Degree of a polynomial gives the highest power of its terms. Yes there is a difference between the degrees of sum and difference of the polynomials.
What is degree of a polynomial?Degree of a polynomial is the highest power that its terms pertain(for multi-variables, the power of term is addition of power of variables in that term).
Thus, in [tex]x^3 + 3x^2 + 5[/tex], the degree of the polynomial is 3 as the highest power in its terms is 3.
(power and exponent are same thing)
What are like terms?Those terms which have same variables raised with same powers.
For example, [tex]x^3[/tex] and [tex]3x^3[/tex] are like terms since variable is same, and it is raised to same power 3.
For example [tex]4x^2[/tex] and [tex]x^3[/tex] are not like terms as the variables are same but powers aren't same.
The given polynomials are:
[tex]c(x) = x^7 + 3x^5 + 3x + 1\\\\p(x) = x^7 + 5x + 10[/tex]
Their sum is
[tex]c(x) + p(x) = x^7 + 3x^5 + 3x + 1 + x^7 + 5x + 10 = (1+1)x^7 + 3x^5 + (3+5)x + 11\\\\c(x) + p(x) = 2x^7 + 3x^5 + 8x + 11[/tex]
(only like terms' coefficients can be added (or subtracted) for addition or subtraction of them )
The sum's degree is 7
Their difference is:
[tex]c(x) - p(x) = x^7 + 3x^5 + 3x + 1 - x^7 -5x - 10 = (1-1)x^7 + 3x^5 +(3-5)x -9\\\\c(x) - p(x) = 3x^5 - 2x - 9[/tex]
Difference's degree is 5
Thus, both's degrees are not same.
Thus, Yes there is a difference between the degrees of sum and difference of the polynomials.
Learn more about subtraction of polynomials here:
https://brainly.com/question/9351663
Given the function f(x)=4x2−3x+4f(x)=4x2-3x+4. Calculate the following values:
f(−2)=f(-2)=
f(−1)=f(-1)=
f(0)=f(0)=
f(1)=f(1)=
f(2)=f(2)=
Answer:
26, 11, 4, 5, 14
Step-by-step explanation:
To find the value of the function, replace the variable with the number and do the arithmetic.
f(-2) = 4(-2)² -3(-2) +4 = 16 +6 +4 = 26
For doing repetitive calculations, it is convenient to write the formula into a calculator or spreadsheet and let it work from the list of values. That is what we did in the attached. It shows a table of x and f(x) for the values of x you are interested in.
The function values are ...
f(-2) = 26f(-1) = 11f(0) = 4f(1) = 5f(2) = 14_____
Additional comment
For evaluating polynomials, either by hand or machine, it is often convenient to rewrite the polynomial in Horner Form. The total number of math operations tends to be reduced. When doing this by hand, the arithmetic tends to be easier.
f(x) = (4x -3)x +4
That is, the powers of x accumulate as each layer in parentheses is multiplied by x and the next coefficient added to the result.
Using this form, ...
f(-1) = (4(-1) -3)(-1) +4
f(-1) = (-7)(-1) +4 = 11
I need help!!!!!!!!!
Answer:
Greatest- 2 × 4/9
Then- 1 2/3 × 4/9
Then- 7/7 × 4/9
Lest- 3/4 × 4/9
Step-by-step explanation:
The right hand fraction you are timing by is the same whilst on the left they grow so you order them and dont focus on the times aspect of the question
One equation in a system of equations is y=2x+10. Which equation below would have to be the second equation so that the system has infinitely many solutions?
Answer:
D
Step-by-step explanation:
y = 2x + 10 is the same thing as y = 2(x + 5) because 2 x x = 2x and 2 x 5 = 10
Simplify Option D
y=2(x+5)y=2x+2(5)y=2x+10As everything is same
i.e
A1/A2=B1/B2=C1/C2Hence infinitely many solutions are present
Angie packed same-size cubes into a rectangular prism.
Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall. PLEASE HELP ME
What is the number of cubes needed to fill this prism?
A.
20 cubes
B.
35 cubes
C.
36 cubes
D.
