Answers
The quotient is the outcome of the division one number or expression known as the dividend, by another number or expression known as the divisor
The option that gives the correct quotient is;
[tex]\mathbf{2\cdot x + 1 + \dfrac{2 \cdot x - 5}{x^2 + x + 1}}[/tex]
Where, the quotient is 2·x + 1, and the reminder is 2·x - 5
The reason the above option is correct is as follows:
The given dividend is 2·x³ + 3·x² + 5·x - 4
The divisor is x² + x + 1
By long division of a polynomial we have;
2·x + 1(Quotient)
(2·x³ + 3·x² + 5·x - 4) ÷ (x² + x + 1 )
2·x³ + 2·x² + 2·x
0 + x² + 3·x - 4
[tex]{}[/tex] x² + x + 1
[tex]{}[/tex] 0 + 2·x - 5
Therefore, we have;
[tex]\dfrac{2\cdot x^3 + 3 \cdot x^2 + 5 \cdot x - 4}{x^2 + x + 1} = 2\cdot x + 1 + \dfrac{2 \cdot x - 5}{x^2 + x + 1}[/tex]
Therefore, the correct option is;
[tex]\mathbf{2\cdot x + 1 + \dfrac{2 \cdot x - 5}{x^2 + x + 1}}[/tex]
Learn more about long division of polynomial here:
https://brainly.com/question/4685886
Related Questions
Ben rolls a number cube 50 times. He records the result of each roll in the table below. Based on the data, which statement is true?
Answers
Answer:
Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.
Chris deposited $445 in a simple interest account at his school's bank, where
the rate of interest is 3.4% per year. What is the balance he withdraws at the
end of two years?
a. $475.26
b. $575.26
c. $425.26
d. $375.26
Answers
Answer:
its a. 475.26
Step-by-step explanation:
445/ 100= 4.45
4.45×3.4=15.13
15.13+445=460.13
460.13+15.13= 475.26
HELP MEEEEEEEEE I REALLY DONT KNOW THIS ONE
Answers
Answer:
[tex]volume = \pi {r}^{2} h \\ = \pi( {5}^{2} ) \times 6 \\ 150\pi \: cubic \: units[/tex]
Answer:
471
Step-by-step explanation:
Using Pi=3.14
First find the area of the bottom circle:
3.14*([tex]5^{2}[/tex])
=78.5
Then multiply the result by the height
78.5*6=471
therefore,
Volume of clylinder: 471 units squared
Please give me brainliest if corrrect :)
Which symbol correctly compares the fractions below?
1/8 ? 1/2
Answers
Answer:
<
Step-by-step explanation:
1/2 = 4/8
=> 1/8 < 4/8
=> 1/8 < 1/2
LEARNING TASK 3:
Directions: Given that b ∥ c with d as
transversal. Find the value of x in the
following.
1. ∠4 = 5x, ∠5 = 120°
2. ∠1 = 100°, ∠7 = 10x
3. ∠2 = 3x - 10, ∠6= x + 30
4. ∠4 = 3x + 10, ∠6= 2x + 20
5. ∠1 = 7x + 9, ∠5 = 5x + 31
Plssss I need this now
Answers
Step-by-step explanation:
1. Angle 5 = 120 degree
Angle 5 = Angle 6 ( alternate exterior angles are equal )
Therfore, Angle 6 = 120 degree
Angle 6 = Angle 4 ( Vertically opposite angles are equal )
Therfore, Angle 4 = 120 degree
Angle 4 = 5x
120 = 5x
120/5 = x
40 = x
Therefore x = 40 degree.
2. Angle 1 = 100 degree
Angle 1 = Angle 7 ( vertically opposite angles are equal )
Therefore, Angle 7 = 100 degree
Angle 7 = 10x
100 = 10x
100/10 = x
10 = x
Therefore x = 10 degree
I want some more time for this question.
Here is a list of numbers.
5 15 30 50 60 90 100 125
From the numbers in the list, write down a multiple of 20.
Answers
can someone help me answer this
Answers
Answer:
(x+7)(x-13) so B is the answer
Answer:
B (x+7(x-13)
Step-by-step explanation:
solve the inequality -2(y+4)>16
Answers
y < -12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
−2y − 8 > 16
Step 2: Add 8 to both sides.
