The remainder of the equation is [tex]\rm 28x+30[/tex].
Given that,
When the equation [tex]\rm 3x^3-2x^2+4x-3[/tex] is divided by [tex]\rm x^2+3x+3[/tex].
We have to find,
The remainder of the equation?
According to the question,
The equation [tex]\rm 3x^3-2x^2+4x-3[/tex] is divided by [tex]\rm x^2+3x+3[/tex].
On the division of the polynomial, the remainder is,
[tex]\dfrac{\rm 3x^3-2x^2+4x-3}{\rm x^2+3x+3}[/tex]
Factorize the equation to convert this into the simplest form,
[tex]\rm 3x^3-2x^2+4x-3\\\\3x^3-11x^2+9x^2+9x+28x-33x-33+30\\\\Taking \ the \ common \ terms \ and \ simplify\ the\ equation\\\\3x^3+9x^2+9x+11x^2+33x-33+28x+30\\\\3x(x^2+3x+3) - 11(x^2+3x+3) + 28x+30\\\\(3x+11) (x^2+3x+3) +28x +30[/tex]
Now, the equation can be written as,
[tex]\rm = \dfrac{(3x+11) (x^2+3x+3) +28x +30}{ x^2+3x+3}\\\\= \dfrac{(3x+11) (x^2+3x+3) }{ x^2+3x+3} + \dfrac{28x +30}{ x^2+3x+3}\\\\= (3x+11) + \dfrac{28x +30}{ x^2+3x+3}\\\\[/tex]
The relation between the divisor, remainder, and quotient is,
[tex]\rm = Quotient + \dfrac{Remainder}{Divisor}[/tex]
On comparing with the equation,
The remainder becomes 28x +30.
Hence, The required remainder of the equation is [tex]\rm 28x+30[/tex].
For more details refer to the link given below.
https://brainly.com/question/25880057
Check
Match the solution set given in inequality notation with the solution set given in interval notation.
17,88
(-0, 7.8)
7.8
(7.8,00)
> 7.8
[7.8,00)
V
7.8
(-0, 7.8)
The Matching of the inequality is
x ≤ 7.8 -> (-∞,7.8]
x < 7.8 -> (-∞,7.8).
x > 7.8 -> (7.8,∞)
x ≥ 7.8 -> [7.8,∞).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
1. x ≤ 7.8
Here the value of is less than equal to 7.8 which means starting from -∞ to 7.8
Thus, the interval is (-∞,7.8]
2. x < 7.8
Here the value of is less than 7.8 which means starting from -∞ to less than 7.8.
Thus, the interval is (-∞,7.8).
3. x > 7.8
Here the value of is greater than 7.8 which means starting from 7.9 to ∞.
Thus, the interval is (7.8,∞)
4. x ≥ 7.8
Here the value of is greater than equal to 7.8 which means starting from 7.8 to ∞.
Thus, the interval is [7.8,∞).
Learn more about Inequality here:
https://brainly.com/question/30231190
#SPJ7
Today only, a desk is being sold at a 29% discount. The sale price is $497.
What was the price yesterday?
Answer: yesterdays price was $700
Step-by-step explanation:
$497 = 71% of the RP (100 - 29)
RP*0.71 = 497
RP = 497/0.71
RP = $700
A class of 30 students visits an art museum and a special exhibit while there.
a. Use the Distributive Property to write and simplify an expression for the cost.
b. Estimate a reasonable value for x. Explain.
c. Use your estimate for x to evaluate both expressions in part (a). Are the values the same?
PRICES:
Museum Exhibit
Child (under 5) Free Free
Student $8 $x
Regular $12 $4
Senior $10 $3
Answer quick!!
A reasonable price for X would be $ 2.
Since a class of 30 students visits an art museum and a special exhibit while there, and the prices were as follows:
Child (under 5) Free Free Student $ 8 $ x Regular $ 12 $ 4 Senior $ 10 $ 3
To estimate a reasonable value for x, the following logical reasoning must be made:
Regular 12 Senior 10 Student 8 = -2 Regular 4 Senior 3 = -1
Therefore, a reasonable price for X would be $ 2.
Learn more about maths in https://brainly.com/question/25916930
1-w+w2 what is complex cube
[tex] \: \: \: \: \: \: [/tex]
[tex]1 + w[/tex]
Step-by-step explanation:
[tex]1 - w + w2[/tex]
use the commutative property to reorder the terms[tex]1 - w + 2w[/tex]
collect like terms[tex] = \: \: 1 + w[/tex]
hope it helpsnumber n is positioned to the left of the number 1 on a number line. Which statement must be true?
