Select the correct answer.
if p(4) = -16, p(-6) = 0, and P(5) P(-6), which statement must be true?
A. (x + 16) is a factor of p.
B. (x + 4) is a factor of p.
C. (x + 6) is a factor of p.
D. (x – 5) is a factor of p.

Answers

Answer 1
Answer: C. (x+6) is a factor of p

Explanation:

p(-6) = 0 means that plugging x = -6 into p(x) leads to p(x) = 0.

If (x+6) was a factor of p(x), then we can say

p(x) = (x+6)q(x)

where q(x) is some other polynomial. Now let's replace x with -6

p(x) = (x+6)q(x)

p(-6) = (-6+6)q(-6)

p(-6) = 0*q(-6)

p(-6) = 0

The value of q(-6) doesn't matter as multiplying 0 with any number leads to 0.

This is all based on the special case of the remainder theorem that says "if p(k) = 0, then (x-k) is a factor of p(x)".

Answer 2

(x+6) is a factor of p.

The answer is option C.

How to solve the function?

p(-6) = 0 means that plugging x = -6 into p(x) leads to p(x) = 0.

If (x+6) was a factor of p(x), then we can say

p(x) = (x+6)q(x)

where q(x) is some other polynomial. Now let's replace x with -6

p(x) = (x+6)q(x)

p(-6) = (-6+6)q(-6)

p(-6) = 0*q(-6)

p(-6) = 0

The value of q(-6) doesn't matter as multiplying 0 with any number leads to 0.

This is all based on the special case of the remainder theorem that says "if p(k) = 0, then (x-k) is a factor of p(x)".

Learn more about function here: https://brainly.com/question/4025726

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Related Questions

what is the sum of this arithmetic series?

Answers

The sum of this arithmetic series is 52.

Answer:

52

Step-by-step explanation:

The ' easiest' method here is to substitute k = 1, 2, 3, 4 into the expression and sum the terms, that is

(- 2 + 6(1) ) + ( - 2 + 6(2) ) + ( - 2 + 6(3) ) + (- 2 + 6(4) )

= (- 2 + 6) + (- 2 + 12) + (- 2 + 18) + (- 2 + 24)

= 4 + 10 + 16 + 22

52

list some odd numbers less than 21

Answers

Answer:1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31

Step-by-step explanation:

Answer:

1,3,5,7,9,11,13,15,17,19

Equation- s=db-6, solve for d

Answers

Answer:

[tex]d \: = \frac{s + 6}{b} [/tex]

Step-by-step explanation:

[tex]s = db - 6[/tex]

Isolate d

[tex]s + 6 = db[/tex]

.

Divide both sides of the equation by b

[tex] \frac{s + 6}{b} = \frac{db}{b} [/tex]

Simplify

[tex] \frac{s + 6}{b} = d \\ d = \frac{s + 6}{b} [/tex]

The answer is solved in the image below

f(x)=2x-2
Find f(3b)

Answers

Answer: 6b-2

Substitute 3b for x
2(3b)-2
6b-2 but can also be written as 2(3b-1)

Which of the following could be the number shown on the number line?
A. 24
B. 20
C. 26
D. 27



Answers

I think that may be a trick question because all the the numbers can be on the number line

Answer. 24

Step-by-step explanation: With every number starting with 2 count the number line up it doesn't past 5 or on 5 so it's not 5. It's past 4 so whats your answer?

Brainliest please I took this very seriously.

.Rebecca's volleyball team is purchasing jerseys. The company charges $150 for a one time set-up fee and $25 for each printed jersey. Which expression represents the total cost of x number of jerseys for the team? *
2 points

Answers

Answer:

y= 25x+150

Step-by-step explanation:

x is the constant rate,which is 25.

and y is the starting number which is 150

K is the midpoint of JL. JK = 2x + 5 and JL = 50.
To solve for x, Steve sets up the following equation: 2x + 5 = 50
Explain the error in Steve's equation.

Answers

steve set the equation equal to 50 which is the entire length of JL. instead he should've set the equation equal to 25, since it's half of 50 and would represent the midpoint. he should've said 2x + 5 = 25

What are the 8 exponent laws?

