Please divide 2x^3 - 8x^2 - 13x + 16 by x - 5 with Polynomial Long Division and explain/show all your steps.

Answer:

3q + 7 = 40

Step-by-step explanation:

The expression 5x^2 - 20x can be factored completely as 5x(x - 4), where 5x is the common factor and (x - 4) is the remaining factor.

To factor the expression 5x^2 - 20x completely, we can look for common factors and apply the distributive property. The given expression has a common factor of 5x, so we can factor it out.

Taking out the common factor, we have:

5x^2 - 20x = 5x(x - 4)

The factor 5x represents the common factor of the terms 5x^2 and -20x. By factoring out 5x, we are left with the expression (x - 4) inside the parentheses.

This means that 5x^2 - 20x can be written as the product of the factors 5x and (x - 4).

To check if the factorization is correct, we can distribute the factors back to the original expression:

5x(x - 4) = 5x * x - 5x * 4 = 5x^2 - 20x

This confirms that the factorization 5x(x - 4) is correct.

Therefore, the expression 5x^2 - 20x can be completely factored as 5x(x - 4).

To learn more about factor visit:

https://brainly.com/question/219464

#SPJ11

By the Comparison Test, the series ∑arctan(n)/n converges. Therefore, the correct option is b) converges.

The given series is ∑arctan(n)/n. We can use the Comparison Test to determine whether the series converges or diverges.Let an = arctan(n)/n.

In this case, we compare the given series to the p-series with p = 1. Since p = 1 is the boundary between a convergent and a divergent series, we use the Comparison Test.

Let bn = 1/n. Since 0 ≤ arctan(n)/n ≤ 1/n for all n, we have an ≤ bn for all n. So, by the Comparison Test, the series ∑arctan(n)/n converges.

We can use the Comparison Test to determine whether the series converges or diverges.

Let an = arctan(n)/n. In this case, we compare the given series to the p-series with p = 1.

Let bn = 1/n. Since 0 ≤ arctan(n)/n ≤ 1/n for all n, we have an ≤ bn for all n.

So, by the Comparison Test, the series ∑arctan(n)/n converges. Therefore, the correct option is b) converges.

To know more about converges visit:

https://brainly.com/question/29258536

#SPJ11

The equation of g(x) include the following: D. g(x) = 4x² + 2

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

In this context, we can logically deduce that the parent function f(x) = x² was translated 2 units up and vertically stretched by 4 units in order to produce the graph of the image g(x), we have:

g(x) = 4f(x) + 2

g(x) = 4x² + 2

Read more on function and translation here: brainly.com/question/31559256

#SPJ1

Answer:

Child's dosage=60 milligram

Step-by-step explanation:

The correct formula is below

C= a/(a+12) ∙ A

Where,

C = child’s dosage in milligrams

a = age of the child

A = adult dosage in milligrams

a=6 year old

A=180 milligrams

C= a/(a+12) ∙ A

=6/(6+12)*180

=6/18*180

=1/3*180

=60

Child's dosage in milligram=60 milligram

Part A:What is the probability of getting a red jellybean on the first draw?

Given information: Red jellybeans = 12  Yellow jellybeans = 8  Green jellybeans = 4   Total jellybeans = 24                           The probability of getting a red jellybean on the first draw is:

Probability of getting a red jellybean=Number of red jellybeans/Total jellybeans=12/24=1/2=0.5

Decimal: P(1st Red)=0.5 Percent: P(1 st Red )=50%

Part B: Let's say you did get a red jellybean on the first draw.

What is the probability that you will then get a green on the second draw?

Now, the total number of jellybeans is 23, since one red jellybean has been taken out. The probability of getting a green jellybean is: Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174 Decimal: P(2nd Green | 1st Red )=0.174 Percent: P(2nd Green | 1st Red )=17%

Part C: If you had gotten a yellow on the first draw, would your answer to Part B be different?

