Using the remainder theorem, which quotient has a remainder of 20?
OA (3r4 – 573 + 5x + 2) = (x - 2)
O B. (3r3 + 702 + 5x + 2) = (x - 2)
Oc. (13 + 5x2 4r + 6) = (x + 5)
OD. (74 – 812 + 16) = (x + 4)
Answers
Answer:
The answer is A. (3x^4-5x^3+5x+2) =(x-2)
Step-by-step explanation:
we see that the polynomial that gives the remainder as 20 is
(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)
Option A is our correct answer.
What is the remainder theorem?The remainder theorem states that when a polynomial p(x) is divided by
(x - a), then the remainder = f(a).
We have,
(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2) ____(1)
We can directly find the remainder as:
x - 2 = 0
x = 2
Putting x = 2 in (1) we get,
= 3 x 16 - 5 x 8 + 5 x 2 + 2
= 48 - 40 + 10 + 2
= 20
The remainder is 20.
(3x³ + 7x² + 5x + 2) ÷ (x - 2) ) _______(2)
x - 2 = 0
x = 2
Putting x = 2 in (2) we get,
= 3 x 8 + 7 x 4 + 5 x 2 + 2
= 24 + 28 + 10 + 2
= 64
The remainder is 64.
(x³ + 5x² - 4x + 6) ÷ (x + 5) ______(3)
x + 5 = 0
x = -5
Putting x = -5 in (3) we get,
= - 125 + 5 x 25 - 4 x (-5) + 6
= -125 + 125 + 20 + 6
= 20 + 6
= 26
The remainder is 26.
([tex]x^{4}[/tex] - 8x² + 16) ÷ (x + 4) _______(4)
x + 4 = 0
x = -4
Putting x = -4 in (4) we get,
= 256 - 8 x 16 + 16
= 256 - 128 + 16
= 144
The remainder is 144.
Thus we see that the polynomial that gives the remainder as 20 is
(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)
Option A is our correct answer.
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Related Questions
Evaluate this exponential expression.
4. (2 + 5)2 - 52 =
Answers
C.171
Step-by-step explanation:
4×7(2)-25
4×49-25
multiply 4×49=196-25
then subtract 196-25=171
Answer:
C. 171
Step-by-step explanation:
[tex]4\cdot (2+5)^2-5^2\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(2+5\right)\::\quad 7\\=4\cdot \:7^2-5^2\\\\\mathrm{Calculate\:exponents}\:7^2\::\quad 49\\=4\cdot \:49-5^2\\\\\mathrm{Calculate\:exponents}\:5^2\::\quad 25\\=4\cdot \:49-25\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\cdot \:49\::\quad 196\\=196-25\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:196-25\:\\:\quad 171\\[/tex]
Camilla has twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now haas three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?
Answers
Answer:
40 blueberry jelly beans
Step-by-step explanation:
Let us represent blue berry beans = b
Cherry jelly beans = c
Camilla has twice as many blueberry jelly beans as cherry jelly beans.
Hence,
b = 2c .........Equation 1
After eating 10 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans.
hence,
b - 10 = 3(c - 10)
b - 10 = 3c - 30
Collect like terms.
- 10 + 30 = 3c - b
20 = 3c - b .........Equation 2
Subtitute 2c for b in Equation 2
20 = 3c - 2c
20 = c
Hence, she had 20 cherry jelly beans.
In the question, we are asked to find how many blueberry jelly beans she had.
Hence,
b = 2c .........Equation 1
Substituting 20 for c in Equation 1
b = 2 × 20
b = 40
Therefore, she originally had 40 blueberry jelly beans
Oscar has received a $4,000 gift and is looking for a bank to start a savings account. Which option would be the best for him at a current inflation rate of 1.5%?
Answers
Here is the complete question
A nominal interest rate of 5%
A real interest rate of 5%
A real interest rate of 3%
A nominal interest rate of 3%
Answer:
A real interest rate of 5%
Step-by-step explanation:
A real interest rate of 5% is the best option for oscar. The nominal rate of interest is a type of interest rate that shows the increase in in percentage of money without the depreciation discount that is usually caused by inflation or the payment of tax.
The real rate of interest shows the real increase in the money that has been paid for an investment. This is after inflation has been discounted and all forms of taxes have been paid.