Answers

Answer:

Step-by-step explanation:

Answer:

Product rule Power rule Quotient rule Negative exponent ruleZero exponent rule Adding/subtracting (like terms only).

Step-by-step explanation:

One Rule ; [tex]x^1 =x[/tex]

Zero Rule [tex]x^0 =1[/tex].

Product Rule ; [tex]x^m x^n = x^m^+^n[/tex]

Quotient Rule;  [tex]x^m/x^n = x^m^-^n[/tex]

Power Rule; [tex](x^m)^n=x^m^n[/tex]

Tower Rule [tex]a^{m^n}[/tex]

Fraction Rule [tex]a^\frac{1}{n} =\sqrt[n]{a^1}[/tex]

Dan spent $19.95 for a shirt, $39.99 for slacks and
$29.88 for a belt. What is a good estimate of how
much he spent on clothes?
A. $60.00
B.
$70.00
C.
$90.00
D.
S100.00

Answers

D 100 is a good estimate of how much he spent on clothes

Each large cookie is 5/6 oz and each small cookie is 4/9 oz.what is the total weight of 2 large cookies and small cookie? Help asap

Answers

Answer:

2 1/9 or 19/9 depends on what answer is required/you want to use

Step-by-step explanation:

First, common denominator

Big cookie = 15/18 oz

Small cookie = 8/18 oz

15*2=30

30+8=38

38/18 = total weight of 2 large and 1 small

2 2/18 mixed fraction

2 1/9 Simplest answer

The total weight of 2 large cookies and small cookie is 2 1/9 oz

Given:

Weight of each large cookie = 5/6 oz

Weight of each small cookie = 4/9 oz

Total weight of 2 large cookies and small cookie = 2(Weight of each large cookie) + Weight of each small cookie

= 2(5/6) + 4/9

= 10/6 + 4/9

= (30+8) / 18

= 38/18

= 2 2/18

= 2 1/9 oz

Therefore, the weight of 2 large cookies and small cookie is 2 1/9 oz

Read more:

https://brainly.com/question/9590043

what is the greatest and least number that can be rounded to 120,000

Answers

Answer:

119,999

Step-by-step explanation:

hope it helps

Is -9 rational, integer, whole, natural, or irrational?

Answers

Answer:

it is a rational, and integer

Answer:

Now according to the definition, 0 is a real number, a rational number, an integer and also a whole number but neither an irrational number nor a natural number. Answer: 0 is a rational number, an integer and also a whole number but neither an irrational number nor a natural number

Step-by-step explanation:

Hope this helps

The temperature at 9:00 AM was 42°F. The temperature dropped 9 degrees per hour for the next seven hours. What is the temperature at 4:00 PM?

Answers

Hey there! I'm happy to help!

Let's call our hours h. Here is what we have going on.

42-9h

4:00 PM is 7 hours after 9:00 AM. So, we will replace the h with 7 and evaluate.

42-9(7)

42-63=-21

Therefore, the temperature would be -21°F.

Have a wonderful day! :D

Find the slope of the line passing through (-2,-3) and (2,7).

Answers

5/2
Change in y is 10 from -3 to 7.
Change in x is 4 from -2 to 2.
Slope is change of y over change in x, so you would get 10/4 and reduce that to 5/2.

Can all lines contain line segments in them?

Answers

Answer: No

Step-by-step explanation: Because not all lines can have to end ponits some needs to go on forever like infinte and not be stop by the end points Hope this is the answer your looking for :).

If ABF= (7x + 20), FBC=(2x - 5), and ABC= 159", find the value of x. x =

Answers

Given :

∠ABF = ( 7x + 20 )°

∠FBC=(2x - 5)°

∠ABC= 159°

To Find :

The value of x .

Solution :

Assuming B the center of a circle .

So , all three given angles must be added to 360° .

[tex](7x+20)+(2x-5)+159=360\\\\9x+15+159=360\\\\x=20.67[/tex]

Therefore , the value of x is 20.67° .

Hence , this is the required solution .

What is the equation of the line passing through the points (–5, –2) and (3, 14) in slope-intercept form?

