Find the remainder when f(x) is divided by (x - k).
f(x) = 4x3 - 5x2 + 2x + 11; k= 3

Answers

Answer 1

3] 4 -5 2 11
12 21 69
----------------------
4 7 23 80

80 would be the remainder
Another method would be to plug 3 into the equation for x
[tex]4(3)^{3}-5(3)^{2}+2(3)+11[/tex] = 4(27) - 5(9) + 6 + 11 = 108 - 45 + 6 + 11 = 63 + 6 + 11 = 80

Answer 2

Answer:

The remainder is 80

Step-by-step explanation:

Given the polynomial

[tex]f(x)=4x^3-5x^2+2x+11[/tex]

we have to find the remainder when the above polynomial f(x) is divided by x-3

By remainder theorem when we put x=3 in f(x) we get the remainder i.e f(3)

[tex]f(3)=4(3)^3-5(3)^2+2(3)+11[/tex]

[tex]=108-45+6+11[/tex]

[tex]=80[/tex]

which is required remainder.

Hence, the remainder is 80

Related Questions

???????????????????????????

Answers

Greetings!

We can substitute the variables, so we only have to solve for one, per eqaution
[tex]x=4y[/tex]
Therefore...
[tex]3x-2y=20[/tex]
Is also equal to..
[tex]3(4y)-2y=20[/tex]

Solve for y.
Combine Like terms.
[tex]12y-2y=20[/tex]
[tex]10y=20[/tex]
Divide both sides by 10.
[tex](10y)/10=(20)/10[/tex]
Simplify.
[tex]y=2[/tex]

Now we can use the value of y to solve the other equation.
[tex]x=4y[/tex]
Is also equal to...
[tex]x=4(2)[/tex]

Solve for x.
Combine like terms.
[tex]x=8[/tex]

The answer would be 8,2

Hope this helps.
-Benjamin

The average mass of a kernel of popcorn is 0.125 g. if 1 pound = 16 ounces, and 1 ounce = 28.3 g, then how many kernels of popcorn are there in 0.500 pounds of popcorn?

Answers

Average mass of a kernel of popcorn = 0.125 g
1 pound = 16 ounces, and 1 ounce = 28.3 g
how many kernels of popcorn are there in 0.500 pounds of popcorn = ?
0.500 pound = 16 x 0.500 ounces = 8 ounces
8 ounces = 8 x 28.3g = 226.4 g
Now divide this quantity by average mass;
226.4 / 0.125
= 811.2 kernels of popcorn

Final answer:

To find the number of kernels of popcorn in 0.500 pounds, first convert the weight to grams and then divide by the average mass of a kernel. The calculation gives an approximate result of 1811 kernels.

Explanation:

To determine the number of kernels of popcorn in 0.500 pounds, we need to convert the weight from pounds to grams and then divide by the average mass of a kernel.

First, let's convert pounds to ounces. Since 1 pound is equal to 16 ounces, we have:

0.500 pounds = 0.500 x 16 = 8 ounces.

Next, let's convert ounces to grams. Since 1 ounce is equal to 28.3 grams, we have:

8 ounces = 8 x 28.3 = 226.4 grams.

Finally, divide the total grams by the average mass of a kernel:

226.4 grams / 0.125 grams = 1811.2 kernels.

Therefore, there are approximately 1811 kernels of popcorn in 0.500 pounds.

He _______ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

Answers

He Sampling method tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases. In practice, the distribution of the sample means approaches a bell-shape curve when n > 30. More specifically speaking, if a random variable X has a mean of µ and a standard deviation of σ, then the sample means are approximately normally distributed with a mean of µ and a standard deviation of [tex] \frac{\sigma}{ \sqrt{n} } [/tex] as the sample size increases.

What is the value of x?

a. -16
b. 120
c. 60
d. 16

Answers

D is the answer to your question

Vertical angles are congruent or equal to each other.

Set the equation:

8x - 8 = 7x + 8

Add 8 to both sides of the equation.

8x - 8 + 8 = 7x + 8 + 8

8x = 7x + 16

Subtract 7x from both sides of the equation.

8x - 7x = 7x - 7x + 16

x = 16

Answer: D) 16

Checking to see if our answer is right.

8x - 8 = 7x + 8

8(16) - 8 = 7(16) + 8

128 - 8 = 112 + 8

120 = 120

Fencing costs $10.15/ft. A customer purchases 8 3/8 ft of fencing for his yard. How much did the customer pay for the fencing? Round to the nearest cent.

