Given that f(x) is a cubic function with zeros at -3, 0, and 7, find an equation for f(x) given that f(-8) = -5.

Answers

Answer 1

Answer:

[tex]\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}[/tex]

Step-by-step explanation:

[tex]f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5[/tex]

[tex]\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}[/tex]

[tex]\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x[/tex]


Related Questions

In this problem, I did part a) correctly, but I got 7 points off in part b) but I don’t know why?

Answers

Answer: You need to prove that ABCD is a rhombus because it's diagonals are always perpendicular, no matter what.

A rhombus is a quadrilateral and:

- its opposite angles have equal measure.

- The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.

- Its diagonals bisect opposite angles.

What is the Scale factor of 35 to 42

Answers

QUESTION. What is the Scale factor of 35 to 42

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[tex]\boxed {\tt 25/35}[/tex]

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The Scale Factor of 35/42 is the relative difference of one fraction or number (a) to another fraction or number prime (a′). In other words, 35/42 is what you multiply (number a) by to get (number a prime).

In a multiplication problem, we have a multiplier, multiplicand, and a product. You could say that (a) is the multiplier, the Scale Factor of 35/42 is the multiplicand, and (a′) is the product:

multiplier × multiplicand = product

multiplier × scale factor = product

a × 35/42 = a′

In the calculator below, you can enter the multiplier (a) as a fraction. We will then multiply it by the Scale Factor of 35/42 and give you the product (a′) in its simplest form possible.

Which triangles are similar?

Triangle A
34/
A
30
37
12
15
h
53
9
62
16
Triangle C
Triangle B
A. Triangles A and C
B. Triangles A, B, and C
C. Triangles A and B
D. Triangles B and C

Answers

Triangle A and C are same because the angles formed by all three sides are same in both triangles.

Hope it helps you....

Please mark as brainlliest!!!

Consider the graph of the of the quadratic function g(x). See below

Answers

Answer:

I believe the correct answers would be...

32.) B

33.) C

Step-by-step explanation:

32.)

Since the function is shifted downward 1 unit from the x-axis, "q" would be -1

33.)

If the function is shifted upward 4 units, the "+4" would be on the outside of the parentheses.

How many times two odd digits appear in a number when you count from 0 to 999?

Answers

hi
It’s......
500
There r 500 odd no between 0-999
This might help u
Byeee

The solution is: It occurred 90 times does the digit 5 occur in all the numbers from 100-999 .

What is Arithmetic progression?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

The nth term of AP : a_n = a + (n – 1) × d

here, we have,

Explanation:

Here, we want to know the number of times the digit occurs

We can solve this with arithemetic progression

The first term here is 105, while the last term is 995

However, the difference between each occurrence is 10

Thus, applying the formula:

T_n = a + (n-1) d

T_n is the last term which is 995

a is the first term which is 105

d is the common difference which is 10

n is the number of terms which we want to calculate

Substituting these values, we have it that:

995 = 105 + (n-1) 10

so, we get,

n = 900/10

  =90

Hence, It occurred 90 times does the digit 5 occur in all the numbers from 100-999 .

To lean more on Arithmetic progression click:

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complete question:

How many times does the digit 5 occur in all the numbers from 100-999 ?

Solve the inequality -3/4(12x+16)<9-5x.

Answers

Answer:

x > -21/4

Step-by-step explanation:

Answer:

x > -24/4

Step-by-step explanation:

-3/4 (12x + 16) < 9 - 5x

-3/4 * 12x - 3/4 * 16 < 9-5x

-9x - 3/4 * 16 < 9 - 5x

-9x - 12 < 9 - 5x

-4x - 12 < 9

-4x < 21

A) y = 5x

B) y = 10x

C) y = 7.5x

D) y = 30x​

Answers

Y=30x is the answer to this

What is the value of the expression?


(323+1715)−(1135+213)


Enter your answer as a mixed number in simplest form by filling in the boxe

Answers

Answer:

690

Step-by-step explanation:

(323+1715)-(1135+213)

(2038)-(1348)

=690

The value of the expression is 690

What is Expression?

An expression is combination of variables, numbers and operators.

The given expression is (323+1715)−(1135+213)

We have to find the value of expression

By using PEMDAS rule we solve the expression

Let us find the value in parenthesis

2038 -1348

We get 690

Hence, the value of the expression is 690

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Simplify the expression w²y³ ÷ wy⁴ please help me thank you for you kindness ​

Answers

Answer:

W/y

Step-by-step explanation:

i'll mark brainliest, thanks in advance!​

Answers

Answer:

not enough information.

