Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees of R? Explain.
Answers
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
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.
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 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!!
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 = 11I hope this helps!
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
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:
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! ^^)
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
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.
Angela $17.5 per hour
no its not proportional because half of 50 is 25 so therefore 42 would not be prportional to 25
6. Solve X^2 - 3x - 10=0 by factoring,
F-5, -2)
G(-2,5)
H{-2,-5)
J{5,-2)
Answers
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 !
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.
Have a nice day :)
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
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.
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.
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
#SPJ6
what is the least common denominator of 4/5 and 3/10?plssreal quick
Answers
Answer:
5
Step-by-step explanation:
whats 6 x 3 + 36 help meeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
54
Step-by-step explanation:
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.
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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
347 is what in expanded form
Answers
Answer:
300+40+7
Step-by-step explanation:
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
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
Need help with this problem and a step by step explanation
Answers
(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
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
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
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
Need answers ASAP
I will give brainliest to first who responds
Answers
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
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
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:
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