[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
How to find the slope
(In general)
Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: Slope =riserun Slope = rise run .
Type of Slope: Visual Description
Undefined: vertical
Negative: downhill
The sequence 2, 9, 20, 35, . . . is another example of a rectangular number pattern, as illustrated in the art below. What is the 50th term of this sequence?
Answer:
345 is the answer
Step-by-step explanation:
use the nth term sequence and you get 7n-5 just substitute 50 and you get that hope I helped!
The 50th term of this arithmetic sequence will be 9655.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The sequence 2, 9, 20, 35, . . . is another example of a rectangular number pattern, as illustrated in the art below.
The first term is 2 and the common difference depending on 'n' will be given as 4n - 3.
Then the 50th term of this arithmetic sequence will be
aₙ = a₁ + (n - 1)d
aₙ = a₁ + (n - 1)(4n - 3)
a₅₀ = 2 + (50 - 1) × (4 × 50 - 3)
a₅₀ = 2 + 49 × 197
a₅₀ = 2 + 9653
a₅₀ = 9655
The 50th term of this arithmetic sequence will be 9655.
More about the arithmetic sequence link is given below.
https://brainly.com/question/12373434
#SPJ2
What’s answer 10? Somebody please?
Answer:
Your table should be right. Plot these on your graph. (4,5) (8,10) (12,15) and (16,20). Hope it helps
Step-by-step explanation:
Lesson. Derative of trigonometric functions
Answer:
Step-by-step explanation:
What are the Derivatives of the 6 Trig Functions?
Derivation of sin x: (sin x)' = cos x.
Derivative of cos x: (cos x)' = -sin x.
Derivative of tan x: (tan x)' = sec2 x.
Derivative of cot x: (cot x)' = -cosec2 x.
Derivative of sec x: (sec x)' = sec x. tan x.
Derivative of cosec x: (cosec x)' = -cosec x. cot x.
a journey by bus takes 45 mins at 40km/h how fast must a car go to undertake the same journey in 25 mins
Answer:
72km/h
Step-by-step explanation:
Bus - 45 mins at 40km/h
Car - 25 mins at ?
First, find the distance travelled by the bus (since, the journey of the two vehicles are the same, the distance would be the same as well)
distance = speed × timedistance = 40 × 3/4 (45 mins = 3/4 of an hour (45 ÷ 60))distance = 30kmNow we can find the speed of the car using the equation
speed = distance ÷ timespeed = 30 ÷ 5/12 (25 mins = 5/12 of an hour (25 ÷ 60))speed = 72km/hwhat is the answer ?????????
Answer:10
Step-by-step explanation: dd
May I please receive help?
Answer:
J= 16.857°
K= 88 .4°
L=74.7°
Step-by-step explanation:
let x represent the angle of J
x° +(4x+21)° +(2x+41)° =180°
x + 4x + 21 + 2x + 41= 180° ( sum of angles in a triangle)
Collect like terms
x + 4x + 2x = 180 - 21 - 41
7x = 180
x =180/7
x=16.857
Therefore,
J = 16.857°
K=4x+21
=4(16.857)+21
= 67.4+21
=88.4°
L=2x +41
=2(16.857)+41
=33.7+41
= 74.7°
Sum of angles in the triangle =
16.857+88.4+74.7=179.9 approximately 180°
Hope this helps....
f(x)=5x-1; find f (-2), f (0), and f (x+1)
Answer:
f(-2) = -11
f(0) = -1
f(x+1)= f (x+1)=5x+4
Step-by-step explanation:
Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y=−4
y=8
Choose the correct answer below.
A.
Parallel
B.
Neither
C.
Perpendicular
A car dealership increased the price of a certain car by 11%. The original price was $45,400.
Answer:
$49,527.27273 or $49,527
Step-by-step explanation:
45,000/11
$4,127.272727 or $4,127
$45,400 + $4,127
$49,527
Please help me I am very confused and I can’t get it wrong!!!!
Answer:
The answer that you are looking for is b
The area of a rectangle is 42 square centimeters it's length is 7 centimeters.
Answer:
6 cm
Step-by-step explanation:
A = l · w Substitute what you know A = 42; l = 7
42 = 7 ·w Solve
42/7 = w
6 = w cm · cm = cm²
A 230 inch pipe is cut into two pieces. One piece is 4 times length of the other. find the length of the shorter piece
Answer: 46 x 4 = 184
184 + 46 is 230
Step-by-step explanation:
In a class of 40 students, 21 like dance, 24 like music and 8 like both the activities. Illustrate it in a Venn - diagram and find the number of students who don't like any of the activity.