Answers

The customer paid about $85.00 for 8 3/8 ft of fencing.

If you just take 10.15x8 3/8 it is $85.01 rounded to the nearest sent

One canned juice drink is 30 percent orange juice, another is 10 percent orange juice. how many liters of each should be mixed together in order to get 20l, that is 12 perfect orange juice

Answers

let there be x litters of 30 percent juice and (20-x) litters of 10 percent juice.

0.30x+0.10(20-x)=20*0.12
0.3x+2-0.1x=2.4
0.2x=0.4
x=2
20-x=20-2=18

mix 2 litters of 30 percent juice and 18 litters of 10 percent juice.

Which of the following numbers is not part of the solution to x > 1?

1
1.2
4
8

Answers

The answer is 1. Because 1=1, 1 is not > 1

Answer:

the answer is 1

hpoe this helps

4=3/4m-6

find the value of m

Answers

4 = 3/4m -6

add 6 to both sides

10 = 3/4m

divide both sides by 3/4

m = 10 / 3/4 = 10 *4 = 40 /3 = 13 1/3

With calculations please

Answers

5) x represents the widgets; y represents the gadgets

Widgets are $3 each ; gadgets are $5 each.

The boss wants AT LEAST 10 widgets and 20 gadgets and total must reach AT MOST $300 per day.

Your inequalities would be:

x ≥ 10 (there must be greater than or equal to 10 widgets made)

y ≥ 20 (there must be greater than or equal to 20 gadgets made)

3x + 5y ≤ 300 (the cost must be less than or equal to 300)

The solution is H.

6) Solve for all possibilities.

I) f(k) + g(k)

= -4k⁴ + 14 + 3k² + (-3k⁴ - 14k² - 8)

= -4k⁴ + 14 + 3k² - 3k⁴ - 14k² - 8

Combine like terms.

= -7k⁴ - 11k² + 6

II) h(k) - r(k)

= 8k⁴ - 3 - 10k² - (-k² + 12k⁴ + 6)

= 8k⁴ - 3 - 10k² + k² - 12k⁴ - 6

= -4k⁴ - 9k² - 9

III) s(k) - t(k)

= -3k⁴ + 5k² - 1 - (4k⁴ + 16k² - 7)

= -3k⁴ + 5k² - 1 - 4k⁴ - 16k² + 7

= -7k⁴ - 11k² + 6

There are only two that result in equivalent expressions which are I and III.

Solution : I and III.

Find the product of 20 x 9 x 5 tell which property you used

Answers

I will be using the associative property. (20 x 9) x 5 = 900
You first multiply 20 x 9, which equals 180, then you multiply 180 x 5, which equals 900.

I used associative property and the product of 20 x 9 x 5 is 900.

What is associative property?

"The associative property states that when an expression has three terms, they can be grouped in any way to solve that expression. The grouping of numbers will never change the result of their operation. The associative property is true for the cases of addition and multiplication. Neither the sum nor the product of the expression changes."

For the given product of 20 x 9 x 5

I am using the associative property.

(20 x 9) x 5 = 900

First multiply 20 x 9, which gives 180

(180) x 5 = 900

Next multiply 180 x 5, which gives 900.

Hence, I used associative property and the product of 20 x 9 x 5 is 900.

Learn more about associative property here

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You randomly select 7 students from a class with 15 male and 20 female students. what is the probability that you will choose exactly 4 females?

Answers

0.3278 Use combination formula ((20C4)*(15C3))/(35C7) = 0.3278 20C4 - combinations of 4 females from 20 15C3 - combinations of 3 males from 15 35C7 - all possible combinations of 7 students from 35 students in total

Final answer:

To find the probability of selecting exactly 4 females out of 7 students, we need to use the hypergeometric distribution.

Explanation:

To determine the probability of selecting exactly 4 females out of 7 students, we need to use the hypergeometric distribution. In this scenario, we have a population of 35 students (15 males + 20 females) and we want to select a sample of 7 students. The group of interest is the females, which consist of 20 students. Since we are selecting without replacement, we need to use the hypergeometric distribution formula:

P(X = k) = (C(K, k) * C(N-K, n-k)) / C(N, n)

where:

N = total population sizen = sample sizeK = number of successes in the populationk = number of successes in the sample

Plugging in the values, we get:

P(X = 4) = (C(20, 4) * C(15, 7-4)) / C(35, 7)

Calculating the combinations, we find that P(X = 4) = 0.416

Learn more about probability here:

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Compare the two ratios by entering >, < , or = in the box. 18 320

Answers

< because 320 is greater than 18

plz mark brainliest.