Answer:
sorry I need points you understand I
Step-by-step explanation:
have -32 points
will you please help me with my math thank you
Answer:$44.69
Step-by-step explanation:
Original cost = $45.87
Cost with sales = 45.87 x 0.10 since 10% is 0.10 as a decimal
New cost = (45.87) - (45.87 x 0.10)
=$41.283
Cost with tax = 41.283 x 1.0825 <- 8.25% is 0.0825 as a decimal
= $44.69
Answer:
$44.69
Explanation
10 Percent of $45.87 is 4.587 rounded to the nearest hundredth is $4.59.
$45.87 - $4.59 is $41.28
8.25% of $41.28 is 3.4056 rounded to the nearest hundredth is $3.41.
$41.28 + $3.41 is $44.69
Line q has a slope of 5 8 . Line r is perpendicular to q. What is the slope of line r ?
Answer:
35
Step-by-step explanation:
fFjfdisgsiditsykdkhxkgdkdjfzmuraltupsfstdyf and I have been thinking of going to for airport cinema a gia couple trip in September so I can do it at night when I'm back for a couple weeks for a couple more weeks to see what I have a pet for kids ages and I get a lot more of them and a gia tha and I get a lot more than I have to do for the rest I think so much better more I the and I get have on to pank I'm getting more pointsHelp! 100 points! I'm also giving brainiest to whoever gives a correct answer to the following questions or nonetheless a solid explanation behind their answer. Thank you and comment for any concerns or issues!
Step-by-step explanation:
1a)
it means that after 14 hours into the experiment the temperature of the liquid reaches exactly the temperature of the surrounding room at that moment : 10° F.
1b)
it is the point (14, 10), and I know, because both lines touch or cross each other at that point, as due to the equality relation both curves contain this point (meaning they have the same result value 10 for the same function argument 14).
4a)
because the slope of the line segment at the end is larger (making the line go up at a much steeper angle) than fire the line segment at the beginning.
4b)
it looks like the experiment started at hour 0 with the liquid being at around -5° F.
and it reached +10° F after about 10 hours.
the x (time) difference is +10 (from 0 to 10).
the y (temperature) difference is +15 (from -5 to 10).
so, the slope at the beginning of the excitement is about +15/+10 = 3/2.
and at the end of the experiment it looks like the last line segment starts at about 20 hours with the liquid at about -3° F. and it ends at hour 30 and at 30°F.
the x (time) difference is +10 (from 20 to 30).
the y (temperature) difference is +33 (from -3 to 30).
so, the slope at the end of the excitement is about +33/+10, which is much bigger than 15/10 at the beginning.
Need help with this math equation
The cost was 1,784. they also had to pay 7.25% sales tax. what was the total amount paid
Answer:
1913.34
Step-by-step explanation:
We multiply 1,784 by 0.00725. OR if you have a calculator that multiplies percentages you can write it out as 1784 * 7.25%.
whats the slope of (-5,-11) and (-2, 1)
Answer:
4
Step-by-step explanation:
which ordered pair is a solution to the system of equalities y<3x y<5
Answer:
(6,2) x=6 y=2
Step-by-step explanation:
y = 5x + 1
Table down below
Help!
Answer:
Answers below
Step-by-step explanation:
-32 -> -7.4
0 -> 1
20 -> 5
PLEASE SOMEONE HELP ASAP I NEED HELP WITH THIS
Answer:
See image
Step-by-step explanation:
Rate of change means how much does the number of snowflakes go up each time (on a different question you might find the number goes down each time)
"Initial value" means whatthe number if snowflakes at step zero. We have to work backwards to find that number. For the equation, fill in the rate in front of the x (we use m for that number) and add in the initial value (b) in the format y=mx+b . The information for the table is in the picture (the step numbers and number of snowflakes)
See image
please help i dont want to fail final exam
Determine the linear equation modeled by the graph.
Answer:
liner equation
Step-by-step explanation:
do nothing
Need help l don’t understand could someone help me?
Answer:
first put the numbers and unknowns to different sides, as in 6x-3x= 14-5, now solve for x, 3x=9, divide each side by 3 to get the value of x, x=3
Step-by-step explanation:
I did it for you. (Step by step)
I hope this helps.