Step-by-step explanation:

We know one side and the vertical angle.  We do not have enough information to determine if the triangles are congruent.

A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than One-fifth? Select three options. choosing 1 blue marble choosing 1 red marble choosing 1 red marble, not replacing it, and then choosing a blue marble choosing 1 white marble, replacing it, and choosing another white marble choosing 1 white marble

Answers

hi i know i'm late but might as well add my answer!

here's your answer: B D E or

B.choosing 1 red marble

D.choosing 1 white marble, replacing it, and choosing another white marble

E.choosing 1 white marble    

hope i helped

   

Answer:

b d and e

Step-by-step explanation:

ya

What’s the solution to 2x - 2 > 2x + 4 ?

Answers

Answer:

This inequality isn't correct.

Step-by-step explanation:

2x - 2 > 2x + 4

Substituting any value for x, the result will be incorrect.

Actually,

2x - 2 < 2x + 4 is correct.

2x - 2x < 4 + 2

0 < 6

Rest of the options

Answers

The answer is D, the last one

Help me please! This is so confusing!

Answers

Answer:

  a) yes, 2, 1/2

  b) b = 2t; t = 1/2b

Step-by-step explanation:

a) The number of batteries is twice the number of toys. Using the variables of part B, this relation is ...

  b = 2t

This is of the form required for a proportional relation: y = kx, with a value of k=2.

__

If we divide the above equation by 2 on both sides, we get ...

 1/2b = t

This is also a proportional relation, with a constant of proportionality of 1/2.

Toys and batteries are in a proportional relationship. The constants of proportionality are 2 or 1/2.

__

b) As we saw above, the equations can be ...

 b = 2t

  t = 1/2b

i'll mark brainliest, thanks in advance!​

Answers

Answer:

SSS

Step-by-step explanation:

are 2 isosceles right triangles congruent, have both sides and angles equal, so the answers are all valid, the simplest is SSS, 2 sides are the same and marked on the drawing, the third is the same accordingly

Yamuna is getting ready to attend Wittenberg University in the fall. She needs 6 notebooks
at $2.19 each and a chromebook at $529.00. If she has $575 to spend, how much does
she have left for lunch?

Answers

Answer:

she has $32.86 left for lunch

Step-by-step explanation:

6 books at $2.19 each equals $13.14. plus the chrome book at 529. 529+13.14= $542.14

$575-542.14 equals $32.86

Which situation involves permutations? A. choosing 5 people out of 15 to participate in a survey B. choosing 3 flavors of ice cream out of 15 for an ice-cream sundae C. choosing a dozen flowers out of 30 to create a bouquet D. choosing first second-, and third-place winners in a cooking contest​

Answers

9514 1404 393

Answer:

  D. choosing first second-, and third-place winners in a cooking contest​

Step-by-step explanation:

Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.

Cooking contest winners involve permutations.

A farmer wants to increase the area of His rectangular pen but keep the pen a rectangular shape. He decides to a 5.7 yards of fencing
to the width of the pen but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Which can be used to determine the original width of the pen?
5.7 (W+9.5) = 77.9
S95219
9.5 (W + 5.7) = 77.9

Answers

Using the equation for the area of a rectangle, the original width of the pen is determined by:

9.5 (W + 5.7) = 77.9

The area of a rectangle of length l and width w is given by:

[tex]A = lw[/tex]

In this problem:

Increases the width by 5.7 yards, hence [tex]w = w + 5.7[/tex], in which w is the original width.The length remains at 9.5 yards, hence [tex]l = 9.5[/tex].The area is of 77.9 square yards, hence [tex]A = 77.9[/tex]

Then:

[tex]A = lw[/tex]

[tex]9.5(w + 5.7) = 77.9[/tex]

For a similar problem, also involving the area of a rectangle, you can check https://brainly.com/question/10489198

Use synthetic division to find the result when 3x^3 + 4x^2 - 5x - 2 is divided by x + 2

Answers

Check the picture below.

-5 1/5 + 3.7 + 5 1/10 how to solve

Answers

Answer:

to find the answer u have to simplify

Simplify the expression using trigonometric identities: sec (–θ) – cos θ.

