p(x) = 3(x + 10x + 5) - 5(x - k)

In the polynomial p(x) defined above, k is a
constant. If p(x) is divisible by x, what is the value
of k?

Answers

Answer 1

First, you should simplify the function expression.

 

3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k

 

In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder.  The first two terms clearly divide by x.  However, the last two do not.  In order for this to work out where k is constant, 5k would have to cancel out the  +15 term, leaving nothing to divide by x.

 

So: 15 + 5k = 0

 

5k = -15

k = -3


Related Questions

At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? Explain. Write an equation to represent this relationship. how do you fill it out.

Answers

Answer:

Step-by-step explanation:

how do you determine volume?

Answers

Answer:   V = πr 2 h

Step-by-step explanation:

To calculate the volume of a cylinder, you must know its height and the radius of the circular base (the distance from the center of the circle to its edge) at the top and bottom. The formula is V = πr 2 h, where V is the Volume, r is the radius of the circular base, h is the height, and π is the constant pi.

simplify this please

Answers

Answer:

0? I tried solving it myself then I put it into my calculator and both times I got 0

HELP ME SOLVEEEE !!!!!

Answers

Answer:

y=2

Step-by-step explanation:

y+7=9(y-1)

y+7=9y-9

y-9y=-9-7

-8y=-16

y=2

>> Answer

_________

[tex] \: [/tex]

[tex] \frac{1}{3} (y + 7) = 3(y - 1)[/tex]

[tex] \frac{y + 7}3 = 3(y - 1) [/tex]

[tex]y + 7 = 9(y - 1)[/tex]

[tex]y + 7 = 9y - 9[/tex]

[tex]y - 9y = - 9 - 7[/tex]

[tex] - 8y = - 16[/tex]

y = 2

How much has James earned since the beginning of the year in 2014? (use pay stub) *
1 point
$1,451.28
$3548.72
$5,000

Answers

Can you give more information?

4) Sally has 10 purple beads, 25 yellow beads and 30 red beads. She is
going to make identical bracelets for her friends. What is the maximum
number of bracelets she can make if she wanted to use all her beads?

Answers

Answer:

5 bracelets

Step-by-step explanation:

The common factor of 10, 25 and 30 is 5

this means that each bracelet will have 2 purple, 5 yellow and 6 red.

Answer:

5 Bracelets

Step-by-step explanation:

the common factor of the numbers 10 25 and 30 is 5

5×2= 10

5× 5 = 25

5x6= 30

these numbers are also multiples of 5.

Convert the units of measure

Answers

Answer:

22.5

Step-by-step explanation:

24 hr in a day

so

540 : 24 = 22.5 or 22 1/2

If lineman works 9 1/2 hours a day on a certain job at $28.70 per hour, what is the pay for a day?

Answers

9.5 x 28.70 = 272.65

Consider the equation below. The value of x in terms of h is . The value of x when h = 4 is .

Answers

The value of x when h = 4 is 4.

The given equation is  :   4(x − 3) = h.  We need to find the value of x in terms of h and the value of x when h = 4.So, we will solve this equation by following the steps given below:

Step 1: Distribute 4 by x and 4 by -3. It gives us:4x - 12 = h

Step 2: Add 12 to both sides of the equation. We get:4x - 12 + 12 = h + 124x = h + 12

Step 3: Divide both sides of the equation by 4. We get:x = (h + 12) / 4

Therefore, the value of x in terms of h is x = (h + 12) / 4.

Now, we need to find the value of x when h = 4. We will put h = 4 in the above equation and get the value of x.x = (4 + 12) / 4 = 16 / 4 = 4.

For more such questions on equation

https://brainly.com/question/29174899

#SPJ8

help me i nedd help...........

Answers

Answer:

The answer is 10 12/85    Hope you pass!

Which is the smallest integer that makes the inequality 2x + 3 > 5 true?​

Answers

0 is the correct answer;

2*0=0, and 0+3=3.

However if we plug in 1 it does not work you see; 2+1=2, and 2+3 = 5.

It has to be > not =

2

Step-by-step explanation:

because if you subtitute 2 for x you would get

2(2) +3>5

4+3=7

7>5

which makes the inequality true

Student Council sells bottled water at the cheerleading completion. At this rate, how many cases of bottled water would they sell in 3 hours? ________________________

Cases Sold: 3 and 6
Time (minutes): 20 and 40

Answers

Answer:

27

Step-by-step explanation:

Lets find the rate of selling:

Let v= the rate of selling, b = number of bottles of water, and t = time:

b over t gives us the [tex]v=\frac{b}{t}=\frac{3}{20}=\frac{6}{40}=0.15[/tex] rate of selling:

3 hours is 60min * 3 = 180 mins, and since v=b/t, vt=b:

(0.15) * 180 = 27 bottles of water


Use complete sentences to describe how you can algebraically determine where the solution region is for a quadratic inequality once the
points of intersection have been found.