What’s 8 more then triple a number?
Answer:
x^3+8
Step-by-step explanation:
Find the y-intercept of the line represented by 2x-3x=6
Answer:
There is no y intercept
Step-by-step explanation:
The x intercept is 6
I hope this helps!
[tex]Subtract[/tex] [tex]3x[/tex] [tex]from[/tex] [tex]2x[/tex]
[tex]=-x+6[/tex]
check the picture and youll know.
Answer:
24
Step-by-step explanation:
18/3/4. 18 divided by 3/4 is 18x4/3 which is 72/3=24
What is the equation of the line that passes
through the points (0, -6) and (-2, -7)?
24a - 12b HELP Me PLZ
pls answer quickly But the answer
which of the following measurement is the smallest?
A) kilogram
B) Gram
C) centigram
D) milligram
Answer: Milligram is the smallest
Step-by-step explanation:
How many solutions exist for the system of equations in the graph?
Select the graph of the solution set that would represent the following expression. x+2<2(x-1)
if any doubt leave a comment
What is the experimental probability of spinning the given result? Round your answer to the nearest hundredth if necessary.
Outcome
A
B
C
D
Frequency
20
11
14
30
C
a.
0.14
c.
0.81
b.
1
d.
0.19
Answer: Option 'c' is correct.
Step-by-step explanation:
Since we have given that
Number of times the spinner spun = 75
Outcomes Frequency
A 20
B 11
C 14
D 30
We need to find the experimental probability of spinning an "A" :
so, Probability of spinning an A is given by
Probability of getting an A is 0.27.
Hence, Option 'c' is correct
please mark me brainiest i am almost an expert!!
What is the equation of the line that passes through the point (-8,3) and has a slope of -1/4 ?
Answer:
y=-1/4x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-3=-1/4(x-(-8))
y-3=-1/4(x+8)
y=-1/4x-8/4+3
y=-1/4x-2+3
y=-1/4x+1
I’m very smart. My hair is dark. I love to eat honey, insects, and bark.
Answer:
the answer to the riddle is black bear
Step-by-step explanation:
hope it helps can I have brain for trying? :))) bless u have a great day/evening
Answer:
the other guy is right it's black bear bears love honey and only one bear is black and thats the black bear
Step-by-step explanation:
) Kora is working on a scrapbooking project. She buys packages of stickers at two different stores.
The price of the stickers at each store is p dollars, but each store offers a different discount
Discount on Packages of Stickers
• Which expression represents the total price Kora
pays for 5 packages of stickers at Store A and
3 packages of stickers at Store B?
3{p - 100) + 512 -0.75) 5(p+1.00 +3(p+0.75)
Store A $1.00 off each package
Store B $0.75 off each package
5(p - 1.00) + 3(p -0.75)
3(p+1.00) + 5(p +0.75)
The expression that can be used to represent the total price is 3(p - $0.75) + 5(p - $1).
The expression that can be used to determine the total amount spent in store A is:
number of stickers bought x ( price of the item - discount) number of stickers bought = 5 price of the stickers = p discount = $15(p - $1)
The expression that can be used to determine the total amount spent in store B is:
number of stickers bought x ( price of the item - discount) number of stickers bought = 3 price of the stickers = p discount = $0.753(p - $0.75)
Total price = 3(p - $0.75) + 5(p - $1)
A similar question was solved here: https://brainly.com/question/25717996
Please find attached an image with the complete question.
2. Use the Distributive Property to simplify the expression (1 point)
4(2x - 4)
8x + 4
8x - 4
8x - 16
4x – 16
Answer:
(c) 8x -16
Step-by-step explanation:
The outside factor multiplies each of the terms inside parentheses.
4(2x -4) = 4(2x) +4(-4) = 8x -16
_____
Additional comment
You can think of parentheses as a "bag". The factor outside tells you how many bags you have. When you dump that many bags (eliminate parentheses), you find that the number of each of the kinds of contents is the number in one bag, multiplied by the number of bags.
If you have 4 bags that each have 2 apples and 4 oranges, your total is 8 apples and 16 oranges.
Why is it a shame that parallel lines have so much in common riddle answer
Answer:
Bc they will never meet (intersect, touch, etc)
Step-by-step explanation:
Parallel do not intersect.
Mark me the Brainliest! Ty!