[tex]\large\underline{\sf{Solution-}}[/tex]
Given that
[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]
and
[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]
So, By using Long Division Method, we have
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: {x}^{2} - 3x + 2\:\:}}}\\ {\underline{\sf{x + 1}}}& {\sf{\: {x}^{3} - {2x}^{2} - x + 2 \:\:}} \\{\sf{}}& \underline{\sf{- {x}^{3} - {x}^{2} \: \: \: \: \: \: \: \: \: \: \:\:}} \\ {{\sf{}}}& {\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: - 3{x}^{2} - x +2 \: \: \: \: \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: \: \: \: 3{x}^{2} + 3x \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: 2x + 2 \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \: \: \: \: \: - 2x - 2\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: 0\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
So,
[tex]\bf\implies \:Remainder = 0[/tex]
Verification
[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]
[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]
[tex] \purple{\rm :\longmapsto\:Remainder = 0}[/tex]
[tex] \purple{\rm :\longmapsto\:Quotient = {x}^{2} - 3x + 2}[/tex]
Now, Consider
[tex]\rm :\longmapsto\:Divisor \times Quotient + Remainder[/tex]
[tex]\rm \: = \: (x + 1)( {x}^{2} - 3x + 2) + 0[/tex]
[tex]\rm \: = \: {x}^{3} - {3x}^{2} + 2x + {x}^{2} - 3x + 2[/tex]
[tex]\rm \: = \: {x}^{3} - {2x}^{2} - x + 2[/tex]
[tex]\rm \: = \: Dividend[/tex]
Hence, Verified
CARRY ON LEARNING
CAN YOU BRAINLEST ME PLEASE
Youth Group Trip
The youth group is going on a trip to an amusement park in another part of the state. The trip costs each
group member $150, which includes $85 for the hotel and
two one-day combination entrance and meal plan
passes. How much is the park per person?
a Write an equation representing the cost of the trip. Let P be the cost of the park pass. What’s the answer?!?!
Answer:
$32.50 = p
Step-by-step explanation:
$150 = 85 = 85 +85 + 2p
65/2 = 2p/2
A quality manager for a publishing company checks 3 of every 250 books printed for typos. At that rate, how many of every 15,000 books will be checked for typos?
Answer:
Print between 25 - 2,000 books. Your price per book will go down as your quantity increases.
Step-by-step explanation:
The x-intercept of f(x) is 5. If g(x)=f(x+2), then what is the x-intercept of g(x)?
Answer:
To find the
x- intercept, we set y=0 and solve for x:0=.5x−3
3=.5x
6=x
So. the x-intercept is
(6,0)
To find the
y-intercept, it's a similar system We set x=0 and solve for y this time.
y=.5⋅0−3
y=−3
That was easy :)
So, our y-intercept is (0,−3)
Just to double check our work, let's graph the equation and see the
x and y- intercepts
graph{y=.5x-3}
Yep,
(6,0) and (0,−3). We were right!
{x: x belongs to N and (x-1)(x-2) = 0}, finite set or infinite set?
Explanation:
We have a set of x values such that (x-1)(x-2) = 0. Breaking that down leads to either x-1 = 0 or x-2 = 0 through the zero product property. Solving each of those equations gets us x = 1 and x = 2 as the two items in this set.
So the original set your teacher gave you turns into the roster form {1,2}. There are two items in this set and we can see it's a finite set since it does not go on forever. Note that everything in this set is a natural number.
In Exercises 9-12, tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer 12. Line 1: (10, 5), (-8, 9) Line 2: (2, -4), (11, -6)
Answer:
They're parallel.
Step-by-step explanation:
The reason they're parallel is because they both have the same slope.
trying to figure it out
Which algebraic expression represents
the phrase "half the value of x" ?
Answer:
½x - 40
Step-by-step explanation:
x^3+10x^2+19x-30/x+6
Answer:
make it an equation
Step-by-step explanation:
It's not an equation.
pls help. i will give brainliest!!!!!!
Answer:
the strong correlation
Take these points. 25 of them. Will Thanks give brainiest and 5 star
Answer:
What do you need help with? Please go easy on me. I'm just a kid.
Step-by-step explanation:
PLZZZ HELP X IS 44 .............
Answer:
y = 136
Step-by-step explanation:
the line is 180 degrees so
180-44 = 136 degrees
Answer:
y=136
Step-by-step explanation:
x=44 y=136
44+136=180
what is the equivalent value 3/2×(−2)
Answer:
= -3
multiplying and dividing fractions
Answer:
-3
Step-by-step explanation:
3/2^(-2)=-3
Hiroto spends \$68 on e-books and paperback books combined. Each e-book he buys costs $5 and each paperback book he buys costs $12. If Hiroto buys e-books and y paperback books which of the following equations best models the situation?
The equation that can be used to model the situation regarding the e-books and paperback is 5x + 12y = 68
The following information can be gotten from the question:
Total amount spent on e-books and paperback = $68
Cost of e-book = $5 each.
Cost of paperback = $12 each
Number of e-books = x
Number of paperbacks = y
Therefore, the equation that can be used to model the situation regarding the e-books and paperback will be:
= 5(x) + 12(y) = 68
5x + 12y = 68
The equation will be 5x + 12y = 68
Read related link on:
https://brainly.com/question/25212173
Express each number in standard form.
a) 1 X 10^3 + 0 X 10^2 + 4 X 10 + 9 X 1
b) 4 X 10^4 + 3 X 10^3 + 8 X 10^2 + 7 X 10 + 0 X 1
c) 8 X 10^6 + 1 X 10^5 + 5 X 1
a) 1,000 + 0 + 40 + 9
b) 40,000 + 3,000 + 800 + 70 + 0
c) 8,000,000 + 100,000 + 5
Please solve with explanation
Answer:
The x coordinate of S is b.
