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].
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Answer:
3^3+4^3=91
3*3*3=27
4*4*4=64
27+64=91
Hey guys, i need help on this one, thanks in advance.
Find the slope of the equation:
x - 5 = 3 ( y + 4 ) -2y + 1
if you could add step's please do.
Answer:
slope = 1
Step-by-step explanation:
1) expand those brackets on the left side my multiplying
x - 5 = 3y + 12 - 2y + 1
2) simplify by collecting like terms
x - 5 = y + 13
3) bring -5 to the right side by adding 5
x = y + 18
4) let's rearrange this equation in the form y = mx + c where m is the gradient (slope) and c is the y intercept. by subtracting 18 on both sides
y = (1)x - 18 (there is a 1 in front of the x, but we don't write it like that. m is 1)
y = x - 18
the slope is the gradient, which is 1
Melanie has 10 packets of 20 biscuits. She puts 3/10 of them on a plate to serve. How many biscuits are being served?
From the problem statement Melanie has 10 packets of 20 biscuits
60 biscuits
Solution
Let us find 3/10 of 10 packets
= 3 packets
In one packet there are 20 biscuits,
Hence in 3 packets there will be
20*3 = 60 biscuits
From the solution above Melanie served 60 biscuits in the plate
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Find the slope for (4,5)and (2,3)
Answer:
1
Step-by-step explanation:
Use the algebra tiles to help you solve the equation. 4x-2=10
Answer:
The solution to this equation is x=3
Step-by-step explanation:
What is an expression that represents 5 times the value of Y plus 4
Answer:
5y+4
Step-by-step explanation:
Answer:
2 plus 5 times n
Step-by-step explanation:
what does x - 9 multiplied by x + 4 equal
Answer:
x^2 - 5x -36
Step-by-step explanation:
multiply x-9 by x to get x^2 -9x. multiply x-9 by 4 to get 4x-36. add these two together to get x^2 - 9x + 4x - 36. simplify to get x^2 - 5x -36
I need help with something in school.
Answer:
what do you need help with
Step-by-step explanation:
:)
Answer:
ask......
Step-by-step explanation:
A rectangular garden has a length of 10.25 feet and a width of 6.2 feet. Another rectangular garden has a length of 20.5 feet and a width of 12.4 feet. How many times greater is the area of the larger garden than the area of the smaller garden?
Answer:
3
Step-by-step explanation
So I am about to ask three math points so whoever comments on this first and answers my next question will get 100 point :)
Answer:
lets get started
Step-by-step explanation:
Mrs. Arnold asked her 30 Geometry students who owned a pet. 16 students own a dog, 12 students have a cat and 6 students did not have a cat or a dog. Thomas wrote the information in a Venn diagram but made an error. Explain where the error occurred.
Answer:
The number is out of the Venn Diagram. The number is supposed to be in the middle if the middle means the students that don’t have a cat nor dog. Hope this helps and hope you pass.
Help Ill give 100 points!
Answer:
0, 1, 1/2
Step-by-step explanation:
First you would have to make them have the same denominators.
The lowest one they share is 24.
What ever you do to the bottom you have to do to the bottom.
1/6, times each by 4.
1 * 4 = 4
6 * 4 = 24
4/24.
Now you have to do the same thnig for 5/8.
But times it by 3, since 8 times 3 is 24.
5 * 3 = 15
8 * 3 = 24
15/24
Now subtract.
15 - 4 = 11/24
the difference is close to one half.
4/24 = 1/6 is close to 0.
15/24 = 5/8 is close to 1.
Answer:
i need the points
Step-by-step explanation:
write the decimal 4.005 as a fraction in the simplest form
Steps to convert decimal into fraction
Write 4.005 as
4.005
-----------
1
Multiply both numerator and denominator by 10 for every number after the decimal point
4.005 × 1000
---------------------
1 × 1000
=
4005
-----------
1000
Reducing the fraction gives
801
--------
200
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Matilda earns 48$ in 4 hours, How many hours does it take her to earn 288$?
Answer:
24
Step-by-step explanation:
If Matilda earns $48 in 4 hours, then she must earn 48/4 (12) dollars per hour. We know she earns $12 per hour, and that she made $288, so we divide the total amount earned (288) by her hourly wage ($12) to find she worked 288/12 or 24 hours.
Matilda will earn $288 in 24 hours.
What are word problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given is that Matilda earns $48 in 4 hours.
Let us assume that it will take her {x} hours to earn $288.
Then, we can write -
there is earning of $48 in 4 hours.
so, there will be earning of $1 ins (4/48) or (1/12) hours.
hence, she will earn $288 in (1/12 x 288) or 24 hours.
Therefore, Matilda will earn $288 in 24 hours.
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Solve for p.
P+3=p-4/2
A: p= -74
B: p= 74
C: p= 10
D: p= -10
Answer:
p = - 10
Step-by-step explanation:
I hope this helps. Good luck
Which is NOT a line of symmetry?
