Given that, 2x^3 + 5x^2+7x + 23 = A(x+1)^3+ B(x + 1)^2 +Cx+ 22 for all values of x, evaluate A, B and C. Hence, state the remainder when 2x^3 +5x^2 + 7x+23 is divided by x^2 + 2x +1.​

Answers

Answer 1

Answer:

A = 2

B = -1

C = 3

remainder= 19

Step-by-step explanation:

A(x+1)³ + B(x+1)² + Cx + 22 =

A(x³ + 3x² + 3x + 1) + B(x² + 2x + 1) + Cx + 22 =

Ax³ + (3A + B)x² + (3A + 2B + C)x + (A + B + 22) =

2x³ + 5x² + 7x + 23

A = 2

3A + B = 5 → 3(2) + B = 5 → B = 5 - 6 → B = -1

3A + 2B + C = 7 → 3(2) + 2(-1) + C = 7 → C = 7 - 6 + 2 →

C = 3

remainder :

(2x³ + 5x² + 7x + 23 )/ (x² + 2x + 1) =

(2x³ + 5x² + 7x + 23 )/ (x + 1)²

(x + 1)² = 0 → x = -1

2(-1)³ + 5(-1)² + 7(-1) + 23 = -2 + 5 - 7 + 23 = 19


Related Questions

Nicole buys three juice boxes to share with her friends the total cost is $5.25 she pays with a $20 dollar bill how much change should she get back?

Answers

Answer:

14.75

Step-by-step explanation:

Subtract $5.25 from $20 to get the result.

What is the y-intercept (b) of the line with the equation y=3x+4

Answers

Answer:

your y-intercept is the line at which that line crosses or bisects the y-axis.

.°. y=4

(10x -20) (6x + 8)°
what is the value of x

Answers

Answer:

X=12

Step-by-step explanation:

Add the two equations together and equate them to 180 due to the geometrical reason that angles on a straight line add up to 180.

10X-20+6X+8=180 (collect like terms)

10X+6X=180-8+20

16X=192 (Divide both sides by 16)

X=12

Hope that helps :)

Rectangle ABCD has vertices A(2, 3),

B(1, 4), C(0, 3), and D(3, 5). Find the

vertices of rectangle A'B'C'D' after a

translation of one units right(+1) and 2 units down(-2)

Answers

Answer:

Step-by-step explanation:

THE FASTEST AND CORRECT ANSWER GETS BRAINLIEST!!! ANSWER TO GET BRAINLIEST!!!!!!!!!

Answers

Hi there!!

i think answer is 16 minutes

Because 5÷3=1.6

Remove the point so it will be 16 min.

Im not sure if my answer is correct

Mykayla is 12 years old, and her mom is 48 years old. What percent of her mom's age is Mykayla's age?​

Answers

Answer:

25%

Step-by-step explanation:

12/48=1/4

1/4=25%

Answer:

Her mom's age is 25% her age! tell me if its right!

Step-by-step explanation:

hope i helped

Azakai writes the expression "one third of the product of 9 and a number." a. Write an Algebraic expression that is equivalent to Azakai's expression. b. Write a second algebraic expression that is different from, but equivalent to your first expression.​

Answers

Let the number be x

[tex] \rightarrow \: 9x = \frac{1}{3} \\ [/tex]

a second algebraic expression that is different from, but equivalent to the first eexpression

[tex]\rightarrow \: x = \frac{1}{27} \\ [/tex]

Answer:

=> let the unknown number be x

so ,

=> 9x = 1/3 ..i)

=> x = 1/27 ...ii) { it's different but equivalent }

Solve for g.
g/6 - -53 = 57

Answers

Step-by-step explanation:

g/6 - -53 = 57

g/6 + 53 = 57

g/6 = 4

g = 4×6 = 24

Select all the correct conversions.