Answers

Answer:

2x-y+2= 0

Step-by-step explanation:

(-5,-2)=(x1, y1)

(3, 14) =(x2, y2)

now,

slope(m)= y2-y1 / x2-x1

=14+2 / 3+5

= 16 /8

=2 units

passing point = (-5,-2) = x1,y1

now,

eqn of the line can be represented as,

y -y1 = m (x-x1)

y +2 = 2 (x +5)

y+2 = 2x +10

y = 2x+10-8

0 = 2x+2-y

2x-y+2 =0 is the required eqn

Answer:

licker 90000000000000000

Graph the line.
y+2x = -2
x
-6
2
4
6
00
can someone help me with this??

Answers

Answer:

below

Step-by-step explanation:

I graphed the function using a graphing tool

find the are of the square 3.5

Answers

Answer:

1.87

Step-by-step explanation:

describe the best answer for kx+3x=4 when solving for x

Answers

Answer:

x = [tex]\frac{4}{k+3}[/tex]

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

1/3,-1,☑8,4.5 which ones greater?

Answers

Answer:

8

Step-by-step explanation:

Arrange the terms in ascending order.

[tex]-1, \frac{1}{3}, 4.5, 8[/tex]

The maximum value is the largest value in the arranged data set.

8

There are two green boxes and two red boxes. How many possible ways are there of arranging the boxes in a row?

A. 4
B. 6
C. 12
D.24

Answers

Four, they said my answer has to be atleast 20 characters long so djdbdbdbdbdbdbdhdbdbdbdhdbdhdhdhdhdhdhdhdhdhdhdhhdhd

how do i find the volume of this shape

Answers

Answer:

Finding the exact volume is physically impossible, however, you can find a rough estimate by calculating side lengths and that stuff

Step-by-step explanation:

A baseball diamond is a square that measures 90 feet on each side. How far does the third baseman have to throw the ball to reach first base?
pls help ​

Answers

Answer:

127.28

Step-by-step explanation:

The formula for the diagonal of a square is:

Diagonal = The square root of: 2, multiplied by the length of one side.

A bow of chocolates contains 18 chocolates squares. Ten of those squares are milk chocolate, 5 are dark chocolate, and 3 are whit chocolate. If Christina randomly chooses a chocolate out of the box, what is the probability of her choosing a white chocolate square?

Answers

I’m pretty sure it is 3/26. Hope that helps!

Classify the following number as rational or irrational 8\5,pi,0,1,4.466...,-6,2

Answers

Answer:

8/5 = Rational

Pi = Irrational

0 = Rational

1 = Rational

4.466... =  Rational

-6 = Rational

2 = Rational

Step-by-step explanation:

Any number that can be written as a fraction with integers is a rational number. The only way something can be irrational is if it goes on forever with no pattern. Hope this helps.

sum of the numbers m and n decreased by their product; write the algebraic expression​

Answers

Answer:   m+n-mn

You can write mn as m*n

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

Explanation:

The sum is the result of adding two or more numbers. Saying the sum of m and n means m+n.

Then we subtract off the product of m and n. The product is the result of multiplying m and n. We say m*n or mn to indicate their product.

Overall, we end up with m+n-mn

12x2= plz get it right plz

Answers

it is 24

12x2=12+12=24

1. Define a Transformations and a reflection. What is the
difference between them?

Answers

Answer:

More advanced transformation geometry is done on the coordinate plane. The transformation for this example would be T(x, y) = (x+5, y+3). A reflection is a "flip" of an object over a line.

What is the answer for 10+2(10n+4)

Answers

Answer:

20n + 18

Step-by-step explanation:

10 + 2(10n + 4)

10 + 20n + 8

20n + 18

Hey there!

[tex]Answer:\boxed{20n+18}[/tex]

[tex]Explanation:[/tex]

[tex]10+2(10n+4)[/tex]

Let's start by distributing.

[tex]10+(2)(10n)+(2)(4)\\10+20n+8[/tex]

Now combine like terms.

[tex]10+20n+8\\(20n)+(10+8)\\20n+18[/tex]

[tex]\boxed{20n+18}\text{ is the answer.}[/tex]

Hope this helps!

[tex]\text{-TestedHyperr}[/tex]

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