Answer:

1/8 is greated than 3/20

Step-by-step explanation:i took test

Need help please
What is the result of dividing 2x^3−3x^2−17x+30 by x + 3?
2x^2+3x−8
2x^2−9x−44
2x^2+3x−26
2x^2−9x+10

What is the result of dividing x^3−7 by x + 2?
x^2−2x+4+15/x+2
x^2−2x+4+1/x+2
x^2−2x+4−1/x+2
x^2−2x+4−15/x+2

What is the remainder when the polynomial 6x^2+11x−3 is divided by 2x−1?

What is the remainder when the polynomial 5x^2+10x−15 is divided by x + 5?

Answers

Use synthetic division for these questions. I did all of them, but only showed my step by step work for one of them. If you have any questions about the other answers or are stuck please comment back on this answer with a question and I'd be happy to respond!

Answers:
1. 2x^2−9x+10
2. x^2−2x+4+15/x+2 (don't forget to put 0's in for the coefficients of [tex] x^{2} [/tex] as well as [tex]x[/tex])
3. The remainder is 4. (In the new equation this would be written as [tex] \frac{4}{2x-1} [/tex])
4.The remainder is 60.

I included my last page of work in case it helps, but it is not step-by-step so if you have questions, please ask!

Final answer:

The quotient and remainder for the provided polynomial divisions are as follows: 1) 2x^2−9x−44, 2) x^2−2x+4+1/x+2, 3) Remainder 1, 4) Remainder 0.

Explanation:

The process of dividing polynomials is similar to the long division method used in arithmetic. For your first question, the result of dividing 2x^3−3x^2−17x+30 by x + 3 comes out to be 2x^2−9x−44.

For the second question, when x^3−7 is divided by x + 2, the result is x^2−2x+4+1/x+2.

Coming to your third question, when the polynomial 6x^2+11x−3 is divided by 2x−1, the remainder is 1.

Lastly, when the polynomial 5x^2+10x−15 is divided by x + 5, the remainder is 0.

Learn more about Polynomial Division here:

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Where is the x-intercept(s) in the graph of y = (x-1)(x+8)/(x+8)(x-6)?

Answers

[tex] \frac{(x-1)(x+8)}{(x-6)(x+8)} = \frac{(x-1)}{(x-6)} [/tex]

The x-intercepts are where the graph crosses the x-axis, in other words what x is when y = 0. This is only when the numerator is zero. After simplifying and factoring out the (x+8), y = 0 only when x = 1.

* When x = 6 the denominator is zero and the function is undefined. x = 6 would then be a vertical asymptote.

Answer:

B: 1

Step-by-step explanation:

Edge 2021

Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating.

Answers

Given that one Friday night, Roman and Malou are busy studying for their Logic exam. Meanwhile, Hadji just tweeted a picture of himself eating crispy pata and sisig. Jeff is sound asleep in his dorm room.

Part A:

The truth value of "Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating." is obtained as follows:

From the scenario, the truth value of the individual statements are as follows:

Roman has a date with Malou is True

Jeff is sleeping is True

Hadji is eating is True

Thus, the truth value of "True" or "True" or "True" is True.

Therefore, the truth value of "Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating." is True.

Part B:

The truth value of "Either Jeff is sleeping or Hadji is not eating" is obtained as follows:

From the scenario, the truth value of the individual statements are as follows:

Jeff is sleeping is True

Hadji is not eating is False

Thus, the truth value of "True" or "False" is True.

Therefore, the truth value of "Either Jeff is sleeping or Hadji is not eating" is True.

Part C:

The truth value of "Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating." is obtained as follows:

From the scenario, the truth value of the individual statements are as follows:

Roman and Malou are on a date is True

Jeff is sleeping is True

Hadji is not eating is False

The truth value of "True" and "True" is True.
The truth value of "True" or "False" is True.

Thus, the truth value of ("True" and "True") or "False" is True.

Therefore, the truth value of "Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating." is True.

Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating. - True b. Either Jeff is sleeping or Hadji is not eating - True c. Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating. - False

HELP
IMPORTANT 20 POINTS

Answers

volume of tub = 20 *10*10 = 2000cm^3

2000*1/16 = 2000/16 = 125 cubic cm of ice scream left

volume of sphere = 4/3*3.14*3^2 = 37.68 / 2 = 18.84

volume of cone = 18.84

18.84 = 1/3 *3.14*r^2*h

18.84 = 9.42*h

h = 18.84 / 9.42 = 2.00 inches tall

What plane contains points D, G, and H?

a. The plane that passes at a slant through the figure.
b. The plane on the bottom of the figure.
c. The plane on the top of the figure.
d. The plane on the front of the figure.

Answers

I think it is d. But I think you should check to make sure.

A regular 40-sided polygon is rotated with its center of rotation at its center. What is the smallest degree of rotation needed to map the polygon back on to itself?

Answers

hey! the answer would be A regular 40-sided polygon has an interior angle equal to:
(40 - 2) (180) /40 = 171 degrees

The interior angle is also the smallest angle that is needed to rotate the polygon and map it unto itself. So, the smallest degree of rotation needed to map the polygon back to itself is 171 degrees.

Answer:

9 degrees

Step-by-step explanation:

i dont know what the other guy is talking about, its 360/40=9

Consider the system of equations

{ -2x + 6y = -8
{ cx + 3y = -4

What value of c would produce a system that has an infinite number of solutions?
Justify your answer.

Explain why there is no value of c that would produce a system with no solution.

Enter your answer, justification, and explanation in the box provided.

Answers

Make the equation the same or a multiple of the other to have an infinite number of solutions. See how the -8/2= -4 and 6/2=3 ? then -2/2 = c
Make c = -1 and they are the same linear equation. (same slope, same intercepts, same line) and therefore have infinite solutions.

In order to have no solutions, the lines cannot cross at all and so they must be parallel but not the same line. Parallel lines have the same slope with different intercepts. if you rearrange both equations in slope intercept form:
y = x/3 - 4/3
y = - cx/3 - 4/3

no matter what you make c the lines will always cross at the y-intercept (0, -4/3). this is a solution and therefore there's no value of c that would produce a system with no solution.

WILL MARK BRAINLIEST ANSWER THIS QUESTION K

Answers

For the first question, the choice at the bottom left corner is the answer.
For the second question, the two equations that represent the system of inequalities are y < 1- 3x and y ≥ 0.5x - 1

If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. (round your answers to two decimal places.)

Answers

Let h = height of the box,
x = side length of the base.

Volume of the box is [tex]V=x^{2} h = 115 [/tex].
So [tex]h = \frac{115}{ x^{2} } [/tex]

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
[tex]S = 2( x^{2} + hx + hx) \\ = 2 x^{2} + 4hx \\ = 2 x^{2} + 4( \frac{115}{ x^{2} } )x[/tex]
[tex]= 2 x^{2} + \frac{460}{x} [/tex]
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

[tex]S' = 4x- \frac{460}{ x^{2} } = 0[/tex]
[tex] 4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86 [/tex]
Then [tex]h= \frac{115}{4.86^{2}} = 4.87 [/tex]
So the box is 4.86 in. wide and 4.87 in. high.

length = 6.13 Width = 6.13 Height = 3.06 Let's use the variable L to represent the length of a bottom edge of the box. With that, the height of the box will be 115 / w^2. Since the box is open, the box will have a bottom, and 4 sides. No top. So the expression for the surface area of the box will be w^2 + 4w(115/w^2) = w^2 + 460/w Since we're looking for a local minimum, that will be at a point where the first derivative of the function is 0. So the first derivative is: 2w - 460/w^2 = 2w^3/w^2 - 460/w^2 = (2w^3 - 460)/w^2 = 2(w^3 - 230)/w^2 The above derivative has a real zero at the cube root of 230 which is approximately 6.126926 So the length of the sides of the box are 6.13 inches and the height of the box is 115/(6.13^2) = 3.06 inches.

A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (4072-01-01-03-00_files/i0260000.jpg), how long is the rectangle? a. 21 inches b. 340 inches c. 20 inches d. 15 inches

Answers

A = L * W
A = 357
W = 17

357 = 17L
357 / 17 = L
21 = L <== length is 21 inches

Answer:

The correct option is: a. 21 inches

Step-by-step explanation:

The area of the rectangle is 357 square inches and width is 17 inches.

Formula for the area of rectangle is: [tex]Area= Length\times Width[/tex]

Suppose, the length of the rectangle [tex]=x[/tex] inches.

So, the equation will be.....

[tex]357=x\times 17\\ \\ \frac{357}{17}=\frac{x\times 17}{17}\ [Dividing\ both\ sides\ by\ 17]\\ \\ 21=x[/tex]

So, the rectangle is 21 inches long.

