If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!

Answers

Answer 1

Step-by-step explanation:

Step 1:  Solve using the first point

(2, 28)

[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]

[tex]28 = 8a + 4b + 2c + d[/tex]

Step 2:  Solve using the second point

(-1, -5)

[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]

[tex]-5 = -a + b - c + d[/tex]

Step 3:  Solve using the third point

(4, 220)

[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]

[tex]220 = 64a + 16b + 4c + d[/tex]

Step 4:  Solve using the fourth point

(-2, -20)

[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]

[tex]-20 = -8a + 4b - 2c + d[/tex]

Step 5:  Combine the first and fourth equations

[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]

[tex]8 = 8b + 2d[/tex]

[tex]8 - 8b = 8b - 8b + 2d[/tex]

[tex](8 -8b)/2 = 2d/2[/tex]

[tex]4 - 4b = d[/tex]

Step 6:  Solve for c in the second equation

[tex]-5 + 5 = -a + b - c + d + 5[/tex]

[tex]0 + c = -a + b - c + c + d + 5[/tex]

[tex]c = -a + b + d + 5[/tex]

Step 7:  Substitute d with the stuff we got in step 5

[tex]c = -a + b + (4 - 4b) + 5[/tex]

[tex]c = -a + b + 4 - 4b + 5[/tex]

[tex]c = -a - 3b + 9[/tex]

Step 8:  Substitute d and c into the first equation

[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]

[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]

[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]

[tex]6 / 6 = (6a - 6b) / 6[/tex]

[tex]1 + b = a - b + b[/tex]

[tex]1 + b = a[/tex]

Step 9:  Substitute a, b, and c into the third equation

[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]

[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]

[tex]220 - 100 = 60b + 100 - 100[/tex]

[tex]120 / 60 = 60b / 60[/tex]

[tex]2 = b[/tex]

Step 10:  Find a using b = 2

[tex]a = b + 1[/tex]

[tex]a = (2) + 1[/tex]

[tex]a = 3[/tex]

Step 11:  Find c using a = 3 and b = 2

[tex]c = -a - 3b + 9[/tex]

[tex]c = -(3) - 3(2) + 9[/tex]

[tex]c = -3 - 6 + 9[/tex]

[tex]c = 0[/tex]

Step 12:  Find d using b = 2

[tex]d = 4 - 4b[/tex]

[tex]d = 4 - 4(2)[/tex]

[tex]d = 4 - 8[/tex]

[tex]d = -4[/tex]

Answer:  [tex]a = 3, b = 2, c = 0,d = -4[/tex]

Answer 2

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4


Related Questions

Which set of numbers is correctly ordered from least to greatest?
24 x 63
5.7 15.758,956 V
63
24 x
S
15.758
4.956 Ve
9566 15.753, 24, 49
63
956 /
15.758
24 x
5

Answers

Answer:

The set of numbers that is correctly ordered from least to greatest is 5.7, 15.758, 24, 49, 63. Is there anything else you would like to know?

Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week. Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.

Answers

Answer:

i am thinking option 1

Step-by-step explanation:

i may be wrong if i am correct me

Hello there i hope you are having a great day :) Your Question : Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week. Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Answer : So the first Michael has $10 in hes saving account. Option 1 puts $100 in each week so 7 weeks would equal to 7 weeks x $100 = $700 that would equal the amount for the bike in 7 weeks or Option 2 Will double the amount in hes account each week so $10 x 2 = $20. 1 week $20 2 week $40 3 week $80 4 week $120 5 week $240 6 week $480 7 week $960. So the Option two Is the best one as Option one would equal to $700 and Option two $960 that would equal left over $260. Hopefully that helps you ❤

How much will the guitar be worth in 10 years?

Answers

Answer:

$44487

Step-by-step explanation:

If you plug in 10 for t, you are left with the following equation:

[tex]V=12000(1.14)^{10}=12000\cdot 3.7072\approx 44487[/tex]. Hope this helps!

Answer: $44,487

Step-by-step explanation:

To solve this, substitute t (the variable for time in the equation) with 10 to represent the value of the guitar after 10 years.

[tex]V = 12000(1.14)^{10}\\V = 12000*3.7072\\\\V = 44487[/tex]

The guitar will be worth $44,487 in 10 years.

Mario writes the equation (r + y)2 = z2 + 4(1/2ry) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.

