Find the remainder when f(x)=2x3+2x2−3x−3 is divided by x−2.

Answers

Answer 1

Given:

The function is:

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

To find:

The remainder when the given function is divided by [tex]x-2[/tex].

Solution:

According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).

We have,

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

This function is divided by [tex]x-2[/tex]. By using the remainder theorem, the remainder is f(2).

Putting [tex]x=2[/tex] in the given function, we get

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

[tex]f(2)=2(8)+2(4)-6-3[/tex]

[tex]f(2)=16+8-9[/tex]

[tex]f(2)=15[/tex]

Therefore, the remainder is 15.


Related Questions

An auto dealership sells minivans and sedans. In January, they sold 10 minivans and 20 sedans. In February, they sold 7 minivans and 14 sedans. During which month did the auto dealership sell a lower ratio of minivans to sedans?

Answers

Answer:

january = 10/20 = 1/2

februry = 7/14 = 1/2

so, we conclude that the auto dealership didn't have a lower ratio, since the ratio is equal in both months.

hope it helps :)

Help please i will give brainliest

Answers

Answer:

48

Step-by-step explanation:

To find how many 1/3 cm length cubes fill the prism, we first need to find the volume, which is equal to

length * width * height = 1 cm * (2 + 2/3) cm * (2/3) cm

= 1 cm * (6/3 + 2/3) cm * (2/3) cm

= 1 cm * (8/3) cm * (2/3) cm

= (8/3) cm ² * (2/3) cm

= (16/9) cm³

Therefore, the volume is 16/9 cm³.

Next, one cube with side lengths of 1/3 has a volume of ((1/3) cm)³ = (1/27)³

We thus need to find how many of 1/27 goes into 16/9

If we multiply 16/9 by 1=3/3 (as 9*3=27), we can equalize the bases, making 16/9 = 48/27

All that's left is to figure out how many times 1/27 goes into 48/27, which is equal to (48/27)/(1/27) = 48

Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).

Answers

Answer:

Ax + By = C is standard form.

y + 1 = (2/3)(x - 8)

distribute the (2/3)

y + 1 = (2/3)x - (16/3)

Multiply each term by 3 to clear the fractions.

3y + 3 = 2x - 16

Subtract 2x from both sides.

-2x + 3y + 3 = - 16

Subtract 3 from both sides.

-2x + 3y = - 19

Correct form typically has the leading coefficient as a positive number so multiply each term by - 1.

2x - 3y = 19

Step-by-step explanation:

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

got it right on edge

S is the centroid of the triangle. Find IT if ST= 9

Answers

Answer:

IT = 13.5

Step-by-step explanation:

Recall: According to the Centroid theorem the Centroid of is ⅔ of the distance of the vertex of the triangle to the midpoint of the opposite side.

This means that:

ST = ⅔(IT)

ST = 9 (given)

Substitute

9 = ⅔(IT)

Multiply both sides by 3

3*9 = 2(IT)

27 = 2(IT)

Divide both sides by 2

27/2 = IT

IT = 13.5

Second time posting this. Please help!! :)

Answers

Answer:

Step-by-step explanation:

[tex]\frac{480+24(x-40)}{x}[/tex]

The numerator of the rational expression the money he earned for 'x' hours

The rate at which William is paid for each hour in excess of 40 hours 24.

x = 50 hours = (40 + 10 ) hours

The amount paid for excess 10 hours = 24 *10 = 240

Total amount earned for the week = 480 + 240 = 720

*** SOMEBODY HELP ME**

Point p is the circumcenter ABC. Point p is the point of concurrency of the perpendicular bisector. Find AS

Answers

Answer:

AS = 46

Step-by-step explanation:

The circumcentre is equally distant from the triangle' s 3 vertices , then

AS = BS = 46

1 by 8 of the passenger of a train where children is there where 40 children traveling in the train on a Saturday how many Abbott were there in that that day?

Answers

Answer:

200 adults

Step-by-step explanation:

1/8 of the passengers (children) is 40

Total passengers in the train is 8/8

Therefore to get the total number of passengers is given by

(8/8) × 40 × (8/1)

= 240 passengers

Adults in the train = Passengers - Children

= 240 - 40

= 200 adults

Identify the range of the function shown in the graph.​

Answers

Answer:           The answer is all real numbers

Step-by-step explanation:

This is the answer because the line goes on infinitely and will pass through all of the numbers (negative, positive). Its not y [tex]\geq \\[/tex] 0 because it passes through 0 when the line goes through x (side to side) axis.

is the equation below a function? explain
d) y2 = x2 + 5​

Answers

Answer:

No

Step-by-step explanation:

y^2 = x^2 + 5​

Rewriting

y^2 - x^2 = 5

This is a hyperbola

We can use the vertical line test to show that it is not a function since a vertical line passes through more than one point.