Answers

Answer:

hwiwj8eie9eiejnebwnw

1.35 - 0.829 SHOW YOUR WORK​

Answers

Answer:

0.521

Step-by-step explanation:

It's just like subtracting

ILL give u 35 points if u answer this. i need help

Answers

The answer is 11xy+4x^2t

Does this graph represent a proportional relationship?
giving brainlist for correct

Answers

Answer:

No

Step-by-step explanation:

because it doesn't pass through the origin.

Find the geometric mean between each pair of numbers

Show your work please
Thank you❤️❤️❤️

Answers

Answer:

1.26

Step-by-step explanation:

geometric mean =sqrt((4/5)*2)=sqrt(1.6)=1.26

The average distance from Earth to the Moon is approximately 384,400,000 kilometers.

What is the average distance, in kilometers, from Earth to the Moon written in scientific notation?

A 3.844 x 10^4 kilometers

B 3.844 x 10^5 kilometers

C 3.844 x 10^7 kilometers

D 3.844 x 10^8 kilometers

Answers

9514 1404 393

Answer:

  D.  3.844 × 10^8 kilometers

Step-by-step explanation:

To write the number in scientific notation, put a decimal point after the most significant digits and write the rest of the significant digits after that. Multiply the number by the power of 10 that tells how many digits are between the most significant digit and the decimal point.

Here, the number has 8 digits between the most-significant digit (3) and the decimal point. Any trailing zeros are assumed to be not significant when the number is written without a decimal point. So, the number is written ...

  3.844 × 10^8 km

(02.05 MC)
Graph g(x), where f(x) = 4x - 2 and g(x) = f(x + 1).

Answers

[tex]\\ \sf\longmapsto f(x+1)[/tex]

[tex]\\ \sf\longmapsto 4(x+1)-2[/tex]

[tex]\\ \sf\longmapsto 4x+4-2[/tex]

[tex]\\ \sf\longmapsto 4x+2[/tex]

g(x)=4x+2

Please explain step by step how to solve. Thank you

Answers

By doing cross multiply, you'll get

6(p-1) = 8(p+10)

Expand

6p-6 = 8p+80

Arrange

-80-6 = 8p-6p

-86 = 2p

Divide by 2 to find p

-43 = p

Answer:

p =

Step-by-step explanation:

First, we can start by cross multiplying.

p−1p+10=86

(p−1)*(6)=8*(p+10)

6p−6=8p+80

After some simplification, we get:

−2p=86

Then we find out that p = -43

If we put it in, and then simplify that, we will get 8/6

If this helped you, consider marking this as brainliest :)

a school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions should they use to build the largest possible athletic complex. Include appropriate units with your answer.

Answers

The area of a shape is the amount of space it occupies.

The dimensions to build the largest possible athletic complex is 100 by 50 feet

Assume the length of the fence is y.

So, we have:

[tex]\mathbf{Area = xy}[/tex]

[tex]\mathbf{Perimeter = 2y + 4x}[/tex]

Substitute 400 for perimeter

[tex]\mathbf{2y + 4x = 400}[/tex]

Divide through by 2

[tex]\mathbf{y + 2x = 200}[/tex]

Make y the subject

[tex]\mathbf{y = 200 -2x}[/tex]

Substitute [tex]\mathbf{y = 200 -2x}[/tex] in [tex]\mathbf{Area = xy}[/tex]

[tex]\mathbf{Area =x(200 - 2x)}[/tex]

[tex]\mathbf{Area =200x - 2x^2}[/tex]

Differentiate

[tex]\mathbf{A' =200 - 4x}[/tex]

Set to 0

[tex]\mathbf{200 - 4x = 0}[/tex]

Collect like terms

[tex]\mathbf{4x = 200}[/tex]

Divide both sides by 4

[tex]\mathbf{x = 50}[/tex]

Recall that: [tex]\mathbf{y = 200 -2x}[/tex]

So, we have:

[tex]\mathbf{y = 200 - 2 \times 50}[/tex]

[tex]\mathbf{y = 200 - 100}[/tex]

[tex]\mathbf{y = 100}[/tex]

Hence, the dimensions to build the largest possible athletic complex is 100 by 50 feet

Read more about areas and perimeters at:

https://brainly.com/question/11957651

I NEED ANSWERS TO THESE QUESTIONS


1.How are the areas of a circle and a parallelogram related?


