Use the grouping method to factor this polynomial completely.
2^3 + 6x^2 + 5x + 15
A. (2x2 + 3)(x + 3)
B. (2x2 + 5)(x+5)
C. ( 2x2 + 3)(x + 5)
D. (2x2 + 5)(x+3)

Answer:

5/6

Step-by-step explanation:

5 divided by 6 is 0.83333333333333333 and so on.

Answer:

D. -3x

Step-by-step explanation:

Terms have the form k or kx^n, where k is a number, x is a variable, and n is a whole number.

-3x follows the above rule, so -3x is a term.

Answer:

D

Step-by-step explanation:

Hi...

Here, I graphed it for you:

Answer:

Therefore, based on the given scatter plot, the set of numbers that matches the points is C. 8,9,8,10,8,11.

Step-by-step explanation:

The scatter plot shown represents a set of nine points on a coordinate plane. Each point consists of an x-coordinate and a y-coordinate. To determine which set of numbers corresponds to the scatter plot, we need to analyze the pattern in the given points.

Looking at the scatter plot, we observe that the x-coordinates range from 0 to 10 with an increment of 1, while the y-coordinates seem to vary.

Now let's examine the given answer choices:

A. .4,4,5,5,6,6

B. .4,10,4,11,4,12

C. 8,9,8,10,8,11

D. 10,10,10,11,10,12

Set C (8,9,8,10,8,11) among these answer choices matches the pattern observed in the scatter plot. The x-coordinates in the scatter plot range from 0 to 10, and the y-coordinates correspond to the numbers provided in set C.

Therefore, based on the given scatter plot, the set of numbers that matches the points is C.

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Given:

Five less than three-fourths of an integer is the same as five  more than one-eighth of the same integer.

To find:

The integer.

Solution:

Let x be the unknown integer.

So, according to the question,

\(\dfrac{3}{4}x-5=5+\dfrac{1}{8}x\)

\(\dfrac{3}{4}x-\dfrac{1}{8}x=5+5\)

\(\dfrac{6x-x}{8}x=10\)

Multiply both sides by 8.

\(5x=10\times 8\)

\(5x=80\)

Divide both sides by 5.

\(x=\dfrac{80}{5}\)

\(x=16\)

Therefore, the required integer is 16 and your equation \(5-\dfrac{3}{4}x=5+\dfrac{1}{8}x\) is incorrect.

=================================================

Explanation:

The sequence {4,1,2} is neither because both arithmetic sequences and geometric sequence are either always increasing or always decreasing. We start off decreasing when going from 4 to 1, but increase to 2.

----------

The sequence {4,20,100} is geometric because we multiply each term by 5 to get the next term. That means the common ratio is 5. Notice how this sequence is increasing.

---------

The sequence {212,106,53} is also geometric. This time the common ratio is 1/2 = 0.5; this sequence is decreasing.

For acceptable x values of √12(x-1)+√√2(x-1)², the option is equivalent to the quotient given here (x-1) ² is \($2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\\) .

The equivalent of the quotient displayed above for allowable x values is

\($\sqrt{1} \cdot 2(x-1)+\sqrt{\sqrt{2}}(x-1)^2$\)

\($2(x-1)+\sqrt[2 \cdot 2]{2}(x-1)^2$\\\)

\(\$2(x-1)+\sqrt[4]{2}(x-1)^2$\\$(2 x-2)+\sqrt[4]{2}\left(x^2+2 x(-1)+(-1)^2\right)$\\$(2 x-2)+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x-2+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x+\sqrt[4]{2}\left(x^2-2 x+1\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-\sqrt[4]{2} \cdot 2 x+\sqrt[4]{2}\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}\right)-2$\\$2 x+\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}-2$\)

\($f(x)=\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$\)

\($\frac{d}{d x}\left(\sqrt{12(x-1)}-\sqrt{2(x-1)^2}\right)$\)

\($\sqrt{12(x-1)}-\sqrt{2(x-1)^2}=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\)

\($\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$\)

\($\sqrt{12(x-1)}=2 \sqrt{3} \sqrt{x-1}$\)

\($\sqrt{2(x-1)^2}=\sqrt{2}(x-1)$\\$=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\\)

Values that might result in a fraction's denominator being equal to zero are excluded. Finding these omitted values is crucial for resolving a rational statement because you cannot divide by 0.

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Answer: The first step would be to subtract 32 from both sides.

Step-by-step explanation:

The answer to the whole equation is -44.

To get -44 you need to get rid of the 32 to get the x to be alone.

