One factor of f(x) = x3 − 14x2 + 61x − 84 is (x − 7). What are the zeros of the function?

Answers

Answer 1

Answer:

-7

Step-by-step explanation:

Because zero is the x, so x=-7 then it's -7

Answer 2

The zeros of the polynomial function is x = 7, x = 3, and x = 4 if one factor of f(x) = x³ − 14x² + 61x − 84 is (x − 7).

What is a polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that:

f(x) = x³ − 14x² + 61x − 84

One factor is (x - 7)

The cubic polynomial can be written as:

f(x) = (x - 7)(x² - 8x + 12)

Or

f(x) = (x - 7)(x - 3)(x - 4)

To find the zeroes equate to zero:

f(x) = 0

(x - 7)(x - 3)(x - 4) = 0

x = 7, x = 3, and x = 4

Thus, the zeros of the polynomial function is x = 7, x = 3, and x = 4 if one factor of f(x) = x³ − 14x² + 61x − 84 is (x − 7).

Learn more about Polynomial here:

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Related Questions

Brenda has two remote-controlled race cars painted blue and red, respectively.The blue car traveled 54 feet 4 secounds.The red car traveled 38 feet im 2 seconds.

Answers

Answer:

The red car is faster compared to the blue car.

The red car is faster by 5.5 feet than the blue car.

Step-by-step explanation:

The objective is to find which car is  faster and by how much

Given that:

The blue car traveled 54 feet in 4 seconds; &

The red car traveled 38 feet in 2 seconds.

Let us determine the number of feet traveled in each second for both cases.

For the blue car:

In 1 second, the car will travel = 54/4 feet

In 1 second, the car will travel = 13.5 feet

For the red car:

In 1 second, the car will travel = 38/2 feet

In 1 second, the car will travel = 19 feet

Thus, the red car is faster compared to the blue car.

The distance at which the red car is faster than the blue car = 19 feet - 13.5 feet

= 5.5 feet

3 and 11
Find the midpoint

Answers

Answer:

7

Step-by-step explanation:

What is the solution of the proportion 3/5=13/x ? Round to the nearest tenth if necessary.

Answers

Answer:  x = 21 2/3

Step-by-step explanation:

3/5 = 13/x

cross multiply  5 × 13,  then divide  by 3.  

65/3 = 21 2/3

It's like multiplying both sides by the reciprocal of the left side.

Point M is the midpoint of A and B
What are the coordinates of point B?​

Answers

Answer:

(6, 7) is where B is.

Step-by-step explanation:

If you go down 1/2 and right 5, you get to M. If you go another 1/2 down and right 5, you will get to B.

This is because M is the midpoint, or center point, of line AB. That means there is equal distance going from A to M and equal distance going from B to M.

#teamtrees #WAP (Water And Plant)

Write the equation of the line, in point slope form that goes through the given point with the given slope. through: (-2,5), slope = -4* O y + 2 = 5(x + 4) O y - 2 = 5(x-4) O y + 5 = -4(x +2) O y- 5 = -4(x + 2)​

Answers

Answer:

y-5 = -4(x + 2)

Step-by-step explanation:

The point slope form is;

y-y1 = m(x-x1)

where m represents the slope

(x1, y1) represents the given point

Thus;

y-5 = -4(x + 2)

Marisa made 60 mums for homecoming. These mums took 48 hours to make. Each mum takes the same amount of time to make. How many hours will it take Marisa to make 20 mums?

Answers

Answer: 25

Step-by-step explanation: 60/48=1.25, 1.25 x 20=25

What is the nth term rule of the quadratic sequence below?
-5, -3,3, 13, 27, 45, 67, ...

Answers

Answer:

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Step-by-step explanation:

Answer:

[tex]u_{n} = 2n^{2} -4n-3[/tex]

Step-by-step explanation:

a +b + c = - 5    First term in sequence

3a + b = 2   Difference between first two terms

2a = 4         Difference between  the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)

2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so  b = -4; 2 - 4 + c = -5  → -2 + c = -5 so c = -3

Graph the line that represents the equation y = -2/3x + 1

Answers

Answer:

Step-by-step explanation:

Simplify the ratio 12:8 and write the ratio in all three forms.

Answers

Answer:

Step-by-step explanation:

1. Simplify

greatest common factor = 4

3:2

a. 3 to 2

b. 3:2

c. 3/2

If a television was 20% off and the amount of the discount was $200 what would the original price be?