−2y − 8 + 8 > 16 + 8
−2y > 24
Step 3: Divide both sides by -2.
−2y/−2 > 24/−2
y < −12
Answer:
y < −12
Step-by-step explanation:
−2(y + 4) > 16
↓
−2y − 8 > 16
↓
y < −12
evaluate 2x + 5 - 10 when x = 12
Answers
2 (12)+5-10= 24+5-10=19
please help meee and show all steps please!!!ty
Answers
Answer:
x = -4 and x = 5
Step-by-step explanation:
Since [tex]x^2 + 2x[/tex] and [tex]3x + 20[/tex] both equal to y, we know that the expressions equal to each other. We can write a new equation base on that.
[tex]x^2 + 2x = 3x + 20[/tex]
Now we solve the equation.
[tex]x^2 + 2x = 3x + 20[/tex]
[tex]x^2 - x = 20[/tex]
[tex]x^2 - x - 20 = 0[/tex]
[tex](x + 4) (x - 5) = 0[/tex]
[tex]x + 4 = 0 ; x -5 = 0[/tex]
[tex]x = -4 ; x = 5[/tex]
150 people attend a play 45 of them are male write the ratio to males to females in its simplest form
Answers
Answer:
9/21
Step-by-step explanation:
45 / 105 = 9/21 (simplified)
STUDENT HOURS KATY 5.5
MIKE 4.25
SAM 7.75
HOLLY 3.5
JAKE 6.25
You've randomly surveyed some students in your science class to find the number of hours per week they study. What is the mean, based on your sample?
A) 4.75 Hours
B) 5.05 Hours
C) 5.25 Hours
D) 5.45 Hours
Answers
Substitute t = 3 and t = 6 to determine if the two expressions are equivalent.
3 (2 t + 5) 6 t + 15
Which statements are true? Select the three correct answers.
A. The value of both expressions when t = 3 is 33.
B. The value of both expressions when t = 3 is 23.
C. The value of both expressions when t = 6 is 41.
D. The value of both expressions when t = 6 is 51.
E. The two expressions are equivalent.
F. The two expressions are not equivalent.
Answers
Answer:
A.The value of both expressions when t=3 is 33.
D.The value of both expressions when t=6 is 51.
E.The two expressions are equivalent.
Step-by-step explanation:
We are given two expressions.
3(2t + 5)
6t + 15
Now let's find the value of these two expressions when t =3 and t = 6
When t =3, the value of the expressions:
3(2*3 + 5) = 3(6 + 5) = 3(11) = 33
6*3 + 15 = 18 + 15 = 33
So the value of both the expressions is 33 when t = 33.
When t = 6, the value of the expressions:
3(2*6 + 5) = 3(12 + 5) = 3(17) = 51
6*6 + 15 = 36 + 15 = 51
The value of both the expressions is 51 when t = 51.
So the following statements are true:
A.The value of both expressions when t=3 is 33.
D.The value of both expressions when t=6 is 51.
E.The two expressions are equivalent.
Question 2
The value of y is directly proportional to
the value of x. If y = 35 when x = 140,
what is the value of y when x = 70?
A) 70
B) 280
C) 140
D) 17.5
Answers
Given the equation y = -3x + 2:
When x is 1, what value of y makes the equation true?
When x is -1, what value of y makes the equation true?
When x is 8, what value of y makes the equation true?
Answers
When x is -1, the y value would have to be 5.
When x is 8, the y value would have to be -22
What two numbers have a product of -40 and a sum of -3?
Answers
Which pair of triangles can be proved congruent by SSS?
Answers
Answer:
My answer is B and C
Step-by-step explanation:
If you put B in the same dimension, all the sides are equal. Similarly for part C, since the sides are the same, the base of the triangles are the same lengtg
Draw root 9 on a number line
Answers
Answer:
Step-by-step explanation:
root 9 looks like
[tex]\sqrt{9}[/tex]
maybe you can solve it now?