Step-by-step explanation:
a)
The coordinates of Point Q are:
(2a+2b)/2, 2c/2
= [(a + b), c].
The slope of the line AB
= (0-2c)/(2b-2a)
= -c/(b-a)
So The slope of the line QS = (b - a) / c = (b - a)/c.
Its equation is
y - c = (b - a)/c ( x - (a+b))
y = (b - a)/c ( x - (a+b)) + c.
The coordinates of Point P are:
(2a+0)/2, 2(c+ 0)/2
= (a, c)
The slope of the line AO
= (2c)/2a
= c/a
So The slope of the line PS = -a/c
Its equation is
y - c = -a/c(x - a)
y = -a/c(x - a) + c
b)
So:
(b - a)/c ( x - (a+b)) + c
= -a/c(x - a) + c
(b - a)(x - a - b) + c^2 = -a(x - a) + c^2
(b - a)(x - a - b) = -a(x - a)
bx - ab - b^2 - ax + a^2 + ab = -ax + a^2
bx - ax + ax + a^2 - a^2 - ab + ab = b^2
bx = b^2
x = b = the x coordinate of S.
c). The point R has the same x coordinate as S So RS is perpendicular to OB.
Bath and Body Works is having a special promotion on fall candles. Every 12th guest is receiving a free pumpkin scented candle and every 36th guest is receiving a free Carmel waffle scented candle. Which number of guests will receive both the pumpkin and caramel waffle scented candles?
Answer:
i d k but now i want candles from bath and body works
Step-by-step explanation:
What is the factored form of this expression?
4t2 − 27t + 18
A.
(4t − 18)(t − 1)
B.
(4t − 3)(t − 6)
C.
(2t − 9)(2t − 2)
D.
(2t − 6)(2t − 3)
Answer:
B
Step-by-step explanation:
Answer:
Have a great rest of your day :)
Step-by-step explanation:
PLS HELP I GOTTA TURN THIS INNN
Answer:
Lauren
Step-by-step explanation:
1/2 is Erin
3/4 is Lauren
Answer:
1/2 for Eric and 6/8 for lauren
Eric: 1/2 = 4/8
Lauren: 6/8
Lauren was more succesful
Step-by-step explanation:
3over 7 = blank over 35
Let blank be x
[tex]\\ \sf\longmapsto \dfrac{3}{7}=\dfrac{x}{35}[/tex]
[tex]\\ \sf\longmapsto 7x=35(3)=105[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{105}{7}[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
anybody answer this question seriously please it has to be correct
Answer: that epuals 2/7
Step-by-step explanation:exam
Write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -3. Then graph the line.
Answer:
y = 4/3x -3
Step-by-step explanation:
you run 15 miles in 150 minutes your brother runs 30 miles in 300 minutes are the rates proportional?
Answer:
im not sure on how to answer that
Step-by-step explanation:
The average mark scores by 29 students in a science test was 56%. Jessica was sick, so she sat the
test later and scored 71%. Including Jessica's score, what was the new value of the mean mark?
Answer:
56.5%
[tex] \frac{29 \times 56 + 71}{30 \times 100} = 0.565 = 56.5\%[/tex]
Add 2 1/2 + (-3 1/3). Write your answer as a mixed number in simplest form.
Answer:
Exact Form: -⅚
Decimal Form: -0.83 repeating
hey guys need help plese feeling like giving out mega points today
Answer:
The choice A.
Step-by-step explanation:
[tex] \frac{( \frac{a}{b} + 1) }{( \frac{b}{a} - 1) } \\ \\ \\ \frac{( \frac{a}{b} + \frac{b}{b}) }{( \frac{b}{a} - \frac{a}{a}) } = \frac{( \frac{a + b}{b}) }{( \frac{b - a}{a}) } \\ \\ \\ ( \frac{a + b}{b} ) \div ( \frac{b - a}{a} ) \\ \\ \\ (\frac{a + b}{b} ) \times ( \frac{a}{b - a} ) \\ \\ \\ = \frac{a(a + b)}{b(b - a)} [/tex]
I hope I helped you^_^
Show that 0.616 = 37/60
Answer:
77/125 = 37/60?
If this is a true or false problem it would be marked false.
Explain the parts of an angle
Answer:
line segments are the lines
rays are line segments that have one vertex
a vertex is the endpoint of a line(usually represented by a dot)
Step-by-step explanation:
Answer these questions pls
1. The constant in the equation is always zero.
Proportional or Non-proportional
2. Y=2x - 4
Proportional or Non-proportional
3.jimmy plans to save $20 every week
Proportional or Non-proportional
Answer:
1. Non-proportional
2. Proportional
3. Proportional
Factor the following expression completely.
16x^5-x^3
A. 1343 1) (4x + 1)
B. 13(41 – 1)
C. (413 – 22)
D. 13(16x2 – 0)
X^(16x^2-1) factor the expression
The answer to the graph
X^3(4x-1)(4x+1)
Write the missing exponent that makes the equation true: 4^t times 2^t = 2^what
4^t × 2^t = 2^what [convert all terms to the same base (2)]
∴ 2^t × 2^t × 2^t = 2^what [use the multiplicat law of exponents]
2^(t+t+t) = 2^what [simplify]
2^3t = 2^what
what = 3t