4 cups = 16 fl oz

9 qt =214 gal

6 gal = 24 qt

8 cups = 2 pt

4 fl oz =12 cup

Answers

4 cups = 32 fl oz
9qt = 2.25 gal
6 gal = 24 qt ✅
8 cups = 3.3307 pt
4fl oz = 0.5 cup

These are all the correct conversions and the only right one is the third one (6 gal = 24 qt)

Answer:

4 fl oz =12 cup

9 qt =214 gal and 6 gal = 24 qt

Step-by-step explanation:

Based on the experiment, what is the probability of landing on heads? Ty flipped a coin and counted how many times it landed on heads and how many times it landed on tails. The frequencies are shown in the following table. Result Number of Times Flipped Heads 26 Tails 30 Based on the experiment, what is the probability of landing on heads? Enter your answer as a fraction, like this: 42/53ur answer as a fraction, like this: 42/53

Answers

Answer:

the possibility of it landing on heads is 50/50

there is a 50% chance of it landing on heads and there is a 50% chance of it landing on tails

Step-by-step explanation:

however, there is also more of a possibility of it landing on tails because of the fact that Ty flipped the coin and it landed on tails more than heads

so I'd say abt 85/100 are the possibilities of it landing on heads

Vera orders some prints of photos that she uploaded to her computer. She orders 3 of the 5 x 7 prints for $0. 89 each, 12 of the 4 x 6 prints for $0. 15 each and 1 of the 8 x 10 prints for $2. 99. She also orders a photo album for $8. 69. Vera pays taxes that are 7% of the total purchase price. Her shipping charges are based on the following table: Amount of Purchase Standard Shipping Express Shipping up to $20 free $3. 50 $50 up to $100 $6. 35 $8. 20 $100 up to $200 $7. 80 $11. 60 $200 and over $10. 50 $16. 45 Vera selects standard shipping and the company bills her credit card $20. 78 for the total of the online purchase. Determine if Vera has been billed correctly for her purchase. A. Vera has been billed correctly. B. Vera has not been charged enough for her purchase. C. Vera has been over charged by $1. 13 for her purchase. D. Vera has been over charged by $3. 50 for her purchase.

Answers

For the total purchase, vera has been overcharged by $3. 50 for her purchase.

What will be the total purchasing price of the vera?

We have information that

3 orders at 0.89$

[tex]=3\times 0.89=2.67[/tex]$

12 orders for 0.15$

[tex]=12\times0.15=1.8[/tex]$

for 1 order 2.99$

[tex]=1\times 2.99=2.99[/tex]$

and also 8.69$ for a photo album

so total amount = 2.67+1.8+2.99+8.69= 16.15$

Now 7% of the tax =[tex]16.15\times1.07=17.2805[/tex]

Thus the difference of the amount =20.78-17.2805=3.5$

Thus the total purchase, vera has been overcharged by $3. 50 for her purchase.

To know more about logical questions follow

https://brainly.com/question/1403435

Answer:

D. Vera has been over charged by $3.50 for her purchase.

Step-by-step explanation:

I just did the assignment!

can i please have the answer

Answers

volume of cuboid : 400 cm²

A cuboid has its base length similar.

volume of a cuboid : side * side * height

[tex]\hookrightarrow \sf 4 * 10 * 10[/tex]

[tex]\hookrightarrow \sf 400 \ cm^2[/tex]

Solution:

We know that:

[tex]\tex\text{Volume of square based cuboid:} \ \text{Length} \times \text{Length} \times \text{Height}[/tex]

[tex]\text{Length = 10 cm}[/tex]

[tex]\text{Height = 4 cm}[/tex]

Finding the volume of the square based cuboid:

[tex]\tex\text{Volume of square based cuboid:} \ \text{Length} \times \text{Length} \times \text{Height}[/tex]

[tex]\tex\text{Volume of square based cuboid:} \ 10 \times 10 \times 4[/tex]

[tex]\text{Volume of square based cuboid:} \ 100 \times 4[/tex]

[tex]\boxed{\bold{\text{Volume of square based cuboid:} \ 400 \ \text{cm}^{3}}}[/tex]

PLEASE HELP!
8th grade math

Answers

The minimum value is -7 and it’s decreasing from x=-10
I believe that these are the answers.