Answers

Answer:

sin θ . tan θ

Step-by-step explanation:

Note : -

sec ( - θ ) = sec θ

Formula / Identity : -

sec θ = 1 / cos θ

sec ( - θ ) - cos θ

= [ 1 / cos θ ] - cos θ

{ LCM = cos θ }

= [ 1 / cos θ ] - [ cos²θ / cos θ ]

= [ 1 - cos²θ ] / cos θ

{ 1 - cos²θ = sin²θ }

= sin²θ / cos θ

{ sin²θ = sin θ . sin θ }

= sin θ . sin θ / cos θ

{ sin θ / cos θ = tan θ }

= sin θ . tan θ

Hence, simplified.

There are 350 students graduating on Sunday. 84% of the students are graduating with Bachelor’s degree in Business. How many students are getting their Bachelor's degree in Business?

Answers

Answer:

294 students

Step-by-step explanation:

To find percentage, convert the percent to a decimal and multiple the total number of students

80% --> 0.8

350*0.8 = 294 students

9514 1404 393

Answer:

  294

Step-by-step explanation:

84% of 350 is ...

  0.84 × 350 = 294

294 students are getting their Bachelor's degree in Business.

__

Additional comment

If your calculator does not have a % key, you can perform the multiplication by converting the percentage to a decimal or using it as a fraction. The % symbol is interchangeable with /100, so 84% = 84/100. Of course, this is eighty-four hundredths, which can also be written 0.84.

Any spreadsheet will accept direct input of numbers with an attached % symbol, so you can use one of those for this calculation, also.

Tell whether the fractions are equivalent. Write = or


2/3 ______ 4/6

Answers

[tex]\dfrac 23 = \dfrac{2 \times 2 }{3 \times 2} = \dfrac 46[/tex]

Please help!!

Choose the definition for the function.

Answers

9514 1404 393

Answer:

  A. {2x, x<1; (x+5)/2, x≥1}

Step-by-step explanation:

The left side of the graph (x<1) has positive slope and a y-intercept of 0. Only one answer choice matches: choice A.

Please help me please help please please help me

Answers

Answer:

3/2

-4

Step-by-step explanation:

y = mx + c

m = slope = y2 - y1 / x2 - x1

= -4 -2 / 0 - 4

= -6/-4

= 3/2

c = y intercept

y when x = 0

c = -4

Answer:

[tex]y = \frac{2 - ( - 4)}{4 - 0}x - 4 \\ y = \frac{6}{4} x - 4 \\ y = \frac{3}{2} x - 4 \\ [/tex]

Im so confused- please help

Answers

Step-by-step explanation:

a/q

x + x - 3 + 2x - 9 = 36

4x - 12 = 36

4x = 36 + 12 = 48

x = 48/4 = 12

x = 12

so,

x = 12

x - 3 = 12 - 3 = 9

2x - 9 = 2(12) - 9 = 15

we know,

area = 1/2 × base × height

so,

→ 1/2 × 12 × 9

→ 1 × 6 × 9

→ 54 inches.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

The perimeter is 36 so, (x+3)+(2x-9)+x = 36 solve and you will get x=12, then substitute x into the triangle you will have 9,12 and 15. Find the area by using 1/2 x base x height and the area is 54 inches^2 . The answer is (b)

A 19 -ft ladder leans against a building so that the angle between the ground and the ladder is 81 ∘. How high does the ladder reach on the building? ft

Answers

Answer:

18.77 ft

Step-by-step explanation:

use SOHCAHTOA

The ladder is a side, which is opposite to the angle. The ladder's side is also the hypotenuse of the triangle, so use sin.

sin(81) * 19 = 18.77 ft

A local animal shelter has many cats and dogs. The shaded part represents the percent of animals that are dogs. If there are 82 dogs, how many animals are there in total?

Answers

Answer:

weel if you divide 82 by 2 then it you will get the number of cats which is 41 then add 82 + 41 =123

Step-by-step explanation:

mark me brainliest

f(3) if f(x) = 2x+2 helpppppppppppppppppp

Answers

Answer:

= 8

Step-by-step explanation:

2x = 2 × 3 is 6 because f(3) then + 2 is 8

3 x 2 = 6

6 + 2 = 8

The correct answer is 8

(Hope this helps can I pls have brainlist (crown)☺️)

Solve for x, please help, thank you

Answers

Answer:x=6

Step-by-step explanation:

x+5x=36

Step 1: Simplify both sides of the equation.

x+5x=36

(x+5x)=36(Combine Like Terms)

6x=36

6x=36

Step 2: Divide both sides by 6.

[tex]\frac{6x}{6} =\frac{36}{6}[/tex]

x=6

Answer:

x=6

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