20 * 57.25

=11.45

Hence, total he paid = 57.25 +11.45 = 68.7

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Answer:

11.45 + 57.25

Step-by-step explanation:

$68.70 is the correct answer because the question asks WHAT IS THE TOTAL COST FOR THE DINNER

The branch of statistics that involves organizing, displaying, and describing data is called _______

Answers

Answer:

Descriptive statistics

Step-by-step explanation:

descriptive statistics

Three consecutive integers have a sum of 81

Answers

(25+27+29=81)
that should be right

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