Answers

Answer:

x+y

Z2

1/2xy

Step-by-step explanation:

(x+y)^2 finds the area of the outer square by squaring its side length.

z^2 + 4 (1/2xy) finds the area of the outer square by adding the area of the inner square and the four triangles.

Help please
If steak costs $8.45 per pound, what will be the total cost of 0.8 pounds of steak?

Answers

Answer:

$6.76

Step-by-step explanation:

Multiply 8.45 by 0.8 and you will get 6.76

The function g(n) = n2 − 16n + 69 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)

Part C: Determine the axis of symmetry for g(n). (2 points)

Answers

Answer:

Step-by-step explanation:

A) y + ? = n^2 - 16n + ? + 69

y + 64 = n^2 -16n + 64 + 69

y + 64 = (n-8)^2 + 69

y = (n-8)^2 + 5

B) vertex is (8,5) because the value of a vertex is always (h,k) from the parent vertex function:

y = a(x-h) + k

it's a minimum only because the (a) value is positive

C) axis of symmetry = 8

is it true that energy never moves

Answers

Answer:

False

Step-by-step explanation:

Energy is transferred from one object to another when a reaction takes place. Energy comes in many forms and can be transferred from one object to another as heat, light, or motion, to name a few.

What's the numerator for the following rational
expression?
7/v+3/v=?/v

Answers

Answer:

54inches 43inches are the 53364inches rye 5t337 the earth stud is 37feet of the 368feet

Answer:

10

Step-by-step explanation:

they all have the same denominator so the only focus is adding the 7+3

Find the exact solution of the equation. 7^x=8

Answers

Answer:

[tex] log_{7}(8) [/tex]

4 blue marbles, 3 green marbles, 7 yellow marbles, and 2 red marbles are in a bag. What is the probability of drawing a blue marble, putting it back in, then drawing a red marbe?

Answers

Answer:

0.375 in fraction is 38.

4/16 + 2/16 = 0.375

Step-by-step explanation:

Pythagorean Theorem: How many yards will the players have to run?

Answers

Answer:

≈ 125.3

Step-by-step explanation:

If we're using the Pythagorean Theorem to solve this, then the formula is:

[tex]a^{2}+ b^{2} =c^{2}[/tex]

So basically, by using this formula, you're finding the length that the soccer players will run diagonally. Plug in the numbers:

[tex]110^2 + 60^2 = c^2[/tex]

12100 + 3600 = [tex]c^2[/tex]

15700 = [tex]c^2[/tex]

Take the square root:

15700 = [tex]c^2[/tex]

[tex]\sqrt{15700} = \sqrt{c^2}[/tex]

125.3 ≈ c

which statement must be true

Answers

Answer:

(C)

Step-by-step explanation:

AD and BC are parallel to each other. They are the same distance but they never touch.  

Your best answer would be C.

Brainilest appreciated.

Five-sixths of a number is 45.
Find the number.

Answers

Answer: The number is 54!!!

Hope it helps!!!



Step-by-step explanation:

Let's call the number x.

So, 5/6 (of or multiplication) = 45

5x = 45* 6

x = 270/5

x = 54

The answer is 54. Hope this helps!

2. Simplify.
–48
O A. 4213
OB. -4213
O C.-4v3
OD. 4V3

Answers

D
48
2 24
12 2
6 2
3 2
2•2V3
4V3

Calculate:|a|−|b|+|c|, if a=−8; b=−5; c=1

Answers

Answer:

The answer is 4.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

|x| just means positive x so the equation turns into 8-5+1

8-5 = 3

3+1 = 4

The shark dove down 48 feet in 6 minutes. How many feet did the shark dive down per minute?

Answers

Answer:

8 ft per minute

Step-by-step explanation:

Take the number of feet and divide by the number of minutes

48 ft / 6 minutes

8 ft per minute

The answer is 8 sorry if I am wrong

Identify the value of r and a1 for each geometric
series.
8 + 4 + 2 + 1 + ...

Answers

Answer:

Step-by-step explanation:

Answer:A,E

second part 1.5,2. .5,8

Step-by-step explanation:

HELP PLEASE!!
There are 12 students in a class: 7 boys and 5 girls. If the teacher picks a group of 5 at random, what is the probability that everyone in the group is a boy?