2. Find the area of a circle with a radius of 6.9 m to the nearest tenth. Leave your answer in terms of π.


3. The average crop circle is between 100 and 300 ft in diameter. Find the area of a crop circle that is 300 ft in diameter. Use 3.14 for π.


4. A baker makes a giant cookie for special occasions that is 16 in. in diameter. How many 4-in. diameter cookies would it take to equal the area of one giant cookie?


5. Compare and Contrast What is the difference between the circumference and area of a circle

6. Reasoning A round pizza has an area of 254.34 in.2. Explain how to estimate the length and width of the square box needed to package the pizza

Answers

I only have the answer for 1, but !

1. The area of a parallelogram is  base times height. Since the area of that rectangle is twice the area of the circle, then the area of the circle is half the base times the height. It will be half of 2πr· r. The area of the circle will be πr2

The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will last between 2.8 and seven years. (a) Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (b) Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.) P < x < =

Answers

Using the normal distribution, we have that:

a) The sketch of the situation is given at the end of this answer.

b) The probability is:

[tex]P(2.8 \leq X \leq 7) = 0.8284[/tex]

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

Mean of 4.1 years, thus [tex]\mu = 4.1[/tex].Standard deviation of 1.3 years, thus [tex]\sigma = 1.3[/tex].

Item a:

The part between 2.8 and 7 years is shaded on the sketch given at the end of this answer.

Item b:

The probability is the p-value of Z when X = 7 subtracted by the p-value of Z when X = 2.8, thus:

X = 7:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{7 - 4.1}{1.3}[/tex]

[tex]Z = 2.23[/tex]

[tex]Z = 2.23[/tex] has a p-value of 0.9871.

X = 2.8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.8 - 4.1}{1.3}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

0.9871 - 0.1587 = 0.8284, thus:

[tex]P(2.8 \leq X \leq 7) = 0.8284[/tex]

A similar problem is given at https://brainly.com/question/25151638

Hepplpppppppppppppppoplllpllppppppp

Answers

Answer:

X = 53°

y = 143°

Step-by-step explanation:

Hope it helps!!!!!!

State whether the following angle measures can form a triangle.
A) 90, 90, 35
B) 60, 27, 93
(PLEASE HELP)
(If you could also please help me with question 4 as well I will give you brainliest)

Answers

Answer:

3.b because 60,27,93

Step-by-step explanation:

can you brainliest me

Answer:

3.b

2.155/⅘

Step-by-step explanation:

hope it's helpful

How to solve 589 divided by 41

Answers

Answer:

14.365

Step-by-step explanation:

do long division or put it in a calculator

what does N equal because i dont know

Answers

Answer:

N = Natural numbers

(5x+4)-3x
Solve it.
No scam

Answers

Answer:

=2x+4

Step-by-step explanation:

Let's simplify step-by-step.

5x+4−3x

=5x+4+−3x

Combine Like Terms:

=5x+4+−3x

=(5x+−3x)+(4)

=2x+4

Answer:

2x+4...

Step-by-step explanation:

Hopefully it helps

Please help. I am not sure how to solve. Please include step by step. Thank you for the help!

Answers

Answer:

[tex]h = \frac{V}{\pi r^{2}}[/tex]

h = 4 cm

Step-by-step explanation:

Given the formula for the volume (V) of a cylinder: V = πr ²h, and the following values for volume and radius:

V = 36π cm³

r = 3 cm

First, solve for h:

V = πr ²h

Divide both sides by πr ²:

[tex]\frac{V}{\pi r^{2} } = \frac{\pi r^{2}h}{\pi r^{2} }[/tex]

[tex]h = \frac{V}{\pi r^{2}}[/tex]

Next, solve for the height of the cylinder by substituting the given values for volume and radius into the formula:

[tex]h = \frac{V}{\pi r^{2}}[/tex]

[tex]h = \frac{36\pi }{\pi (3^{2})}[/tex] → π cancels out.

[tex]h = \frac{36}{9}[/tex]

h = 4 cm

Write an inequality to represent this situation (1 point):
Jake earned more than $49 dollars.

Answers

The inequality that represents the situation is:

[tex]E_J > 49[/tex].

Jake earnings are unknown, so it is going to be represented by a variable, that we are going to call it [tex]E_J[/tex].

His earnings are of more than 49 dollars, that is, [tex]E_J[/tex] is greater than $49, which means that the following inequality models this situation:

[tex]E_J > 49[/tex].

A similar problem, also involving an inequality built to represent a situation, is given at https://brainly.com/question/22312773

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