If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.

Answers

Answer: [tex]26.4\ \text{days}[/tex]

Step-by-step explanation:

Given

Half life of radioactive substance is [tex]T_{\frac{1}{2}}=20\ \text{days}[/tex]

Initial amount [tex]A_o=2\ \text{days}[/tex]

Amount left at any time is given by

[tex]\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}[/tex]

It takes 26.4 days to reach 2 gm.

Solve the proportion.
14
y +9
-
10
15
y = [?]

Answers

Answer:

y=12

Step-by-step explanation:

14          10

----- =  --------

y+9         15

Using cross products

14*15 = 10 (y+9)

210 = 10(y+9)

Divide by 10

210/10 = 10(y+9)/10

21 = y+9

Subtract 9

21-9 = y

12 =y

what is 8^100 / 8^50 is 8^50?

Answers

Answer:

8^50

Step-by-step explanation:

8^100 / 8^50

We know that a^b / a^c = a^(b-c)

8^(100-50)

8^50

write an equation of the circle with center (-2,-9) and radius 10

Answers

Answer:

[tex](x+2)^{2}[/tex] + [tex](y+9)^{2}[/tex] = 100

Step-by-step explanation:

Standard Equation of a Circle

[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]

(h,k) = center of circle

r = radius of circle

Substitute in given. Watch the negatives.

Lucia gave Brenda half of the cash she had in the store counter at the end of the day. Brenda put the money in her purse and added one half of the amount she had from her own savings. Brenda had saved half of what Lucia earned in the store that day. Brenda took her purse and went to the dog shelter and brought food and treat packet for 5 dogs. Each packet cost her $15. How much money did Lucia earn at the store that day?

Answers

Answer:

$100

Step-by-step explanation:

The amount Lucia gave Brenda = Half the amount in the store counter

The amount Brenda added to the money Lucia gave her = Half the amount in her (Brenda) savings

The amount Brenda had saved = Half of the amount Lucia earned in the store that day

The number of food and treat packets Brenda bought = 5

The cost of each packet = $15

Let x represent the amount Lucia earned and let y represent the amount Brenda saved

We have;

x/2 = y

x/2 + y/2 = 15 × 5 = 75

Therefore, we get;

y + y/2 = 75

(3/2)·y = 75

y = 75 × 2/3 = 50

y = 50

From x/2 = y, we have;

x/2 = 50

x = 2 × 50 = 100

The amount Lucia earned in her store that day, x = $100

Express 34C21 as a sum of two terms from pascals triangle.

Answers

Given:

The combination is:

[tex]^{34}C_{21}[/tex]

To find:

The [tex]^{34}C_{21}[/tex] as the sum of two terms from pascals triangle.

Solution:

According to the pascals triangle:

[tex]^{n+1}C_{r+1}=^nC_r+^nC_{r+1}[/tex]

We have,

[tex]^{34}C_{21}[/tex]

Using the pascals triangle formula, we get

[tex]^{34}C_{21}=^{33}C_{20}+^{33}C_{21}[/tex]

Therefore, [tex]^{34}C_{21}=^{33}C_{20}+^{33}C_{21}[/tex].

2cm + 5cm + 6.4cm cuboid

Answers

Answer:

64 volume of the cuboid

formula used is lbh multiplies together.

Mark me as brainliest

Hope it helps:)

Step-by-step explanation:

A ball is thrown into the air with an upward velocity of 36 ft/s. It’s height h in feet after t seconds is given by the function h = -16t^2 + 36t + 9. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the balls maximum height ?

Answers

Answer:

Time taken for the ball to hit the ground back = 3.08 s

Step-by-step explanation:

h(t)= -16t² + 48t + 4

when will rhe object come back to hit rhe ground?

When the ball is at the level.of the ground, h(t) = 0.

0 = -16t² + 48t + 4

-16t² + 48t + 4 = 0

Solving the quadratic equation

t = 3.08 s or t = -0.08 s

Since the time cannot be negative,

Time taken for the ball to hit the ground back = 3.08 s

Hope this Helps!!!

Step-by-step explanation:

A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet

Answers

Answer:

Step-by-step explanation:

starting point: 140 feet below sea level.=-140

she then decends= 7(4.5)=31.5

-140-31.5=-171.5

finally she ascends 112.2 feet

-171.5+112.2=-59.3 feet or 59.3 feet below sea level

Answer:

It's B

Step-by-step explanation:

The scatter plot shows the number of cars and trucks sold by 10 different employees at a car and truck dealership during a month.

How many employees sold more cars than trucks?



Enter your answer in the box.