Are the following equations parallel, perpendicular, the same line, or none of these -4x = -5y + 30
5y = -4x + 30

Answers

Answer:

parallel

Step-by-step explanation:

HELP PLEASE APPRECIATED Margarita is driving at the speed of s-4/ s^2- 9s + 20 miles per hour.

The distance Margarita covers in s-5/4 hours is ___ miles.
Give the answer in simplest form.

Only correct answers and please show your work so I can refer to it on my other problems. thank you.

Answers

d = V • t ... displacement = velocity • time
d = [(s – 4) ⁄ (s² – 9s + 20)] • [(s – 5) ⁄ 4] ... rearrange terms
d = (s – 4) • (s – 5) ⁄ [4(s² – 9s + 20)] ... factor denominator
d = (s – 4) • (s – 5) ⁄ [4(s – 4) • (s – 5)]
d = ¼ mile

The distance Margarita covers in [tex]$ \frac{s-5}{4} $[/tex]hours is [tex]$ \frac{1}{4} $[/tex] miles.

Given that Margarita is driving at the speed of [tex]$ \frac{s-4}{s^2 - 9s + 20} $[/tex] miles per hour, we can express the distance function as:

[tex]\[ d(s) = \text{speed} \times \text{time} = \left( \frac{s-4}{s^2 - 9s + 20} \right) \times s \][/tex]

[tex]\[ d\left(\frac{s-5}{4}\right) = \left( \frac{s-4}{s^2 - 9s + 20} \right) \times \frac{s-5}{4} \][/tex]

Let's simplify this expression:

[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{(s-4)(s-5)}{4(s^2 - 9s + 20)} \][/tex]

[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{s^2 - 9s + 20}{4(s^2 - 9s + 20)} \][/tex]

[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{1}{4} \][/tex]

What is the total displacement of a student who walks 3 blocks east, 2 blocks north, 1 block west and then 2 blocks south?

Answers

The total displacement is 2 since its last position is 2 blocks east from the initial position

The total displacement of the student is 2 block east.

We know that displacement refers to less distance that shows the difference between the starting & the final position.

Based on this,

y = 2 -2 = 0

x = 3 - 1 = 2

So, we can conclude that the total displacement of the student is 2 block east.

Learn more about the displacement here: brainly.com/question/11934397

Why do elephants have pointy tails

Answers

i'm finding it hard to see how this is math... real smart, btw. Thanks for the free points!

Pointy tails help make elephants more streamlined and aerodynamic

Find the measure of angle e.
A. 70°
B. 130°
C. 100°
D. 110°

Answers

Knowing about corresponding angles, we know that m∠d = 70°.

The sum of the measures of the angles d and g is equal to 180°. Or in other words, they are supplementary.

Knowing this, we can use algebra to build an equation and solve for g.

70° + m∠g = 180°
m∠g = 110°

And finally, using the knowledge of vertical lines, ∠g is complementary to ∠e.

So, m∠e is equal to 110°.

Write an equation of the line in slope-intercept form of the line that passes through the point (-5, 1) and is parallel to the line x – 5y = 8. show your work.

Answers

-5y=-x+8
y=1/5x-8/5

y-1=-5(x+5)
y-1=-5x-25
y=-5x-24

What is the product of 3x(x^2+4)

Answers

Answer:

[tex]3x^3+12x[/tex]

Step-by-step explanation:

[tex]3x(x^2+4) = 3x\cdot x^2 + 3x\cdot 4 = 3x^3+12x[/tex]

Simplify:
(3-4i)(1+5i)-(2-i)

Show all of your work please

Answers

So first you want to do the multiplication.

(3-4i)*(1+5i)

So what you want to do is multiply everything inside the parenthesis by everything inside the other parenthesis.

Or,

3 * 1 + 3 * 5i + -4i * 1 + (-4i) * 5i

Or,

3 + 15i + -4i - 20i

Then,

3 + -9i

3 - 9i - (2 - i)

Open the parenthesis, and since it has a minus before it reverse the operator inside of the parenthesis.

3 - 9i - 2 + i

Or,

1 - 8i

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Find the remainder when f(x) is divided by (x - k). f(x) = 4x3 - 5x2 + 2x + 11; k= 3

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Find the remainder when f(x) is divided by (x - k).
f(x) = 4x3 - 5x2 + 2x + 11; k= 3