Answers

Answer:

The original price of the television would be 1000$

y = (x - 4)(x-8)
Distribution

Answers

Answer:

[tex]y= x^{2} -12x+32[/tex]

Explanation:

[tex]y=x^{2} -8x-4x+32\\y= x^{2} -12x+32[/tex]

for a school field trip there must be 20 students to 2 adults, 30 students to 3 adults, and 60 students to 6 adults. identify the student to adult ratio.

Answers

Answer:

7

Step-by-step explanation:

...

Write 36 as a Product of is prine
numbers
Write the factors in order, from smallest
to largest
36

Answers

Answer:

Step-by-step explanation:

Factors of 36 = 1 2 3 4 6 9 12 18 36

the Prime Factors of 36 are: 2, 2, 3, 3.

This is the answer

Answer:

36 = 2*2*3*3

or

2^2 * 3^2

Step-by-step explanation:

Break 36 into prime factors

36 = 6*6  

Since 6 isn't a prime number, factor 6

36 = 2*3   * 2*3

2 and 3 are prime numbers

In order from smallest to largest

36 = 2*2*3*3

or as exponents

36 = 2^2 * 3^2

You are tasked with buying pizza for a party that has 100 guests. 40 guests are children, and 60 guests are adults. Half of the children want pizza, and two thirds of the adults want pizza. Children will eat one slice of pizza, and adults will eat two slices of pizza. A pizza pie can be cut into 8 slices and costs $9 dollars per pie.

Answers

Total slices required for children,

[tex]C = \dfrac{40}{2}\times 1\\\\C = 20\ slices[/tex] .

Total slices required for adults,

[tex]A=\dfrac{2}{3}\times 60\times 2\\\\A = 80\ slices[/tex]

So, total slices required are, 20 + 80 = 100 .

Number of pizza, n = 100/8 = 12.5

So, he has to order 13 pizza cause pizza cannot be purchased in fraction.

Total price, P = 13 × 9 = $117 .

Hence, this is the required solution.

1.find the domain,range and function.

{(-6, 4), (5, -1), (0, 3), (-2,4)}

Domain:
Range:
Function

Answers

Answer: domain: {-6, 5, 0, -2}

Range: { 4, -1, 3, 4}

Function: Yes it is a function

HELP PLEASEE THIS IS MY LAST QUESTION ILL MARK BRAINLIEST

Answers

Answer:

F. y = 9.5x + 22.5

Step-by-step explanation:

let the number of shirts be x

For every shirt he pays $9.50 and $22.5 is the additional price

What is the solution set for |x/2|=8?

Answers

Answer:

D) x=16 and x=-16

Step-by-step explanation:

D) x=16 and x=-16

If you replace x with either one of them and then take the absolute value, you would have 8.

How do I solve this and check all the solutions?

Answers

Answer:

x = 2

Step-by-step explanation:

(Square both sides)

20 - 8x = x^2

(Solve 20 - 8x = x^2)

x = 2 , x = 10

x = 10 is false, so the answer is x = 2.

Answer:

x=2

Step-by-step explanation:

√20-8x=x

2√5-2x=x (by simplfing redical expression)

4(5-2x)=x^2 (square both side)

20-8x=x^2

20-8x-x^2=0

-x^2-8x+20=0

x^2+8x-20=0

x=2

Note:There is a another answer x=-10 But it's wouldn't fit out with this equation

[tex]-0.2\sqrt{x^2}[/tex] You have to simplify this

Answers

Answer:

The simplified answer to that is -0.2x.

Hope this helps and if you could mark this as brainliest. Thanks!

Answer:

-0.2x

Step-by-step explanation:

If x is negative then,

-0.2(-2) = 0.4

)If 1 gallon is equal to 4 quarts, then 6 gallons would equal ___ quarts.

Answers

Answer:

24

Step-by-step explanation:4x6

Answer:

24

Step-by-step explanation:

Use long division to find the quotient below.
(15x2 + 2x2 - 75) - (3x-5)
O A. 5x2 - 9x + 15
B. 5x2 + 9x + 15
C. 5x2 + 12x + 15
D. 5x2 - 12x + 15

Answers

A. Is your answer. Hope this helps!
The answer is A have a good day!

a rental car company charges a customer $60 plus $0.32 per mile. write the equation that best describes the relationship between the cost, y, of renting the car and the number of miles, x, the car was driven​

Answers

Answer:

0.32x + 60= y

Step-by-step explanation:

Will mark brainliest! Please help I have no idea!