3*3 = 9
so root 9 = 3
mark 3 on the number line
“ write all your answers with a positive exponent so your answer will be in the form of x^# or 1/(x^#)
Answers
Answer:
Step-by-step explanation:
5). [tex]\frac{1}{x^{-9}}[/tex] = [tex]\frac{1}{\frac{1}{x^9} }[/tex]
= [tex]x^{9}[/tex]
6). [tex]\frac{1}{x^{-2}}=\frac{1}{\frac{1}{x^2} }[/tex]
= x²
7). [tex]x^{-6}=\frac{1}{x^6}[/tex]
8). [tex]\frac{1}{x^{-7}}=\frac{1}{\frac{1}{x^7} }[/tex]
= [tex]x^{7}[/tex]
9). [tex]x^{-8}=\frac{1}{x^8}[/tex]
10). [tex]\frac{1}{x^{-3}}[/tex] = [tex]\frac{1}{\frac{1}{x^{3}}}[/tex]
= x³
explain how you would apply the distributed property to solve the expression 3 (6x+7-4y
Answers
Answer:
I would do the math
# 1 - Need Help With This
Answers
Answer:
b & f
Step-by-step explanation:
I'm smart and it's common sense
Giving brainlist to whoever answers
Answers
Answer:
bro check my explanation
Step-by-step explanation:
the answer is 62cm3.
if I am right.
please give a brainliest
Evaluate function expression.
who can help ?
Answers
Given:
The graph of two function f(x) and g(x).
The expression is:
[tex]-1\cdot f(-8)-4\cdot g(4)[/tex]
To find:
The value of the given expression.
Solution:
From the given graph, it is clear that
[tex]f(-8)=-5[/tex]
[tex]g(4)=3[/tex]
Substitution [tex]f(-8)=-5[/tex] and [tex]g(4)=3[/tex] in the given expression, we get
[tex]-1\cdot (-5)-4\cdot 3[/tex]
[tex]=5-12[/tex]
[tex]=-7[/tex]
Therefore, the value of the given expression is -7.
help me for brainiest:(
Answers
Answer:
27 ft²
Step-by-step explanation:
area is L•W so each squares area is 3•3 =9. theres 3 squares so 9•3 =27
pls help help help help help help
Answers
Answer:
y=3x+6
Step-by-step explanation:
its in y=mx+b form
m is the slope
b is the y-int
hope this helps
11) Prove quadrilateral ABCD is a parallelogram A(-2, 8), B(2, 7), C(5, 1), and D(1, 2) *
Answers
9514 1404 393
Explanation:
The quadrilateral will be a parallelogram if the diagonals bisect each other. That is, their midpoints are the same point. We don't actually need to calculate the midpoint. Rather, we can calculate the point that has double the coordinate values.
If (A+C) = (B+D), the quadrilateral is a parallelogram.
A +C = B +D
(-2, 8) +(5, 1) = (2, 7) +(1, 2)
(-2+5, 8+1) = (2+1, 7+2)
(3, 9) = (3, 9) . . . . . the figure is a parallelogram
_____
Of course, the midpoint of the diagonals is (3/2, 9/2).
Ben says he will sell Catalina a ring that he found in his yard. Ben and Catalina look at the ring and decide that they are not sure what it is, probably just a shiny stone. Catalina pays Ben $10 for the ring. The ring turns out to be a diamond worth much more than $10. Ben wants the ring back, and Catalina refuses. What is the most likely result
Answers
Answer:
If both parties are over the age of 18, a lawsuit is likely to occur.
Step-by-step explanation:
Ben would likely try and sue Catalina for theft, however she wouldn't be found guilty because of the transfer of property, goods, and or services was entirely legal in this case.
How many constants are in the word IMPOSSIBLE
Answers
Answer:
6
Step-by-step explanation:
ANSWERS ASAP PLEASE Questions 1-4, WILL GIVE BRAINLIEST
Answers
Answer:
1) 23^a+b
2) 5^5
3) 11^x-y
4) 2^10
Step-by-step explanation:
if they have the same base numbers then they are pretty easy to combine. multiplication means you add the exponents, and division means you subtract the exponents. for number 2, you would make them the same base by making 25 -> 5^2 and then just add the exponents.
What is the solution to the system of equations below? Please show work.
Y = 3/4x - 3
3x - 4y = 12
1) (4,0)
2) (0,-3)
3) no solution
4) infinite solution
Answers
Answer:
2) (0,-3)
Step-by-step explanation:
hello :
put x=0 and y= -3 in this system !
Y = 3/4x - 3
3x - 4y = 12
- 3 = 3/4(0) - 3 means : -3 = -3 ......true
3(0) - 4(-3) = 12 means : 12= 12 ......true