MATHEMATICS COLLEGE

(1) -3x-4y+11z from-9y+6z-3x
(2) 3x⁴-4x³+7x-2 from 9-7x⁴+6x³-2x²-11x

Answers

Answer 1

Answer:

Answer:

1) 5y + 5z

2) 10x⁴ - 10x³ + 2x² + 18x - 11

Step-by-step explanation:

Given the subtraction of the following polynomial expressions:

(1) -3x - 4y + 11z from -9y + 6z - 3x

In order to make it easier for us to perform the required mathematical operations, we must first rearrange the terms in the subtrahend by alphabetical order.

-3x - 4y + 11z

-3x - 9y + 6z ⇒ This is the subtrahend.

Now, we can finally perform the subtraction on both trinomials:

$\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}} \right.}$

In the subtrahend, the coefficients of x and y are both negative. Thus, performing the subtraction operations on these coefficients transforms their sign into positive.

$\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:\:0x\:+\:5y\:+5z$

The difference is: 5y + 5z.

(2) 3x⁴- 4x³ + 7x - 2 from 9 - 7x⁴ + 6x³- 2x² - 11x

Similar to the how we arranged the given trinomials in Question 1, we must rearrange the given polynomials in descending degree of terms before subtracting like terms.

3x⁴- 4x³ + 7x - 2 ⇒ Already in descending order (degree).

9 - 7x⁴ + 6x³- 2x² - 11x ⇒ -7x⁴ + 6x³- 2x² - 11x + 9

In subtracting polynomials, we can only subtract like terms, which are terms that have the same variables and exponents.

$\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.}$

In the minuend, I added the "0x²" to make it less-confusing for us to perform the subtraction operations.

The same rules apply in terms of coefficients with negative signs in the subtrahend, such as: -7x⁴, - 2x², and - 11x ⇒ their coefficients turn into positive when performing subtraction.

$\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:10x^4-10x^3+2x^2+18x\:-11$

Therefore, the difference is: 10x⁴ - 10x³ + 2x² + 18x - 11.

Related Questions

Help please asp. !!!
I need help with my homework
Scura makes sun block and their annual revenues depend on how much they sell. Let x be the quantity of 5 oz. bottles of sun block that they make and sell each year measured in 1000 's of bottles. Thus if x=10 then they make and sell 10000 bottles of sun block each year. If x=25 then they make and sell 25000 bottles of sun block each year.a. If x=50 how many bottles of sun block does Scura make and sell?b. What is x equal to if Scura produces and sells 45000 bottles of sunblock?
You have a plate of 50 cookies. Ten have chocolate chips and 14 have pecans. On the cookies mentioned in the preceding sentence, 6 have both chocolate chips and pecans. You select a cookie at random. What is the probability that your cookie has chocolate chips or pecans
Jordan Ellen recycle cans Jordan recycle seven cans for every 12 cans Ellen recycled last week how many total cans did Jordan and Ellis recycle last week.

From 12 teachers to 48 teachers using perecent

Answers

Answer:

Teachers increase = 300 %

Step-by-step explanation:

Method to increase or decrease:

Change= Actual - Original

Actual= 48

Original= 12

Change= 48-12= 36

$P= (Change)/(Original) * 100$

$P= (36)/(12) * 100$ %

$P= 3 * 100$ %

$P= 300$ %

Multiply (4x-3w)(5x-7w)

Answers

Answer:

20x² - 43xw + 21w²

Step-by-step explanation:

We use FOIL to expand the expression:

F - First

4x(5x) = 20x²

O - Outside

4x(-7w) = -28xw

I - Inside

-3w(5x) = -15xw

L - Last

-3w(-7w) = 21w²

20x² - 28xw - 15xw + 21w²

Combine like terms and add up using correct signs and you should get your answer.

Answer:

$20 {x}^(2) - 43xw + 21 {w}^(2)$

solution,

$(4x - 3w)(5x - 7w) \n = 4x(5x - 7w) - 3w(5x - 7w) \n = 20 {x}^(2) - 28xw - 15xw + 21 {w}^(2) \n = 20 {x}^(2) - 43xw + 21 {w}^(2)$

Hopethishelps...

Goodluck on your assignment..

6 X 9 =
6 X (5 + 4)
6 X 9 = (6 X 5) + (6 X 4)
6 X 9 =
6 X 9 =
54

Answers

You gave us the answer it will be 54.

Answer:

Step-by-step explanation:

9(6)=54

6(9)=54

54=(30)+(24) 54=54 so it is true

9x6=54

Two teams A and B play a series of games until one team wins four games. We assume that the games are played independently and that the probability that A wins any game is p. What is the probability that the series lasts exactly five games?

Answers

Answer:

4pq(p³+q³)

Step-by-step explanation:

Exactly 5 game would be when 4 wins and 1 loss of a particular person

loss has to be one of the first 4 games

A wins: qp⁴ + pqp³ + p²qp² + p³qp

= qp⁴ + qp⁴ + qp⁴ + qp⁴ = 4qp⁴

B wins: pq⁴ + qpq³ + q²pq² + q³pq

= pq⁴ + pq⁴ + pq⁴ + pq⁴ = 4pq⁴

A wins or B wins:

4pq⁴ + 4qp⁴ = 4pq(q³+p³)

Help please! I’ll give brainliest!

Answers

the second one down from the top

The following are the ages (years) of 5 people in a room: 25, 18, 17, 13, 24 A person enters the room. The mean age of the 6 people is now 22. What is the age of the person who entered the room?

Answers

Answer:

See Below:

Step-by-step explanation:

Average is take by adding all the terms together and dividing by the number of terms. In this case it terms is people in the room.

22= (25+18+17+13+24+x)/6

Where 22 is the average age. The numerator is all the known ages added together, plus x which is the age of the person who just entered. Divided by 6 because you are finding the average age of 6 people.

22 = (25+18+17+13+24+x)/6 Multiply both sides by 6

132= 97+ x Subtract 97 from both sides.

35 = x

The person who just entered the room is 35 years old.

Final answer:

To solve this, we first find the total age of the original five people, then the total age of all six with the given mean age. By subtracting these, we find that the age of the person who entered is 35 years old.

Explanation:

This problem can be solved using simple arithmetic. First, we calculate the total age of the first 5 people, which is 25 + 18 + 17 + 13 + 24 = 97 years. Then, we need to determine the total age of all 6 people. We're told the mean (average) age of these 6 people is 22. We find the total by multiplying the mean by the number of people, so 22 * 6 = 132 years. Finally, to find the age of the person who entered the room, we subtract the total age of the first 5 people from this new total, i.e. 132 - 97 = 35 years. So, the person who entered the room is 35 years old.