42 cubes
WILLL GIVE THE BRAINLIEST PLEASE HELP ME IN A RUSH
Answer:
the answer is 42 can i have brainliest please:)
Step-by-step explanation:
3x7x2=42
Answer:
42
Step-by-step explanation:
help me please i don't uderstand
Answer:
(a) d = 2.1 (b) a = 8.7
Step-by-step explanation:
[tex]d^{2}+d^{2} = 3^{2}[/tex]
[tex]2d^{2} = 9\\d = \sqrt[2]{9/2} = 2.1[/tex]
The hypotenuse = 5*2 = 10
[tex]5^{2} + a^{2} = 10^{2}\\a^{2} = 100 - 25 = 75\\a = \sqrt{75} = 8.7[/tex]
helpppppp pleaseeeeeee
Joe will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $51.98 and costs an
additional $0.17 per mile driven. The second plan has an initial fee of $59.98 and costs an additional $0.13 per mile driven. How
many miles would Joe need to drive for the two plans to cost the same?
Answer:
200
Step-by-step explanation:
This problem is about linear equations. We assume Joe drive X miles, and the total cost is $Y, then we can get:
Plan I: Y=51.98+0.17X
Plan II: Y=59.98+0.13X
When both plans cost the same, 51.98+0.17X=59.98+0.13X. We will get X = 200
Hi! -2x + y = -11 4x + 4y = 4 System by substitution!!!
Answer:
Point Form:
(
8
3
,
−
5
3
)
Equation Form:
x
=
8
3
,
y
=
−
5
3
Answer:
x=4, y=-3, or (4,-3)
Step-by-step explanation:
Hi there!
We are given the following system of equations:
-2x+y=-11
4x+4y=4
And the problem wants us to solve it by substitution
In substitution, we will solve one of the equations for one of the variables to equal an expression containing the other variable, then substitute that expression as the variable it equals into the other equation, solve that equation, then use the value of the solved variable to solve for the first equation we made (the one that is a variable equaling an expression containing the other variable)
It's easier to do this when one of the variables already has a coefficient of 1, as we can just move a couple of terms around without having to multiply or divide anything; for example, in the first equation, -2x+y=-11, y already has a coefficient of 1
So we can just add 2x to both sides, in order to solve the equation for y
-2x+y=-11
+2x +2x
______________
y=2x-11
Now substitute this expression into the the second equation as y.
So, 4x+4y=4 would become 4x+4(2x-11)=4
Now we need to solve 4x+4(2x-11)=4
Do the distributive property:
4x+8x-44=4
Combine like terms
12x-44=4
Add 44 to both sides
12x=48
x=4
We found the value of x
Now we need to find the value of y
Substitute 4 as x in y=2x-11
y=2(4)-11
Multiply
y=8-11
subtract
y=-3
The answer is x=4, y=-3, or as a point, (4, -3)
Hope this helps!
See more on solving systems by substitution here:
https://brainly.com/question/24420448
Help if you understand Thanks
Answer:
b
Step-by-step explanation:
Repeating domain (x-values) does not represent a function.
Option b does not have any repeating domains.
Hope this helps!
Answer:
The answer is the third one.
Step-by-step explanation:
Hopefully this is helpful :)
Help me pls
1. In a two-digit number, the sun of the two digits is 10. If the two digits are reversed, the original number is less than the new number by 36. Find the original number.
2. In a two-digit number, twice the tens digit is less than the units digit by 3. If the two digits are reversed, the new number is greater than twice the original number by 18. Find the original number
1) The pairs of numbers are:
19 and 91, which do not satisfy the condition
28 and 82, which do not satisfy the condition
37 and 73, which satisfy the condition
45 and 54, which do not satisfy the condition
The number is 37.
Another method:
10x+y+36 = 10y+x, or
9x+36 = 9y, or
x+4= y …(1)
x+y = 10, or
y = 10-x …(2)
Equate (1) and (2)
x+4 = 10-x
2x = 10–4 = 6, or x = 3 so y = 10–3 = 7.
So the number is 37
( Sorry I can answer number 1 i'm in a rush and I don't really use my brain it's useful but also not. I hope someone answer your question number 2 'ᴗ' Good luck! I also hope my answer is useful. )
please help ASAPPPP SOMEONE :(
Answer:
rip
Step-by-step explanation:
which choice shows angles that are complementary and adjacent?
Answer:
1st one is adjacent
2nd one is complementary
3rd one is adjacent
4th one is complementary
Jake is buying a sweater with a price of $30 shown on the tag. The store is having a sale that will reduce the price by 30%. Sales tax of 5% will be added to the final purchase price. What is Jake’s total cost for the sweater? (I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $22.05)
Reducing
30-30*0.3=
21
21+21*0.05=22.05
Just an answer and a simple explanation are needed. Please and thank you!