Answers

Answer:

0.027

Step-by-step explanation:

The number of groups of 5 boys that we can have from 7 boys is 7C5 = 21

The number of groups of 5 boys that we can have from 12 students is

12C5 = 792

then the probability = 21/792 = 0.026515151515

by the way you can calculate 12C5 and 7C5 using a calculator.

Mr. Eichmann 's salary is $42,000. This year, he receives a raise of 7%. What will be his salary this year?

Answers

His salary will be 44,940. 7 percent of 42,000 is 2,940, added to his 42,000 dollar salary gives you $44,940

will give brainliest plz helppp!!!!

Answers

Answer:

A. True

B. False

C. False

D. False

Step-by-step explanation:

Write an equation of the line that passes through (2, −2) and is parallel to the line y=3x+9.

Answers

Step-by-step explanation:

Parallel lines have the same slope, so we know that our line will have a slope of 3 because y = 3x + 9 has a slope of 3. Now, we can use the point-slope formula of the line to find the equation.

We have y - y₁ = m (x - x₁)          (m = 3, x₁ = 2, y₁ = -2)

               y- (-2) = 3 (x - 2)

               y + 2 = 3x - 6

               y = 3x - 8

Hope this helps!

Answer:

y = 3x - 8

Step-by-step explanation:

We know that parallel lines have the same gradient. In this situation we want want to work the equation of the line that is parallel to y = 3x + 9 and passes through ( 2 , - 2 ). We know that equations of lines usually go in the format of    y = mx + c

↔ Where 'm' is the gradient / slope

↔ Where 'c' is the y - intercept

Using the information in the first sentence we can set up an equation to find the value of 'c'

⇒ Form the equation

→ y = 3x + c

⇒ Substitute ( 2 , -2 ) into the equation to find the value of c

→ -2 = 6 + c

⇒ Minus 6 from both sides to isolate c

→ -8 = c

⇒ Put the value of c back into y = 3x + c

→ y = 3x - 8

So equation of the line that passes through ( 2, −2 ) and is parallel to the line y = 3x + 9 is y = 3x - 8

Use the given circle. Find the length s to the nearest tenth.

a) 10.5 in
b) 5.2 in
c) 3.3 in
d) 20.9 in

Answers

Answer: its A

Step-by-step explanation:

Any smooth curve connecting two points is called an arc. The length of arc s to the nearest tenth is 10.5 in.

What is the Length of an Arc?

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]

where θ is the angle, which arc creates at the center of the circle in degree.

The length of the given arc s, with an angle made at the center equal to (2/3)π and radius of 5 inches can be represented as,

[tex]\text{Length of Arc} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]

[tex]\text{Length of Arc s} = 2\pi \times (5)\times \dfrac{\frac23\pi}{2\pi}[/tex]

                        [tex]=10.472\approx 10.5\rm\ in[/tex]

Thus, the length of arc s to the nearest tenth is 10.5 in.

Learn more about Length of an Arc:

https://brainly.com/question/1577784

Find the range of the data in the box plot below.​

Answers

Answer:

Range: 20

General Formulas and Concepts:

Statistics

Range - the difference between the highest and lowest point

Step-by-step explanation:

Step 1: Define

Find values from box-and-whisker plot.

Highest point recorded = 25

Lowest point recorded = 5

Step 2: Find Range

Set up:                    25 - 5Subtract:                 20

What is the answer to this question?

Answers

Answer:

The answer is 480 in^3

Step-by-step explanation:

Right rectangular prism calc - find V

volume = h * w * l where h is prism height, w is its width and l its length.

Bruce and Krista are going to buy a new furniture set for their living room. They want to buy a couch, a coffee table, and a recliner. They have narrowed it down so that they are choosing between 4 couches, 5 coffee tables, and 9 recliners. How many different furniture combinations are possible?

Answers

Answer:

There are 180 possible combinations for the furniture.

Step-by-step explanation:

4*5*9=180

Answer

180 combinations

Step-by-step explanation:

To figure out the number of combinations, we multiply 4*5*9. 4*5 equals 20 and 20*9 equals 180.

What is the slope of the line represented by y=3/4x-1 ? A. –1 B. -3/4 C. 3/4 D. 1

Answers

Answer:

3/4

Step-by-step explanation:

In the above equation the y-intercept is -1 and the slope of the equation is 3/4

Answer:

The answer is C or 3/4.