1
2
3
4
5
Answer:
Line 3 is the only one that is not a line of symmetry.
x/2 = y/3
find value of x, y if x+y =30
Answer:
x=12, y=18
Step-by-step explanation:
What did Diocletian do to change the way the Roman Empire was ruled?How would we add -3 + (-9) on the number line?
What percentage of 50 is 12?
Answer:
that would be 24%
Step-by-step explanation:
Now we can see that our fraction is 24/100, which means that 12/50 as a percentage is 24%.
Answer:
24%
Step-by-step explanation:
the fraction form is 24/100, meaning the percentage is 24% put of 100%
Joseph removes 5/8 gallon of white paint from a can.
Then he adds 5/8 gallon of blue paint to the can.
Write and evaluate an addition expression to find
the overall increase or decrease in the amount of
paint in the can.
Create the expression from the data:
The gallon of paint begins as a whole: 8/8
Then he removes 5/8 gallons of paint from the can: - 5/8
Then he adds 5/8 of a different colored paint to the can: + 5/8
Now combine:
8 / 8 - 5 / 8 + 5 / 8 = 8/8
The paint can is full, then he removes an amount from the can. He then pours more paint into the can that is equal to the amount he originally removed. Therefore, the paint can remained full.
PLS HELP round to the nearest hundredth
Solve the following system of equations.
8x+3y=18
-7x-4y=-13
x= y=
Answer:
x=3
y=-2
Step-by-step explanation:
Just ask!
Hope this helps.
(✿◡‿◡)
Could somebody please help with this math?
Answer:
87
Step-by-step explanation:
the slope is very easy you can solve it in easy way all you have to do is give me your phone
The Andromeda galaxy is 2.54 million (2.54x106) light years from earth. If light can travel 5.865 trillion (5.865x1012) miles in a
year then how many miles is the Andromeda galaxy from earth?
O 1.48971x1019
O 2.309055x106
3.325x106
O 8.405x1018
Answer: 1.48971 x 10^19
Step-by-step explanation: 1-light year is approximately 5.865 x 10^12 which is 5,865,000,000,000 kilometers or 6 trillion miles in 1-year. The Andromeda galaxy is indeed 2.54 million light-years from Earth which is the closest galaxy to our Milky Way Galaxy.
The best way to this is to put this into a scientific calculator. If it shows 1.48971E19, the E stands for exponent and the 19 next to the E stands to the 19th power. That is written as 1,489,710,000,000,000,000 miles!! from Earth. That's a lot of zeros. That's the reason scientific notation is used; to avoid all those zeros and express very small/large figures.
Hope this explanation helps.
PLEASE HELP WILL MARK BRAINEST!!!
they biked 220 kil
that is the answer
Correlation coefficients
(Exit
Topic 3: Assessment Form C
Hugo's exercise data is shown. Use the trend line y = 3.5x + 10 to complete the sentence.
Laps
7 8 9 10 11
Time (min)
35.5
37
41.5
45
49.5
It will take Hugo about
min to run 6 laps
Answer:
35.5
Step-by-step explanation:
Plzzzzz helpmeeeee plzzzzzz
* Help!
* Need steps!
* Answer only if you know, thanks!
[tex]\text{Given that,}~3x-y = 12\\\\\\\dfrac{8^x}{2^y} =\dfrac{(2^3)^x}{2^y } = \dfrac{2^{3x}}{2^y} = 2^{3x-y} = 2^{12}[/tex]
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve ~
[tex] \sf3x - y = 12[/tex][tex] \sf3x = y + 12[/tex]now, evaluate the value of given expression ~
[tex] \sf \dfrac{ {8}^{x} }{ {2}^{y} } [/tex][tex] \sf \dfrac{{(2 {}^{3} ) }^{x} }{ {2}^{y} } [/tex][tex] \sf \dfrac{2 {}^{3x} }{ {2}^{y} } [/tex]Now, plug the value of 3x from the previous equation ~
[tex] \sf \dfrac{(2 ){}^{y + 12} }{ {2}^{y} }[/tex][tex] \sf2 {}^{ \ \cancel y + 12 - \cancel y} [/tex][tex] \sf{2}^{12} [/tex]Therefore , the required expression is ~ 2¹²
what is the answer???
Answer:
[tex] \frac{65}{97} [/tex]
Cosine ∅ = adjacent ÷ hypotenuse
Rounded to the nearest hundredth the answer is 0.670.
We know
[tex]\boxed{\sf cos\Theta=\dfrac{Base}{Hypotenuse}}[/tex]
Now
[tex]\\ \sf\longmapsto cosU=\dfrac{SU}{TU}[/tex]
[tex]\\ \sf\longmapsto cos U=\dfrac{65}{97}[/tex]
[tex]\\ \sf\longmapsto cosU=0.67[/tex]