Answer:
KL = 51
Step-by-step explanation:
1: Make an equation
[tex]10x -2 = 5x-8 + 7x -12[/tex]
the 10x is the JL line which is the whole line segment
2: start solving by getting all x to be on one side
[tex]10x-5x-7x = -8 -12 +2[/tex]
3: simplify
[tex]-2x = -18[/tex]
4: solve for x
[tex]x=9[/tex]
5: plug x back into KL
[tex]7(9)-12 = 51[/tex]
HELP PLEASE
A 180-ounce bag weighs more than an 11-pound bag. True or false?
True
False
Answer:
True
Step-by-step explanation:
Just a tip, there are 16 ounces in a pound, and just searching 180 ounces into pounds can help with this stuff to if you don't want to do math yourself
Answer: False
Step-by-step explanation: Pound weighs more in ounce.
Celia has some cakes.
2/3
of the cakes are chocolate cake and
6/7
of the remaining cakes are cheesecakes. The rest of the cakes are carrot cakes.
What fraction of the cakes are carrot cakes?
Leave your answer as a fraction in the simplest form.
The carrot cakes are the fraction of the cake given by [tex]1 - \frac{6}{7}[/tex] multiplied by [tex]\frac{1}{3}[/tex]
The fraction of the cakes that are carrot cakes is [tex]\underline {\dfrac{1}{21}}[/tex]How are the cakes evaluated as fractions?The fraction of the cake that are chocolate cake = [tex]\dfrac{2}{3}[/tex]
The fraction of the remaining cake that cheesecakes = [tex]\dfrac{6}{7}[/tex]
The rest of the cakes = carrot cakes
Required:
The fraction of the cake that are carrot cakes
Solution:
The fraction of the cakes that are not chocolate cake = [tex]1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}[/tex]
The fraction of the remaining cakes that are cheesecake = [tex]\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}[/tex]
The fraction of the cake that are carrot cake = [tex]\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}[/tex]
The fraction of the cakes that are carrot cake is [tex]\underline{\dfrac{1}{21}}[/tex]Learn more about fractions here:
https://brainly.com/question/3840488
Special right triangle 30-60-90 degrees lesson 3 homework
I need help please! There are only 3 answer choices.
A cat climbed up a 6.5 ft ladder. If the ladder is placed at a 75 degree angle of elevation, then how far up the tree is the top of the ladder?
A) 5.9 feet
B) 6.3 feet
C) 6.7 feet
Answer:
B) 6.3 feet
Step-by-step explanation:
sin Θ = opp/hyp
sin 75° = h/6.5
h = 6.5 sin 75°
h = 6.3
Answer: B) 6.3 feet
If r = 12.5 and s = |−13|, which of the following inequalities is not true?
r ≠ s
r < s
r ≥ s
r ≤ s
Answer:
C is not true
Step-by-step explanation:
r is not larger than or equal to s
The _____ is a point estimate of the population mean for the variable of interest. a. sample mean b. geometric mean c. median d. sample
There are different ways to estimate a variable. The sample mean is a point estimate of the population mean for the variable of interest.
What is a point estimate of the population mean?A point estimate is known to be the value of a sample statistic that is often applied as one estimate of a specific population parameter.
The sample mean is defined simply as a form of average value seen in a sample. A sample is known to be the little portion of a whole.
Learn more about sample mean from
https://brainly.com/question/7597734
Directions: Solve the following inequalities. Be sure to follow the rules for operations with signed numbers.
1. -4x + 2 > 0
2. +5x > x + 4
3. 3x + 4 < 10
4. -10x + 5 -4 > 4x + 3
5. 6x + 3 < 7x - 10
6. 2x - 4 < 8x + 2
7. -3s + 3 > 3
8. 4s + 2s > 6
9. 6t < 12
10. 11x < 121
11. 3x > 36
12. 25x < 500
13. 16r < 8 (10)
14. 6s > 216
15. 8x < 64
cot 75= 2 - square root 3
Answer:
The value of cot 75° is 2 - √3 or 0.2679(approx).
Step-by-step explanation:
I hope it helps!
Muffin<3
The table shows the purchases of two customers at a concession stand at the basketball game. Hamburgers Drinks Total Cost Customer 1 2 $13.00 Customer 2 3 7 $21.00 You want to buy 8 drinks and 9 hamburgers for you and your friends. How much do you expect to pay?