B.-8 it is the lowest point on the graph

C. Decreasing it goes gone from the two points

Hope this helps

8. Mrs. Reed bought 6 carnations that were
$0.39 each. How much money did she
spend?

Answers

Answer:

2.34

Step-by-step explanation:

:)

2.34

Multiply 0.39 by 6!

grade 5 classify the quadrilateral​

Answers

Answer:

Step-by-step explanation:

A quadrilateral is a four-sided shape. Two sides of a shape are parallel if lines placed along them never cross. In a quadrilateral, parallel sides must be opposite sides. This means they do not share a vertex.

Answer:

A simple example could be a square or a rectangle. They both have four sides and they have parallel lines.

Step-by-step explanation:

PLEASE MARK AS BRAINLIEST!!!

5(x + 4)
What is the answer?

Answers

Answer:

9x

Step-by-step explanation:

PEMDAS, x + 4 = 4x

4x+5=9x

=9x

Hope this helps

Answer:

5x+20

Step-by-step explanation:

Simplify:

5(x + 4)

5x + 20

−3 (x+4) −2 ≥ 2x+6
Solve for X.

Answers

Answer:

[tex]x \leqslant - 4[/tex]

Step-by-step explanation:

[tex] - 3(x + 4) - 2 \geqslant 2x + 6[/tex]

[tex] - 3x - 12 \geqslant 2x + 6[/tex]

[tex] - 3x14 \geqslant 2x + 6[/tex]

[tex] - 3x - 2x \geqslant 6 + 14[/tex]

[tex] - 5x \geqslant 20[/tex]

[tex] \frac{ - 5x}{ - 5} \leqslant \frac{20}{ - 5} [/tex]

[tex]x \leqslant - 4[/tex]

WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER, YOU MUST CHANGE THE SIGNS:

[tex] \leqslant \\ \geqslant \\ > \\ < [/tex]

Hope It Helps
Brainliest plss! :)

Abby is decorating the bulletin board outside her classroom. She needs 1/4 of a sheet for each Easter egg and 4 full sheets for the title. if she has 18 sheets how many Easter eggs can she make

Answers

Answer:

3.5 easter eggs, or if you round, 3 total eggs

Step-by-step explanation:

18-4=14

14/4=3.5

She can make 3.5 easter eggs, or if you round, 3 total eggs

Please help, and if you do, please answer all three questions. 30 points!! Everything is listed below!!

Answers

Answer:

the answer is 45%.

Step-by-step explanation:

if you add 5% divided by 3 = 15%.

So if you add all of those plus the 30% you will be getting 45%.

There are 2 squares, 2 triangles, 2 hexagons, and 2 circles in a teacher’s bag of shapes. If a student randomly selects 1 shape from the bag, what is the probability that the student selects a circle?

a 0.75

b 0.5

c 0.25

d 0.2 pls hurry

Answers

C. 0.25 because you add all them to make a fraction 2/8 because there is two circles

What are some differences of a credit and debit card?

Answers

Answer:

A credit card you have to pay back the money you spend to the credit card company.

While with a debit card it takes money straight out of your bank account.

22.40 tourists are coming from Switzerland to visit Mt Everest. They planned to stay at Everest base camp for 4 days. For this purpose they ordered some squared base pyramid tent in Nepal. A tent can holds people and each person have o fitx3ft space on the ground withi 48 cu. of air to breadth. Find the total cost of all tents at the rate of Rs.560 per feet square



Answers

The cost of 32.57ft^2 is Rs. 18,239.2 which is the cost of renting one tent.

Data;

Height = 48cu = 48 cubic feet = 3.63 feetedge length = 3ftarea = ?

Area of a Square Pyramid

The formula of a square pyramid is given as

[tex]A = l^2 + 2l\sqrt{\frac{l^2}{4} + h^2} \\[/tex]

Let's substitute the values and solve for the area of the square pyramid.