Step-by-step explanation:

This equation is in point-slope form or Y= mx+b. The variable m represents slope. So, just look for the number that stands in place of m. Hope this helps! Please mark Brainliest! :)


Which statement best summarizes the main idea of the above passage from
"An Indian Father's Plea"?
A. Wind-Wolf learned much of what he learned from public school.
B. Wind-Wolf has a different educational background than many
other children.
O C. Wind-Wolf looks and acts differently than the other children in his
school.
D. Wind-Wolf will often answer questions at school using answers
he learned from those in his tribe.

Answers

Answer:

Had to look for the missing passage and here is my answer. Based on the passage from  "An Indian Father's Plea", I can say that the statement that shows the best summary about this is option D: Wind–Wolf has begun denying his native culture because it conflicts with his school culture. Hope this helps.

Step-by-step explanation:

Students in grade 7 and 8 were asked which food they liked best the results are shown in the table below?

Answers

Answer:

55% if the students like hotdods

Answer:

55%

Step-by-step explanation:

I will mark brainliest! The question is the image attached, please help!

Answers

Answer:

x=20 and y=128.Option 2

Step-by-step explanation:

Since,the angles are vertically opposite,they are equal(property)

Therefore,

(3x-8)=(2x+12)

3x-8=2x+12

3x-2x=12+8

x=20,

Now,

Since,the angles are formed in a straight line,their sum is equal to 180(property)

Therefore,

y+(2x+12)=180

y+2×20=180-12

y=168-40

y=128

Therefore,x=20 and y=128

option 2 would be your answer because it explains the missing part where y is.

what is the inequality

Answers

Answer:

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b.

Other Questions
Which represents the solution(s) of the system of equations, y = -x2 + 6x + 16 and y = - 4x + 37? Determine the solution setalgebraicallyO (325)(-3, 49)(3,25) and (79)(-3, 49) and (-7, 65) What is moko? ( someone help me with this one ) George still has 40 percent of his book to read. If George has read 180 pages, how many pages does he still have to read? How do you know? a line passes through (2,-6) and had a slope of 5/2. Write an equation in slope-intercept form for this line. PLSSS HELP ILL GIVE BRAINLIEST AND 10 PTS PER QUESTION AND A BONUS ON CERTAIN QUESTIONS (20 points 2 questions) Two factors that caused rapid economic growth during the Gilded Age wereOa decrease in steel production and a decrease in the value of goods.an increase in prices and a decrease in the value of goods.an increase in steel production and an increase in the value of goods.an increase in prices and a decrease in steel production Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for , and round your answer to the nearest tenth. a cone with a height of x and a radius of w, a cylinder with a diameter of y and a height of z please help me Use the formula to help you answer the question below. Do not include unitsin your answer.Rate . Time = DistanceHow many hours will it take to complete a 45-km bike ride if you go 12 km perhour the whole time? Which of the following will increase the boiling point of water?Adding more waterAdding sugarRemoving some of the waterNone of the above How do you know when expression are equivalent When you increase the length of your workout, you are increasing ___________. Which expression is equivalent to m n + z?n m + nz + m zm z + nz + n m Horace takes a taxi uptown, and the fare is $12.78. He wants to give the driver a 10% tip.If Horace gives the driver a $20 bill, how much change should he ask for? how did darwins theory of evolution change the way biologists thought about classification categories Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C? On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3). A Is congruent to B and B Is congruent to C A Is congruent to A, B Is congruent to B, C Is congruent to C Each triangle is a right triangle. Each triangle is an isosceles triangle. Pretty easy question in physics but no one answers them in that subject so I put it here What is the meaning of the term "arms race"? The value of x 3y, for x = -2 and y = 3, is -24. True False Stephanie and alejandrowere planning thier wedding.Stephine saved up four times.more money than alejandrobecause he lost his job at walmart. Together $15,600 How much did each one save ?steps ? The diagram below shows PQT; its altitude, which is segment PR; and some of its measurements.(a)What is mTPR? Show or explain how you got your answer.For Parts (b), (c), and (d), write the exact answer in simplified radical form.(b)What is the length, in inches, of segment PR? Explain your answer.(c)What is the length, in inches, of segment TR? Explain your answer.(d)What is the length, in inches, of segment PQ? Explain your answer.