Yes, because there is only 1 rotten egg yellow jellybean and if it were chosen in the first draw, it would not be returned back to the container. Therefore, the total number of jellybeans would be 23 for the second draw, and the probability of getting a green jellybean would be:

Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174

Thus, the answer would be the same as Part B.

Part D: What is the conditional probability of the dependent event "red then green?"

Given that one red jellybean and one green jellybean are selected: Probability of the first jellybean being red is 1/2

Probability of the second jellybean being green given that the first jellybean is red is 4/23

Probability of "red then green" is calculated as follows: Probability of red then green=P(Red) × P(Green|Red)= 1/2 × 4/23 = 2/23  Decimal: P(1st Red and 2nd Green )=2/23  Percent: P(1st Red and 2nd Green )=8.70%

To learn more about finding Probability :

https://brainly.com/question/25839839

#SPJ11

Answer:

The graph of the polynomial function f(x) = x^4 + x^3 - 2x^2 will depend on the behavior of the function as x approaches infinity and negative infinity, as well as the location and behavior of any local extrema.

To determine the behavior of the function as x approaches infinity and negative infinity, we can look at the leading term of the polynomial, which is x^4. As x becomes very large (either positive or negative), the x^4 term will dominate the expression, and f(x) will become very large in magnitude. Therefore, the graph of the function will approach positive or negative infinity as x approaches infinity or negative infinity, respectively.

To find any local extrema, we can take the derivative of the function and set it equal to zero:

f(x) = x^4 + x^3 - 2x^2

f'(x) = 4x^3 + 3x^2 - 4x

Setting f'(x) equal to zero, we get:

4x(x^2 + 3/4x - 1) = 0

The solutions to this equation are x = 0 and the roots of the quadratic expression x^2 + 3/4x - 1. Using the quadratic formula, we can find these roots to be:

x = (-3 ± sqrt(33))/8

Therefore, the critical points of the function are x = 0 and x = (-3 ± sqrt(33))/8.

To determine the behavior of the function near each critical point, we can use the second derivative test. Taking the second derivative of f(x), we get:

f''(x) = 12x^2 + 6x - 4

Evaluating f''(0), we get:

f''(0) = -4

Since f''(0) is negative, we know that x = 0 is a local maximum of the function.

Evaluating f''((-3 + sqrt(33))/8), we get:

f''((-3 + sqrt(33))/8) = 11 + 3 sqrt(33)/2

Since f''((-3 + sqrt(33))/8) is positive, we know that x = (-3 + sqrt(33))/8 is a local minimum of the function.

Evaluating f''((-3 - sqrt(33))/8), we get:

f''((-3 - sqrt(33))/8) = 11 - 3 sqrt(33)/2

Since f''((-3 - sqrt(33))/8) is also positive, we know that x = (-3 - sqrt(33))/8 is another local minimum of the function.

Based on this information, we can sketch the graph of the function as follows:

Therefore, the statement that describes the graph of this polynomial function is: "The graph of the function has a local maximum at x = 0 and two local minima at x = (-3 ± sqrt(33))/8. As x approaches infinity or negative infinity, the graph of the function approaches positive or negative infinity, respectively."

Answer:

It varies directly

k = \(\frac{5}{3}\)

Step-by-step explanation:

Table:

    x      y

   7       11

   8       13

   9       15

   10      17

Problem:, determine if y varies directly as x

Solution:

  The equation to determine if they vary directly is;

         y ∝  x

         y  = kx

From the table, y varies directly as x. As y increases, x also increases.

To find k, use any convenient value of y and x  ;

     y  = 15 and x  = 9;

        15 = k x 9

        k = \(\frac{15}{9}\)  = \(\frac{5}{3}\)

Answer:

-1

Step-by-step explanation:

im guessing you need this fast so i wont put a explaniation

Answer:

1/2x-1

Step-by-step explanation:

-3-(-4)/-4-(-6)

1/2 slope

y-(-4)=1/2(x-(-6)

y+4=1/2(x+6)

y+4=1/2x+3

y=1/2x+3-4

y=1/2x-1

Answer:

explanation

Step-by-step explanation:

the reason for your statement is just your explanation of why you think that.

