Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees of R? Explain.

Polynomial Function R Is The Difference Of Two Degree-2 Polynomial Functions P And Q. What Are The Possible

Answers

Answer 1

Answer:

D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.

Step-by-step explanation:

The possible degrees are 0, 1, and 2. Let's explain why by assuming the following is given:

P = 6x² - 3x - 2

Q = 3x² + 2x - 6

Let R = P - Q

Thus:

(6x² - 3x - 2) - (3x² + 2x - 6)

Open parentheses by distributing the factor of -1

6x² - 3x - 2 - 3x² - 2x + 6

Add like terms together

6x² - 3x² - 3x - 2x - 2 + 6

R = 3x² - 5x + 4

The leading term of R has a degree of 2. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 2.

Also, let us assume the following:

P = 4x² + 4x - 3

Q = 4x² + x - 8

Let R = P - Q

R = (4x² + 4x - 3) - (4x² + x - 8)

R = 4x² + 4x - 3 - 4x² - x + 8

Collect like terms

R = 4x² - 4x² + 4x - x - 3 + 8

R = 4x + 5 (4x² cancels 4x²)

The leading term of R has a degree of 1. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 1.

Also, let us assume the following:

P = x² + 2x - 3

Q = x² + 2x - 8

Let R = P - Q

R = (x² + 2x - 3) - (x² + 2x - 8)

R = x² + 2x - 3 - x² - 2x + 8

Collect like terms

R = x² - x² + 2x - 2x - 3 + 8

R = 5 (x² cancels x², and 2x cancels 2x)

The polynomial R has a degree of 0. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 0.

Therefore we can conclude that:

D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.


Related Questions

12(8 – 5) idk to anwsher plz hefp

Answers

Answer:

36

Step-by-step explanation:

12(8-5)

12 * 3

36

Answer:

36

Step-by-step explanation:

(8-5) =3  then u do

12x3=36

Dylan makes $336 for 32 hours of work, and Angela makes $420 for 42 hours of work.

1] How much do Dylan and Angela each make per hour?

2] Is Dylan’s wage for 25 hours proportional to Amber’s wage for 42 hours? Why or why not?

Answers

Answer:

Step-by-step explanation:

1 . Dylan : $336/32 hrs = 10.50/ hr Angela : $420/42hrs = $ 10.00/hr

2. No because $ 10.50x25 262.50 where ambers is 15 420 there unit rate is different.

Dylan $10.5 per hour
Angela $17.5 per hour
no its not proportional because half of 50 is 25 so therefore 42 would not be prportional to 25

A taxi driver charges a fee if $4 plus 1.50 per mile. If you total was $13 how manu miles did you take

Answers

Answer:

6

Step-by-step explanation:

you need to do this (13-4)/1.50

what is the value of x in the equation 2/3(6x-9)=2(x+12)

Answers

Answer:

x=15

Step-by-step explanation:

hope this helps

6. Solve X^2 - 3x - 10=0 by factoring,
F-5, -2)
G(-2,5)
H{-2,-5)
J{5,-2)

Answers

Answer:

x₁ = 5

x₂ = - 2

Step-by-step explanation:

Hi there !

x² - 3x - 10 = 0

x² + 2x - 5x - 10 = 0

x(x + 2) - 5(x + 2) = 0

(x - 5)(x + 2) = 0

x - 5 = 0 => x₁ = 5

x + 2 = 0 => x₂ = - 2

Good luck !

Given a linear equation with a slope of - 13/4, determine the slope of a line that is perpendicular. Enter the answer as a fraction.

Answers

Answer:

4/13

Step-by-step explanation:

To find the perpendicular slope, find the negative reciprocal, which is 4/13 in this case. All you do is flip the numerator and denominator, and change the sign.

Answer:

4/13 should be the answer as it is the reciprocal.

Step-by-step explanation:

I learned this like 2 or 3 years ago so im a bit rusty but im pretty sure thats the answer

Mary has a bag with 80 pieces of candy. She gives ¼ of her candy to John and 10% to Lisa. How much more candy did she give to John then Lisa?