Answer:
As follows,
Step-by-step explanation:
Plz help will give Brainliest
[tex] = 2ac \: + ab \: + 3a \: - 2bc[/tex]
see the attachment!!
hope it helps
Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the force exerted on the object. If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2 ?
Answer:35N
Step-by-step explanation:
Cross multiply and divide to find the missing value
May I please receive help?
Answer:
1 and 2 are parallel. 1 and 3 are perpendicular. 2 and 3 are perpendicular.
Answer: I'm gonna try my best. 1). neither 2). Parallel 3).perpendicular
Step-by-step explanation:
Graph f(x) = -2/3x - 3
Answer:
go to desmos. com there's a free graphing calculator that helps
9/6 × 4/5
1
) 36/11
) 6/5
) 32/30
) 13/15
Answer:
6/5
Step-by-step explanation:
9×4=36
6×5=30
36/30÷2
18/15÷3
6/5
x>-1
help please!!!!!
Answer:
but if it was x>1 it would be less equal to
Step-by-step explanation:
x < 1 is greater than
A popular laptop sells for $199.99. Since sales are so
good, the store raises the price by 13%. What is the cost
of the laptop after the markup?
Answer:
I believe the price after the markup would be $225.99, I hope this helps! :)
Answer:
Step-by-step explanation:
Increase % = 13%
[tex]New \ Cost = \dfrac{100+raise \ percent}{100}*199.99\\\\=\dfrac{113}{100}*199.99\\\\= 225.98\\[/tex]
PLZZ HELP REALLY QUICK QUICKK QUICKKK HELPP
Answer:
$1.62
Step-by-step explanation:
1. To find how much Erin spent, we have to multiply 0.54 by 3.
[tex]0.54 * 3[/tex] [tex](0.5*3)+(0.04*3)[/tex] [tex]1.5 + 0.12[/tex] [tex]1.62[/tex]Therefore, Erin spent $1.62.
The perimeter of a rectangle is 84 cm. If the length is 17 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation
B) Solve your equation in part [A] to find the width of the rectangle.
Answer: The rectangle is
cm wide.
PLS HELP I NEED THIS ASAP
Answer:
width = 25cm
Step-by-step explanation:
perimeter = 84
length =17
A) 84 = 17(2) + 2w
B) 84 = 34 + 2w
-34 -34
50=2w
/2 /2
25=w
it a car is traveling at 60 miles an hour how long will it take to travel 1 mile
en una reunión de 162 alumnos había 15 hombres mas que 6 veces las mujeres ¿cuantos hombres y cuantas mujeres habra?
This shows that there are 141 men and 21 women in the meeting
Let the number of men present be x
Let the number of women present be y
If the total number of students present in the meeting is 162, hence;
x + y = 162 ............ 1
If there were 15 men more than 6 times the women, then;
x = 6y + 15 ...................2
Substitute equation 2 into 1:
6y + 15 + y = 162
7y + 15 = 162
7y = 162 - 15
7y = 147
y = 21
Recall that x = 6y + 15
x = 6(21) + 15
x = 126 + 15
x = 141
This shows that there are 141 men and 21 women in the meeting
Learn more here: https://brainly.com/question/13805464
WILL MARK BRAINLIEST
Answer:
26
Step-by-step explanation:
3³ is basically 3×3×3 which equals to 27
1² is 1×1 which obviously is 1 lol
so,
27 - 1
= 26
Answer: 3*3*3 - 1*1 = 26
Step-by-step explanation:
An airplane on autopilot took 5 hours to travel 3,590 kilometers. What is the unit rate for kilometers per hour?
Answer:
695 km per hour
Step-by-step explanation:
12. The function t = 19m + 65 represents the temperature t (in degrees Fahrenheit)
of an oven after preheating for m minutes.
The temperature in Fahrenheit after preheating for 2 minutes is 103⁰F
The question looks incomplete but we can as well find the temperature in Fahrenheit after preheating for 2 minutes
Give the function t = 19m + 65 that represents the temperature t (in degrees Fahrenheit) of an oven after preheating for m minutes.
If t = 2,
t = 19(2) + 65
t = 38 + 65
t = 103⁰F
Hence the temperature in Fahrenheit after preheating for 2 minutes is 103⁰F
Learn more here:https://brainly.com/question/16510024
Emmanuel went to Circuit City to buy a refrigerator for $3,652. This week at Circuit City, all kitchen appliances have a discount of
35%. If Emmanuel goes to Circuit City this week, how much will he pay for the refrigerator?
$1.278.20
$4.930.20
$2.373.80
53,617 00
Answer:
The answer is C
Step-by-step explanation:
May I please receive help?
Can you please put a more bigger picture?