The third section of the Original Dixieland One Step typically repeats twice.

The first section is usually composed of 8 bars of music, the second section is usually 16 bars, and the third section is 8 bars in length. After the first 8 bar section, the second section is then repeated.

This is followed by the third section which will repeat twice. This means that the entire composition is made up of three 8 bar sections and two 16 bar sections of music.

This is a common structure for ragtime pieces as the 8 bar sections provide a contrast to the longer 16 bar sections. This creates a distinctive sound that is unique to ragtime and the Original Dixieland One Step.

For more questions like Ragtime piece visit the link below:

https://brainly.com/question/12112990

#SPJ4

Answer:

y = 3x + 3

Step-by-step explanation:

slope: 3

y int: 3

The tangent ratio is used to solve for a missing angle in a right triangle by dividing the length of the side opposite the angle by the length of the side adjacent to the angle.

Using the tangent ratio, we can find a missing angle in a right triangle by taking the inverse tangent (arctan) of the ratio. For example, if we know the length of the side opposite an angle and the length of the side adjacent to the angle, we can use the tangent ratio to find the value of the angle.

Using the cotangent ratio, we can also find a missing angle in a right triangle by taking the inverse cotangent (arccot) of the ratio. If we know the length of the side adjacent to an angle and the length of the side opposite the angle, we can use the cotangent ratio to find the value of the angle.

The main difference between using the tangent ratio and the cotangent ratio is the order of the sides in the ratio. The tangent ratio involves the opposite side divided by the adjacent side, while the cotangent ratio involves the adjacent side divided by the opposite side.

Both the tangent and cotangent ratios are useful tools for solving right triangles and finding missing angles. The choice between using one or the other depends on the given information and the specific problem at hand.

know more about tangent ratio :brainly.com/question/12760368

#SPJ11

Because the quadrilateral ABCD in the diagram has four equal-length sides (AB=BC=CD=DA) and all of its angles are right angles, we can determine that it is a triangle.

We know that AB = BC = CD = DA because a square has four sides that are all identical. This indicates that triangles ADB and CDB have the same side, AB.

Additionally, we are aware that a square's diagonals are congruent. Angles ADB and CDB are opposing angles of the square in this instance and are hence congruent.

Thus, AB has two congruent sides, while ADB and CDB have two congruent angles. This indicates that the two triangles are congruent according to ASA Congruence (Angle-Side-Angle).

Learn more about triangles here:
brainly.com/question/2773823
#SPJ1

It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To know more about recommended guideline refer here:

https://brainly.com/question/28617982#

#SPJ11

Answer:

A checking account

Step-by-step explanation:

It's called a checking account

Answer:

Step-by-step explanation:

If Greg earned $32 for washing cars and that was twice as much for mowing lawns, then you will need to divide that amount by 2 to find out what was made.

2m = 32

Divide each side by 2:

2m/2 = 32/2

m = 16

Im sorry i cant help but if it lets you try to copy paste the question onto whatever you can

To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

Using these rules, we can find the vertices of image U′V′W′ as follows:

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).

Answer:   ( -8)+(6)= 14

                (-3)+8 = 11

                12+(-13) = 25

           -14-16= -30

        6+(41) =47

Answer/Step-by-step explanation:

Length of AC:

Given that AB = x + 2, and BC = 7x - 3, therefore,

\( (x + 2) + (7x - 3) = AC \) (segment addition postulate)

Simply the expression for the length of segment AC

\( x + 2 + 7x - 3 = AC \)

Collect like terms

\( x + 7x + 2 - 3 = AC \)

\( 8x - 1 = AC \)

Length of QR:

Given that PQ = 8y + 5, and PR = 13y + 25, therefore,

QR = (13y + 25) - (8y + 5) (PQ + QR = PR)

Simplify the expression to for the length of segment QR

QR = 13y + 25 - 8y - 5

Collect like terms

QR = 13y - 8y + 25 - 5

QR = 5y + 20

Answer:

the answer is 48

Step-by-step explanation:

Answer:

\(x = 600\)

Step-by-step explanation:

Let's right our equation

\( \frac{x}{4} + 30 = 180\)

This due to our straight angle

Subtract 30 from both sides

\( \frac{x}{4} = 150\)

Multiply both sides by 4

\(x = 600\)

Brainliest please :)

Answer:

5/3 or 1 2/3 cups of sugar.