[tex]A = l^2 + 2l\sqrt{\frac{l^2}{4} + h^2} \\\\A = 3^2 + 2*3\sqrt{\frac{3^2}{4} + 3.63^2} \\A = 9 + 6{\sqrt{15.43} } \\A = 32.57ft^2[/tex]

Since the cost of 1 square foot  = Rs. 560

32.57 ft^2 = x

[tex]1sq = 560\\32.57 = x\\x = 32.57 * 560\\x = 18,239.2[/tex]

The cost of 32.57ft^2 is Rs. 18,239.2 which is the cost of renting one tent.

Learn more on area of square pyramid here;

https://brainly.com/question/22744289

Like buys 5 identical pencils for 30p how much would 1 pencil cost how much would 7 pencils cost

Answers

1 pencil is 6p and 7 pencils would cost 35p

Help please it’s due tommorow and I don’t know how to do it

Answers

Answer:

Where is the question?

Step-by-step explanation:

Where is the question?

Answer:

theres nothing here, you forgot to attach something or this is a prank

Step-by-step explanation:

Bertie Beetle walks so that he is the always exactly the same distance from Crumb A and Crumb B

Answers

The intersection of the circle with the arc drawn would be at points C and D.

How is an arc of a circle formed?

In Geometry, an arc is a trajectory that is formed when the distance from a given point has a fixed numerical value.

How to show the path that Bertie walked?

The steps that are to be taken to determine points C and D include:

Crumb A should be taken as the center of the circle and the radius of the arc would be 1.3 cm.Crumb B should be taken as the center of the circle and the radius of the arc would be 3.5 cm.The intersection of the circle with the arc drawn would be at points C and D.

Read more on arc length here: https://brainly.com/question/20594692

#SPJ1

Complete Question:

Bertie Beetle walks so that he is always exactly 1.3 cm from Crumb A. Adam Ant walks so that he is always exactly 3.5 cm from Crumb B. There are only two points at which they can meet - mark the points with crosses.

Find the Surface Area of the cone.

(Round the answer to nearest tenth.)
( use π = 3.14 )

Thanks!
~

Answers

Answer:

[tex]\sf \huge{\boxed{\sf area = 653.1 cm^2}}[/tex]

Explanation:

[tex]\sf \boxed{\sf area \ of \ cone=\pi r^2 +\pi rl }[/tex]

Given:

radius: 8 mslant height: 18 m

using this formula:

[tex]\hookrightarrow \sf \pi r^2 + \pi rl[/tex]

[tex]\hookrightarrow \sf (3.14)(8)^2 +(3.14)(8)(18)[/tex]

[tex]\hookrightarrow \sf 653.1 cm^2[/tex]

A computer randomly generates whole numbers from 1 to 20.find the probability that the computer generated a 12 or a multiple of 3

Answers

Answer:

[tex] \frac{3}{10} = .3 [/tex]

Step-by-step explanation:

3,6,9,12,15,18

[tex] \frac{6}{20} = \frac{3}{10 } [/tex]

PLS HELP
_______exists when a figure can be reflected such that a pre-image and the image are the same
(will give brainliest)

Answers

Answer:

Hello! symmetry

Step-by-step explanation:

Symmetry is a mirror image of an image.

Cut a hexagon in half for example

_AnnieTheDreamGirl, 3.9.22

please help no links!

Answers

I'm not sure you're not giving enough information but I'd probably go with B

*If you don’t know the answer please don’t comment*

1. Based on the information in the two-way table, what is the probability that a person selected at random is a left-handed male?
(Two-way table at the bottom)

A.) 4%

B.) 6%

C.) 52%

D.) 38%


2. Based on the information in the two-way table, what is the probability that a person selected at random is a right-handed?

A.) 56%

B.) 44%

C.) 10%

D.) 90%

Answers

Answer:

1.A

2.D

Step-by-step explanation:

Brainliest pls hardstuck ambitious

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