Answers

Answer:

the decimals should line up.

Answer:

press the right arrow 3 times

Step-by-step explanation:

to properly subtract any numbers the value of the digits need to be in line

Andrea ordered a computer on the Internet. The computer cost $1399 plus 6 1/2% sales tax. What was the total amount Andrea paid for her computer?

Answers

Answer:

$1,489.94

Step-by-step explanation:

Answer:

1,489.94

Step-by-step explanation:

6.5% = 0.065

1399x 0.065= 90.935

1399 + 90.935 = 1,489.94

Pls show the work

2x - 3y = 12

Answers

Answer:

y= -2/3x - 4

x= 3/2y + 6

Step-by-step explanation:

2x - 3y = 12 (plus 3y)

2x = 3y +12 (divide by 2)

x = 3/2y + 6

2x - 3y = 12 (minus 2x)

-3y = 2x + 12 (divide by -3)

y = -2/3x - 4

Please help me answer 16 please

Answers

Answer:

SSS

Step-by-step explanation:

I can identify that these triangles are congruent by using the SSS (Side, Side, Side) postulate theorem. I know this because first, second, and home triangle share the same side as the third, second, and home triangle, meaning they are congruent, so are the other sides of the angle since the question states they are congruent.

4x +5y =24
2x+7y=21​

Answers

Use elimination
Multiply second equation by 2
4x + 14y = 42
4x + 5y = 24
Now subtract both
9y = 18
Y = 2
Plug 2 into equation to solve for x
4x + 5(2) = 24
4x = 14
x = 3.5, y = 2

Answer:

x = 3.5, y = 2

Step-by-step explanation:

This is a system of equations.

Original equations:

[tex]4x+5y=24\\3x+7y=21[/tex]

Substitute y and solve for x:

[tex]y=\frac{24-4x}{5} \\2x+7y=21[/tex]

Substitute the value for y and simplify:

[tex]2x+\frac{7(24-4x)}{5} =21[/tex]

[tex]2x + \frac{(168 - 28x)}{5}=21[/tex]

Multiply by 5 on both sides

[tex]10x + 168-28x = 105[/tex]

Simplify [tex]-18x = -63[/tex]

[tex]x = 3.5[/tex]

Plug in the value for x into either equation:

→ [tex]4*3.5 + 5y=24[/tex]

→ [tex]14+5y=24[/tex]

→ [tex]5y=10[/tex]

→ [tex]y=2[/tex]

How do I solve 4x+23>-21

Answers

Answer:

Inequality Form:

x>-11

Step-by-step explanation:

Interval Notation:

(-11,\infty )

Answer:

Step-by-step explanation:

4x + 23 > -21

4x > -21 -23  (moving 23 to the right side of equation changes the +23 to  -23

4x > -44  (adding -21 to -23)

x > -11  (dividing both sides of equation by 4, this keeps the equation the same

Solution:  x > -11  (x is greater than negative 11)

A full strip plus another half of a strip of staples contains 315 staples

Answers

Answer:

[tex]210 staples[/tex]

Step-by-step explanation:

Lets solve this equation:

[tex]x(fullstrip)+\frac{1}{2}x(halfstrip)=315.[/tex]

Combine terms:

[tex]x+\frac{1}{2}x=\frac{3}{2}x \frac{3}{2}x=315[/tex]

[tex]x=315*\frac{2}{3}[/tex]

[tex]x=210[/tex]

So a full strip contains 210 staples.

Hope this helps :D please hit the crown

What are three consecutive even integers whose sum is 66

Answers

Answer:

21,22,23

Step-by-step explanation: i love fried chicken look at my skin color

Answer:

Smallest integer: 20

Middle integer: 22

Largest integer: 24

Step-by-step explanation:

Denote the smallest integer as "x"; hence the next integer will be "x + 2", and the third will be "x + 4".

Using the information, set up an equation:

x + x + 2 + x + 4 = 66

Simplify

x + x + 2 + x + 4 = 66

3x + 6 = 66

Inverse operations

3x + 6 = 66

    -6      -6

3x = 60

/3     /3

x = 20

Smallest integer: 20

Middle integer: 22

Largest integer: 24

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