Step-by-step explanation:

First, divide by 3 to find the amount of sugar per third.

2 1/2 ÷ 3

5/2 * 1/3

5/6

Second, multiply by two.

5/6 * 2

5/6 * 2/1

10/6

5/3 or 1 2/3

Best of Luck!

Answer:

\(-\frac{42y}{x}\)

Step-by-step explanation:

Apply the fraction rule: \(\frac{-a}{b}=-\frac{a}{b}\)

\(=-\frac{336x^2y^3}{8x^3y^2}\)

Divide the numbers: \(\frac{336}{8} =42\)

\(=\frac{42x^2y^3}{x^3y^2}\)

Apply the exponent rule: \(\frac{x^a}{x^b}=\frac{1}{x^{b-a}}\)

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

\(=\frac{42y^3}{y^2x^{3-2}}\)

Subtract the numbers: \(\:3-2=1\)

\(=\frac{42y^3}{xy^2}\)

Apply the exponent rule: \(\frac{x^a}{x^b}=x^{a-b}\)

\(\frac{y^3}{y^2}=y^{3-2}\)

\(=\frac{42y^{3-2}}{x}\)

Subtract the numbers: \(3-2=1\)

\(=-\frac{42y}{x}\)

Answer:

10/9

Step-by-step explanation:

10/9

Just flip-flop the numerator and denominator

Deejilani, this is the solution:

Jim conclusion that on the next roll a 3 is more likely to occur is not true.

Actually, a 3 has the same probability to occur that the other five numbers:

The probabilities are:

P(1) = 1/6

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

As you can see, the probabilities are exactly the same because the die is fair.

Answer:

I'm gonna say false

GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.

Hope this helps!

Answer:

Standard Deviation = 3.22

Variance = 10.36

Step-by-step explanation:

x          P(x)           x × P(x)              x²             x² × P(x)

19         0.20           3.8                  361               72.2

10         0.20             2                   100                20

11          0.30           3.3                   121                36.3

12         0.20           2.4                   144               28.8

13          0.10            1.3                   169                16.9

____________________________________________

                            12.8                                         174.2            => Total

Mean Formula

\(\mu_x = \sum(x \times P(x))\) \(= 12.8\)

\(\mu_x^2 = 163.84\)

Variance Formula

\(\sigma _x^2 = \sum[x^2 \times P(x)] - \mu_x^2\)      

   \(= 174.2- 163.84\\\\=10.36\)

Standard Deviation Formula

\(Standard\ deviation, \ \sigma_x = \sqrt{Variance}\)

                                   \(=\sqrt{10.36}\\\\=3.218\)      

Option - B : Decision support system is a flexible tool for data analysis, since its reports do not have a fixed format.

  Decision support systems, a subset of business intelligence, are created to help organisations make sensible business decisions based on vast volumes of analysed data. Huge volumes of data are analysed using an interactive information system called a decision support system (DSS) to aid in the direction of business choices. A DSS aids management, operations, and planning levels of an organisation in making better decisions by assessing the importance of uncertainties and the tradeoffs involved in selecting one option over another. A DSS uses a variety of raw data, papers, personal knowledge, and/or business models to aid users in making decisions. A DSS may make use of relational data sources, cubes, data warehouses, electronic health records (EHRs), income projections, sales projections, and other sources.

For such more questions on Data analysis :

brainly.com/question/28840430

#SPJ4