Answers

Answer:

12 pieces

Step-by-step explanation:

80 pieces of candy

1/4 is 25% or 20 pieces of candy

10% would be 8 pieces of candy

subtract the two. Your answer is 12

Answer:

He had 14 more pieces

Step-by-step explanation:

So 80/4 is 20 pieces. So we know John has 20. Now she has 60 left since 80-20 is 60. Now 10 percent of 60 would be 6 pieces. We can subtract 6 from 20 to find out how many more pieces John had. 20-6 is 14. So John had 14 more than Lisa

There are 16 squares and 20 triangles. What is the simplest ratio of squares to total shapes?

Answers

Answer:

1:6

Step-by-step explanation:

There are 20 triangles and four squares, so we know the first part of the ratio is 4. The total number of shapes is 24, so we get 4:24, and if we simplify, we then get 1:6.

Hope this helps!

There is a total of 16 squares, then the ratio of squares to total shapes is 4:9.

What is an arithmetic operation?

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given information provided by the question is,

Total number of squares = 16

Total number of shapes = 16 + 20 = 36

Ratio between squares and total shapes,

= 16 : 36

= 4 : 9.

To know more about arithmetic operation:

https://brainly.com/question/13585407

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Explain how you can determine that the following
system has one unique solution – without actually
solving the system.

2x+y = 4
2y = 6- 2x

Answers

you can graph it with the calculator or on graph paper and see where the two lines would cross
you would put them in slope-intercept form (y=mx+b)

so
2x + y = 4 would become
y = -2x + 4

and

2y = 6 - 2x becomes
y = -x +3

graph them and see where they cross. hope this helps!!

Find m a. 90
b. 31
c. 59

Answers

Answer:

i think its B

sorry if its wrong im not really sure by my answer

Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the article to learn key facts about the economics of organic produce and answer a few questions.

Which is a reason that organic farming is more expensive than conventional farming?



How many years must a farm be run organically before its produce can be labeled as “organic”?



What is a benefit of crop rotation?

Answers

Answer:

Which is a reason that organic farming is more expensive than conventional farming?

Organic farmers must pay for a costly certification process

How many years must a farm be run organically before its produce can be labeled as “organic”?

3

What is a benefit of crop rotation?

Rotating crops can help build healthy soil.

Step-by-step explanation: Hope you pass! :)))

first one is C second one is 3 third one is A

hope i helped

Can someone help me figure out what are the two checkpoints?

Answers

Answer:

13,000 ft.

Step-by-step explanation:

X -------10960----------C---------------D---------------Y

The entire race (from X to Y) is 7 miles.  There are 5,280 ft. in one mile, so 7 miles is 36960 ft.

If we subtract 10,960 from 36,960, then we get the distance from C to Y.

36960-10960 = 26000

They tell you D is at the midpoint between C and Y

So if we divide 26,000 by 2, then we know the distance from C to D and from D to Y.

26000/2 = 13000

The checkpoints are C and D, so the distance between them is 13,000 ft.

The third option is correct: 13,000 feet

Have a nice day :)

What is the remainder of 2x3 − 7x2 + 5x − 1 divided by (x − 3)?

−211
5
−133
2

Answers

By the remainder theorem, the remainder upon dividing p(x) = 2x³ - 7x² + 5x - 1 by x - 3 is p(3),

p(3) = 2(3)³ - 7(3)² + 5(3) - 1 = 5

whats 6 x 3 + 36 help meeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

54

Step-by-step explanation:

The crew on a fishing boat caught four fish that weighed a total of 1,080 pounds. The
tarpon weighed twice as much as the amberjack
and the white marlin weighed twice
as much as the tarpon. The weight of the tuna was 5 times the weight of the
amberjack
How much did each fish weigh?
The amberjack weighed
pounds.
The tarpon weighed
pounds.
The marlin weighed
pounds.
The tuna weighed
pounds.
Kk

Answers

Answer:

Step-by-step explanation:

First, We highlight key details. Here we can use the information 1,080 pounds, tarpon weighed twice as much as the amberjack, the white marling weighed twice as much as the tarpon, and the tuna weighed 5 times the weight of the amber jack. And....I'm lost. Do you think you could help me figure it out by finding the first one? if you do that would be great, and I'll be sure to update my question. Thank you! ^^)

I need some help I suck at math‍♂️‍♂️

Answers

Answer:

x = 11

Step-by-step explanation:

Add 7/6 to each side, so it now looks like this: 5/6x = 55/6Divide each side by 5/6 to cancel out the 5/6 next to x. It should now look like this: x = 11

I hope this helps!



Martel sold 7 cups of lemonade at his lemonade stand. How many fluid ounces did he sell?