Answer:30.69230769 in decimal form

399/13 in percent form

30 9/13 in fraction form

These are all the means in different forms.

Step-by-step explanation:

If the equation (13 + 4i) + n = 0, then the value of n is option (d) -13 - 4i

Additive inverse is a concept in mathematics that refers to the opposite of a given number, such that when the number is added to its additive inverse, the result is zero

To solve for n, we can isolate it by moving (13 + 4i) to the other side of the equation and then taking the additive inverse of both sides.

Starting with: (13 + 4i) + n = 0

Subtracting (13 + 4i) from both sides: n = - (13 + 4i)

Taking the additive inverse of both sides: n = -13 - 4i

Therefore, the correct option is (d) -13 - 4i

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We are given a function y = -4x^3 - 9x^11, and we need to find its first and second derivatives.

To find the first derivative, we apply the power rule and the constant multiple rule. The power rule states that the derivative of x^n is nx^(n-1), and the constant multiple rule states that the derivative of kf(x) is k*f'(x), where k is a constant. Applying these rules, we can find the first derivative of y = -4x^3 - 9x^11.

Taking the derivative term by term, the first derivative of -4x^3 is -43x^(3-1) = -12x^2, and the first derivative of -9x^11 is -911x^(11-1) = -99x^10. So, the first derivative of y is dy/dx = -12x^2 - 99x^10.

To find the second derivative, we apply the same rules to the first derivative. Taking the derivative of -12x^2, we get -122x^(2-1) = -24x, and the derivative of -99x^10 is -9910x^(10-1) = -990x^9. Therefore, the second derivative of y is d^2y/dx^2 = -24x - 990x^9.

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Answer:

Step-by-step explanation:

Answer: D) subtract one x block from the left side and subtract two numbered blocks from the right side

Step-by-step explanation:

Answer:

Answers below!

Step-by-step explanation:

-9 x -5 = 45

45 x - 6 = -270

-270 x -3 = 810

The answer is positive because a negative multiplied by a negative equals a positive number.

-9 x -5 = 45

45 x 6 = 270

270 x -3 = -810

This answer is negative because a negative multiplied by a positive  equals a negative number.

Answer:

Yes, the value of x does answer the question since the question is asking how much do the two have on their subway cards. This is an example question so the answer is given to you for you to read. I'm not sure if this is what you're confused about, but the answer does answer the question.

Answer:

Yes

Step-by-step explanation:

If 2x + 20 is 1.5x more than x + 20 then we get:

2x + 20 = 1.5(x + 20)

since 2x + 20 is 1.5x more than x + 20.

If we solve then we get the same answers as the example where x = 20 and 2x = 40.

Answer:

23/12

Step-by-step explanation:

4x - 2/3 = 7

4x - 2/3 + 2/3 = 7 + 2/3

4x = 23/3

x = 23/12

Step-by-step explanation:

600=150%

?= 100%

crossmultiplication

=400

600g=150%x

600 is therefore 150% of 400

The expected value of buying car insurance is $794.5.

Insurance is a contract between an individual or entity and an insurance company, in which the insurance company agrees to provide financial protection or reimbursement against losses in exchange for payment of premium. It is a form of risk management, mainly used to hedge against the risk of a contingent or uncertain loss.

The expected value of buying car insurance is the sum of the product of the value and the probability of each outcome. To calculate the expected value, we multiply the probability of having an accident by the average coverage paid ($2,500), and add it to the product of the probability of not having an accident multiplied by the insurance cost ($600).

So, expected value = (0.105 * $2,500) + (0.895 * $600) = $267.5 + $527 = $794.5

Therefore, the expected value of buying car insurance is $794.5.

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Answer:

Letter B is the statistic.

\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

a) The probability that a tire will be too narrow is 0.252492. b)The probability that a tire will be too wide is 0.091211. c) , the probability that a tire will be defective is 0.252492 + 0.091211 = 0.343703.

a. To calculate the probability that a tire will be too narrow, we need to find the area under the normal distribution curve that falls below the lower specification limit.

Using the Z-score formula, we calculate the Z-score for the lower specification limit as follows:

Z = (Lower specification limit - Mean) / Standard deviation

Z = (22.8 - 23) / 0.15

Z = -0.666667

Next, we find the corresponding area from the standard normal distribution table or using a calculator. The area to the left of Z = -0.666667 is approximately 0.252492.

b. To calculate the probability that a tire will be too wide, we need to find the area under the normal distribution curve that falls above the upper specification limit.