[tex]\bold{\huge{\blue{\underline{Solution}}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
Customer 1 bought 2 hamburgers and 4 drinks at a cost of $13.00Customer 2 bought 3 hamburgers and 7 drinks at a cost of $21.00[tex]\bold{\underline{ To \: Find :- }}[/tex]
We have to find the total cost of 8 drinks and 9 hamburgers[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]
Let the cost of hamburgers and drinks be x and y
According to the question,
[tex]\sf{ 2x + 4y = 13.00 ...eq( 1 ) }[/tex]
[tex]\sf{ 3x + 7y = 21.00 ...eq(2) }[/tex]
Solving eq( 1 ) we get :-
[tex]\sf{ 2x + 4y = 13 }[/tex]
[tex]\sf{ 2x = 13 - 4y }[/tex]
[tex]\sf{ x = (13 - 4y)/2 ...eq(3)}[/tex]
Subsituting eq(3) in eq( 2 ) :-
[tex]\sf{ 3( 13 - 4y)/2 + 7y = 21 }[/tex]
[tex]\sf{ 39 - 12y/2 + 7y = 21 }[/tex]
[tex]\sf{ 39 - 12y + 14y = 42}[/tex]
[tex]\sf{ 2y = 42 - 39 }[/tex]
[tex]\sf{ 2y = 3 }[/tex]
[tex]\sf{ y = 3/2 }[/tex]
Subsituting value of y in eq(3) :-
[tex]\sf{ x = 13 - 4(3/2)/2}[/tex]
[tex]\sf{ x = 13 - 2(3)/2}[/tex]
[tex]\sf{ x = 13 - 6/2}[/tex]
[tex]\sf{ x = 7/2 }[/tex]
Therefore,
[tex]\sf{ Cost\: of \:8 \:drinks}[/tex]
[tex]\sf{ = 8 * 3/2 }[/tex]
[tex]\sf{ = 4 * 3 }[/tex]
[tex]\sf{ = 12.00 dollars}[/tex]
And
[tex]\sf{ Cost\: of \:9 \:hamburgers }[/tex]
[tex]\sf{ = 9 * 7/2 }[/tex]
[tex]\sf{ = 63/2}[/tex]
[tex]\sf{ = 31.50 dollars}[/tex]
Total cost of the 8 drinks and 9 hamburgers
[tex]\sf{ 12.00 + 31.50}[/tex]
[tex]\sf{\red { = 43.50 \:dollars}}[/tex]
Hence, The total cost paid by you for 8 drinks and 9 hamburgers is $43.50 .
please please please help
Answer:
32
4 cups
Step-by-step explanation:
Answer:
ratio
Step-by-step explanation:
0 to 100
i dont know the second one srry
A robot can complete 7 tasks in
2
3 hour. Each task takes the same amount of time.
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
the answer is fourteen (14)
Is what's below a complete sentence or a fragment?
Iris West is very happy today.
Answer:
complete sentence
Step-by-step explanation:
it has a subject and a verb
Answer:
I would say sentence.
Step-by-step explanation:
It has punctuation, a subject, and a verb, so I would say it's a sentence.
(56x + 16y) × 0,4/x = 32
what is x and y?
Answer:
112x + 32y
----------------
5x
Step-by-step explanation:
x and y are variables
1- Convert the expression
2- Simplify the expression
3- Calculate
Given cos 0 = 1/6 and angle 0 is in Quadrant IV, what is the exact value of sin 0 in
simplest form? Simplify all radicals if needed.
cos 0 = 1/6
1 - cos²0 = sin²0
sin²0 = 35/36
in quadrant IV (4) the cos is positive sin is negative.
sin0 = - √35/6
Will someone please help me with this?!? It’s simple but my answer isn’t correct. I would appreciate it so much
Answer:
(2x + 1)(3x - 2)
Step-by-step explanation:
f(x) = 6x² - x - 2
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 2 = - 12 and sum = - 1
the factors are + 3 and - 4
use these factors to split the x- term
6x² + 3x - 4x - 2 ( factor the first/second and third/fourth terms )
= 3x(2x + 1) - 2(2x + 1) ← factor out (2x + 1) from each term
= (2x + 1)(3x - 2) , then
f(x) = (2x + 1)(3x - 2) ← in factored form
Ok I need help please?
Answer:
Step-by-step explanation:
1. 4/1
2. 5/1
3. 1/8
4. 2/3
5. 3/4
6. 4/12 = 1/3, 8/12 = 2/3
7. 2/5, 3/5