Answers

Answer: Your answer is 56 fluid ounces

Step-by-step explanation: 1 cup (in the us) is equivalent to 8 fluid ounces (in the us) and 8 times 7 is 56!

Hope this helps, if not, comment below please!!!

Answer:

56 fluid ounces

Step-by-step explanation:

One cup has 8 fluid ounces and one fluid ounce is 0.13 cups.

cup * 8 = fl-oz

Which expression is equivalent to the given expression after using the distributive property? 9(x + 3) + 15x




9 · x + 9 · 3 + 9 · 15x



9(x + 3 + 15)x



9 · x + 3 + 15x



9 · x + 9 · 3 + 15x

Answers

Answer:

9 • x + 9 • 3 + 15x

Step-by-step explanation:

You have to divide 9 by each term inside the parenthesis. 15x isnt multiplied or added to anything else so it stays the same.

i need your help and to try this out so can you please answer dis
-2(x+6)

Answers

Answer:

12x - 12

Step-by-step explanation:

-2(x  + 6)

open the parenthesis

-2 * x + -2 * 6

-2x - 12

-2x - 12

I will give the BRAINIEST!!! Please help!!

The partial blueprint for an office building shows one outer wall and a perpendicular inner wall. Which of the following could be the equation of the inner wall, if the outer wall is represented by the equation y = 2/5x-1

a. y= -5/2x -4
b. y= -2/5x-4
c. y=5/2x-4
d. y=2/5x-4​

Answers

Answer:

a. y= -5/2x -4

Step-by-step explanation:

An equation that is perpendicular to another equation must have the opposite slope. In other words, the perpendicular equation will be the opposite sign & the reciprocal of the equation it is perpendicular to. In this case, the perpendicular slope is -5/2x. Therefore, the only answer possible is a.

the two Marked angles are congruent yes or no will mark brainest​

Answers

Answer:

true

Step-by-step explanation:

if the vertical lines are not parallel, then the corresponding angles are not congruent.

8x + 2 = 14x - 76

8x - 14x = -76 -2

-6x = -78

x = 13

8(13) + 2 = 14(13) - 76

106 = 106---- equal

the vertical lines is a bit confusing.... they looks like not a parallel lines

347 is what in expanded form

Answers

Answer:

300+40+7

Step-by-step explanation:

If 40x = 400, then A. x equals 100. B. x equals 10. C. I equals 4. O D. x equals 1. E. requals 0 ).​

Answers

Answer:

B- x= 10

Step-by-step explanation:

40x=400 ->  40 x 10= 400

The value of x in the expression 40x = 400 by combining like terms would be 10. Hence, option B is true.

Given that,

The expression is,

40x = 400

Used the concept of expression by combining like terms.

Here, the expression is,

40x = 400

Divide both sides by 40,

x = 400/40

Therefore, the solution of x is,

x = 10

So, Option B is true.

To learn more about the divide visit:

https://brainly.com/question/28119824

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I need help really quickly with this one!

Answers

Answer: A (y = 1)

Step-by-step explanation:

when dividing, dividing by 0 equals an undefined fraction, therefore, if y was equal to 1, it would cancel out the y - 1, making it 0. I hope that's right :0

what is the least common denominator of 4/5 and 3/10?plssreal quick​

Answers

Answer:

5

Step-by-step explanation:

The least common denominator of 4/5 and 3/10 would be 5.

Need help with this problem and a step by step explanation

Answers

the answer b
(i can’t explain and if i did it would be confusing)
but here’s this:
the lower the number, the more to the right

What is the range of the function f(x) = 2x+3

Answers

Answer: (-∞,∞)

Step-by-step explanation: The line extends forever in both directions meaning that the endpoints will be negative infinity and infinity.

the ordered pair (x,y)=(2,-3) is a solution to which of the following systems of equation

Answers

Answer:

Y=2x-7

Step-by-step explanation:

Gloria deposited $500 into a bank account that earned 7.5% simple interest each year. She earned $225 in interest before closing the account.

No money was deposited into or withdrawn from the account.

How many years was the money in the account?

Round your answer to the nearest whole year.

Answers

Answer:

6

Step-by-step explanation:

7.5 % × 500 = 37.5

37.5 × 6 = 225

Answer:

6

Step-by-step explanation:

Need answers ASAP
I will give brainliest to first who responds

Answers

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