Using the Z-score formula, we calculate the Z-score for the upper specification limit as follows:

Z = (Upper specification limit - Mean) / Standard deviation

Z = (23.2 - 23) / 0.15

Z = 1.333333

Next, we find the corresponding area from the standard normal distribution table or using a calculator. The area to the right of Z = 1.333333 is approximately 0.091211.

c. The probability that a tire will be defective is the sum of the probabilities of it being too narrow and too wide, since being outside the specification limits indicates a defect.

Therefore, the probability that a tire will be defective is approximately 0.252492 + 0.091211 = 0.343703.

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Answer:

➢ 0.9

➢ -95

➢ -79

\(BlackSparkles...\)

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The singular points of the differential equation are x = -6 and x = 0, which is an irregular singular point.

To find the singular points of the differential equation, we need to determine the values of x for which the coefficients of y'', y' and y become zero or infinite.

In this case, the coefficient of y'' is (x+6), which is zero only at x = -6. The coefficient of y' is -x^2, which is zero at x = 0. However, it is also infinite at x = 0, so we need to check if this is a regular or irregular singular point.

To do this, we can substitute y = (x^r) into the differential equation, where r is a constant. We get:

(x+6)r(r-1)x^(r-2) - x^r + 8x^r = 0

Simplifying, we get:

r(r-1) + 2r - 8 = 0

r^2 + r - 8 = 0

(r+2)(r-4) = 0

Thus, the possible values of r are -2 and 4. Substituting these back into y = (x^r), we get two solutions: y = x^(-2) and y = x^4.

Therefore, the singular points of the differential equation are x = -6 and x = 0, which is an irregular singular point.

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We will see that the parabola must open downwards, then the value of c must be negative, and thus, the correct option is A, c = -8.

The general quadratic equation is written as:

y = a*x^2 + b*x + c

Where a is the leading coefficient, and it defines if the parabola opens up or down, depending on its sign.

And we know that we have two real solutions, so the discriminant (4*a*c in the general equation) must be positive.

Then:

4*a*c> 0

Now, notice that the vertex of the parabola is above the x-axis, then the parabola only will intercept the x-axis if it opens downwards, then a must be negative.

Then the value of c also must be negative, due to the above inequality.

Then the only option that could be the value of c is option A, c = -8.

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Answer:

-2x-5=4x-29

-2x-4x=-29+5

-6x =-24

x=-24/-6

x=4

hence proved

Answer: think it would be 60.9 correct me if I'm wrong

Answer:

\(9.5s \: + \: 16p \: = 24.\)

Step-by-step explanation:

\(if \: the \: numbers \: of \: shirts \: is \: s.\\ if \: the \: numbers \: of pants \: is \: p. \\then \: the \: inequality \: that \: represents \: \\ the \: numbers \: of \: shirts \: and \: pants \: you \: can \: afford \: is : \\ 9.5s \: + \: 16p \: = 24.\)

Answer:

9.5s + 16p = 24

Step-by-step explanation:

k12

The required solution to the given equation is x = 106.04, which is the correct answer that would be option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question following:

x - 69.80 = 36.24

We have to determine the solution to the given equation

As per the question, we have

x - 69.80 = 36.24

Add 69.80 on both sides of the equation, and we get

x - 69.80 + 69.80 = 36.24 + 69.80

x = 106.04

Hence, the correct answer would be an option (A).

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(a) Two descriptive statistics cited from the survey are: a. Of those investment managers surveyed, 44% were bullish or very bullish on the stock market.

b. Of those investment managers surveyed, 23% selected health care as the sector most likely to lead the market in the next 12 months.

These statistics describe the proportions or percentages of investment managers with certain attitudes or preferences based on the survey results. (b) Inference about the average return expected on equities over the next 12 months for the population of all investment managers: Based on the survey, the average expected return over the next 12 months for equities among the investment managers surveyed was 11.3%. Therefore, we can infer that the estimated average expected 12-month return on equities for the population of investment managers is likely to be around 11.3%. However, it's important to note that this is an inference and not a definitive conclusion, as the survey represents a sample of investment managers and may not perfectly represent the entire population.

(c) Inference about the length of time it will take for technology and telecom stocks to resume sustainable growth: The survey found that the managers' average response for the length of time it would take for technology and telecom stocks to resume sustainable growth was 2.3 years. From this, we can infer that the estimated average length of time it will take for technology and telecom stocks to resume sustainable growth for the population of investment managers is approximately 2.3 years. Again, this is an inference based on the survey data and may not be an exact representation of the entire population.

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