Answers

Answer:

3 employees

Step-by-step explanation:

The best way to obtain a solution is to note the coordinate if each point on the scatter plot :

Where, the x - axis represents the number of cars sold and y - axis represents the number of trucks sold.

So, the number of employees that sold more cars than trucks exists where the x - axis value is greater than its corresponding y-axis value.

The scatter plot points : (2,4) (4,3) (3,7) (3,9) (4,8) (5,6) (5,7) (6,6) (9,0) and (10,1)

Points where x-axis > y-axis with each coordinate representing an employee :

(4,3) ; (9,0) and (10,1) = 3 employees.

To make a disinfecting solution, Alana mixes 2 cups of bleach with 5 cups of
water. What is the ratio of water to the total amount of disinfecting solution?

Answers

Answer:

Step-by-step explanation:

Ok

how to solve (n^(3)+3n^(2)+3n+28)-:(n+4) in long polynomial division?

Answers

Answer:

Open the image. (Hope you don't mind about bad writing)

There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that
the first horse selected is tan and the second horse selected is brown?
20/81

5/18

2/9

1/20

Answers

Answer:

5/18

Step-by-step explanation:

The total number of horses present is 9

The probability that the first selected horse is tan is 4/9

So , now for the second choice , we are left with 8 total horses of which 5 is brown

The probability is 5/8

So the joint probability is the product of this two

That will be;

5/8 * 4/9 = 5/18

If you roll a standard number cube 42 times, how many times do you expect the cube to show a five?
Round your answer to the nearest whole number if needed.

Answers

Answer:

5

Step-by-step explanation:

this is probability

probability of 5 occuring once is = 5/42=0.119

therefore, probability of 5 occuring in 42 times is;

42 x 0.119=4.998

approximately 5

Grade improvement and study motivation

Answers

Answer:

yes you are write because when our results come with good marks and grade the we are motivate .

Step-by-step explanation:

thanks mark me brainlist

Si gasto el 90% de mis ahorros, me queda la decima parte de los que habia ahorrado?

Answers

Answer:

Si

Step-by-step explanation:

100% - 90% = 10%

10% = 0.10 = 1/10

Respuesta: Si

I’m horrible at math and I need to study for the TSI. Help? 4/5+1/10+5/6

Answers

Answer:

4 ÷ 5 + 1 ÷ 10 + 5 ÷ 6 = 1.733

Step-by-step explanation:

4/5 + 1/10 + 5/6

One thing you can do is make the denominator equal.

4/5(2/2) + 1/10 = 8/10+1/10 = 9/10

9/10 +5/6

Or you could cross multiply, by multiplying the denominator with the opposite numerator (this is the numerator) then multiply the denominator ( this is the denominator)

(6(9)+5(10))/6(10) = 104/60 then simplify to 26/15

Someone please help me!! I don’t know the answer!!

Answers

Answer:

Step-by-step explanation:

Remark

The measurement of the arc is 3Pi

that represents 108 / 360 of the circle.

Equation

108/350 2 * pi * R = 3* pi

Solution                            

Pi is on both sides of the equation. They both cancel.

108/360 = 0.3

0.3 * 2 * R = 3

0.6 * R = 3

R = 3/0.6

R = 5

The answer would be R= 5

dididjdjdjdhjdjdh < so that i could answer

Three events A, B and C are defined over a sample space, S. Events A and B are independent. Events A and C are mutually exclusive. Given that P(A)= 0.04, P(B)=0.25, P(C)=0.20 and P(B/C)=0.15. Find for P(C/B)

Answers

Answer:

[(b/c)=0.15)]

Step-by-step explanation:

Answer:  0.12

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

Work Shown:

P(B/C) = P(B and C)/P(C) ... conditional probability formula

P(B and C) = P(C)*P(B/C)

P(B and C) = 0.20*0.15

P(B and C) = 0.03

------------

P(C/B) = P(C and B)/P(B) .... note the swap of B and C

P(C/B) = P(B and C)/P(B)

P(C/B) = (0.03)/(0.25)

P(C/B) = 0.12

------------

Extra notes:

The fact that events A and B are independent is not relevant.The fact A and C are mutually exclusive isn't used here either.This problem can be solved through Bayes' Theorem.Another alternative you can do is to set up a 3 by 3 contingency table to help solve this problem.

Find AC, given that line AD is the perpendicular bisector of BC

Answers

Answer:

wouldn’t it just be 21? because both are the same but mirrored

what is x(2)+y(6) if x=4 and y=(-4)


Also, can anyone just talk?

Answers

Answer:

-16

Step-by-step explanation:

Follow . PEMDAS

plug the numbers in

4*2 =8 and -4*6=24

add both...

-16.

Step-by-step explanation:

4(2)+(-4)(6)

8-24

-16

hope it helps..

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