What is the quotient when (x + 3) is divided into the polynomial 2x2 + x

What is the unit rate for meters per second if a car travels 494 meters in 26 seconds?

timurjin [86]

the unit rate is 19 meters per second

4 0

3 years ago

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

Korvikt [17]

Remember that to factoring by grouping, we should split the expression into tow pairs that have something in common. The idea is that after factoring each pair, we get a binomial common factor. Is worth pointing out that you can pair factors in more than one way.

Let's check how to determine the factors of our expression by grouping:

Step 1. Look for common multiples between the terms.

Notice that 4 and 8 are multiples of 2, 8 is a multiple of 4, and all of them are multiples of 1, so we are going to try more than one pairing combination.

Step 2. Look for common factors between the variables.

Usually, we want to pair variables with higher exponents so when we factor each pair, we end up with another common factor in binomial form.

Step 3. Factor each pair; if you end with another binomial common factor, you nailed it. If not, try again.

Les't apply our steps to our expression $4x^3+x^2-8x-2$

Applying step 1, we are pairing $4x^3$ and $-8x$ . Remember to pair the remaining factors as well.

$(4x^3-8x)+(x^2-2)$

The common factor in the first pair is $4x$ , so lets factor that out

$4x(x^2-2)+(x^2-2)$

Look! we have the binomial common factor $(x^2-2)$ . Unfortunately, $4x(x^2-2)+(x^2-2)$ is not in our given choices, so let's try again:

This time we are going to group the higher variables (step 2) $4x^3$ and $x^2$

$4x^3+x^2-8x-2$

$(4x^3+x^2)+(-8x-2)$

The common factor in the first pair is $x^2$ , and the common factor in the second one is -2, so let's factor out both of them:

$(4x^3+x^2)+(-8x-2)$

$x^2(4x+1)-2(4x+1)$

This time, we got option A.

We can conclude that the correct answer is: A) x2(4x + 1) – 2(4x + 1)

3 0

3 years ago

An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the

iragen [17]

Answer:

A. P("Select 2 black balls and then select 2 white balls")=35/768

Step-by-step explanation:

A. First, we have to get an idea of what our experiment talks about:

If I take a black ball, then we note its color and put it back to the urn with 2 more balls of the same color.

So, every time that we take a ball the quantity of balls in the urn changes with the probability that we had before replacing. The first case (that the first ball you select is black) would go like this:

P("Select a black ball first try") = 7 (number of black balls)/12 (total of balls in the urn)

P(B₁)=7/12

Then, the amount of balls in the urn rise to 14 (12 + 2 balls added) and now the quantity of black balls it´s 9 (7 + 2 added). The urn currently has 9 black balls and 5 white balls, of course:

P("Select black ball second try after getting a black ball before") = 9 (number of black balls)/ 14 (total of balls in the urn)

P(B₁B₂)=9/14

<u>Notice that while we keep taking black balls, the quantity of white ball keeps constant</u> and, for the probability that we take a white ball, we just consider the change in the number of balls in the urn

P(B₁B₂W₃)=5/16

And now, we consider the new white balls that are put in the urn (2 white balls, for a total of 18 and 7 white balls):

P(B₁B₂W₃W₄)=7/18

Because all these probabilities are chained and everything comes from the first ball we choose <u>(if you use a tree diagram, they will be in the same branch</u>), we multiply the probabilities to find the probability that all happens in the same experiment:

P(B₁)*P(B₁B₂)*P(B₁B₂W₃)*P(B₁B₂W₃W₄) = 7/12 * 9/14 * 5/16 * 7/18 = 2205/48384

P(B₁)*P(B₁B₂)*P(B₁B₂W₃)*P(B₁B₂W₃W₄)=35/768

And this is the final answer

7 0

3 years ago

Help me guy it is hard

Galina-37 [17]

The answer is B, you will need at least 6 spring roll wrapper packages.

The way you get the answer is by turning the word problem into an expression. You can make this into the fraction (17*6+15*3)/(25). 17 is the number of adults and you multiply this by how many spring rolls Jill wants to give each adult, which is 6, you can do the same for the children. Next the denominator is 25 which represents the amount of spring roll wrappers per each package. When you simplify the answer comes around to 5.88, but since you cant buy 88% of a spring role wrap package you have to buy another whole one, which makes the answer six.

5 0

3 years ago

PLEASE HELP I"LL GIVE BRAINLEAST

nirvana33 [79]

Answer:

7.5 % Tax rate

Step-by-step explanation:

I used used the calculator to figure out the rate

$2,400 X 7.5%= 180

4 0

3 years ago

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What is the quotient when (x + 3) is divided into the polynomial 2x2 + x - 15?