So oscar should invest his $4000 on a savings account whose real interest rate is 5% per year
what is the answer? first corret answer will get branliest
Answers
Answer:
the second one I believe as they have the same shape and size
Answer:
oop
Step-by-step explanation:
here’s a graph of the equation x + 3y = 6 select all coordinates pairs that represent a solution to the equation A) 0,2 B) 0,6 C) 2,6 D) 3,1 E) 4,1 F 6,2
Answers
Answer:
(0,2) (3,1)
Step-by-step explanation:
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The correct option is A and D.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
If we want to know whether a point is a solution to the equation or not, substitute it in the line and check whether both sides of the equation are equal or not.
A) 0,2
x + 3y = 6
0 + 3(2) = 6
6 = 3
B) 0,6
x + 3y = 6
0 + 3(6) ≠ 6
18 ≠ 6
C) 2,6
x + 3y = 6
2 + 3(6) ≠ 6
2 + 18 ≠ 6
D) 3,1
x + 3y = 6
3 + 3(1) = 6
3 + 3 = 6
6 = 6
E) 4,1
x + 3y = 6
4 + 3(1) ≠ 6
4 + 3 ≠ 6
F) 6, 2
x + 3y = 6
6 + 3(2) ≠ 6
6 + 6 ≠ 6
Hence, the correct option is A and D.
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If m∠ABD = 70° and m∠CBD = 30°, then m∠ABC = ?
Answers
21/[2*(19-14)-3] (the / means division btw)(* means multiply)
Answers
Answer:
The answer you're looking for is 3
Step-by-step explanation:
Answer:
[tex]3[/tex]
Step-by-step explanation:
Start with:
[tex]\frac{21}{[2*(19-14)-3]}[/tex]
First, subtract the values in your parentheses.
At this point, we can remove the brackets.
[tex]\frac{21}{2(5)-3}[/tex]
Multiply.
[tex]\frac{21}{10-3}[/tex]
Subtract.
[tex]\frac{21}{7}[/tex]
Simplify.
[tex]3[/tex]
-27 divided by 3
haha i’m really bad
Answers
Answer:
-9
Step-by-step explanation:
negative divided by positive = negative.
Select the solutions of the equation. x2 + 3.5x - 2 = 0
Answers
Answer:
x₁ = -4
x₂ = 0.5
Step-by-step explanation:
x² + 3.5x - 2 = 0 * 2
2x² + 7x - 4 = 0
(2x + 8)(2x -1)/2 = 0
2(x + 4)(2x - 1)/2 = 0
(x + 4)(2x - 1) = 0
x + 4 = 0
x₁ = -4
2x - 1 = 0
2x = 1
x₂ = 1/2
x₂ = 0.5
A rectangular lot is 140 meters long and 100 meters wide. Give the length and width of another rectangular lot that has the same perimeter but a larger area.
Answers
Step-by-step explanation:
Length of rectangle is 140 m and its breadth is 100 m
Perimeter = sum of all sides
For rectangle, P = 2(l+b)
P = 2(140+100)
P = 480 m
Area = length × breadth
For a rectangle, A = lb
A = 140 × 100
A = 14000 m²
We need to write the length and breadth such that it has the same perimeter but a larger area.
Let the length is 110 m and breadth is 130 m.
Perimeter, P = 2(110+130)
P = 480 m
Perimeter is same as previous
Area, A = 110 × 130
A = 14300 m²
Area is more than the initial area.
Hence, this is the required solution.
answer:
it's [tex]\boxed{L=130, \W=110}[/tex]
explanation:
[tex]\boxed{L=140}\\\boxed{W=100}\\P=2(L+W)\\P=2(140+100)\\\boxed{P=480m}\\A=L*W\\A=140*100\\\boxed{A=14000m^{2}}[/tex]
It's easy to get a Length and Width with an equal Perimeter as this rectangle, how? the key is in the Perimeter formula for rectangle, it is literally 2 times the sum of the Length and Width, so [tex]2(L+W)=2(sum)[/tex], that means we can change the value of both the Width and the Length as long as the sum of both the Length and the Width is equal;
[tex]\boxed{L=140}\\\boxed{W=100}\\L+W=140+100=\boxed{240}[/tex]
to change these values and still have a perimeter equal to 480 meters, and an area larger than 14,000 meters square, we gotta have a length and a width that have a sum of 240 and still maintain a hundred place value, for example 130 and 110, not 150 and 90, because [tex]150*90=13500[/tex] which is less than our goal; while [tex]130*110=14300[/tex], note that as long as one of the values doesn't fall below 100 you're solid.
Point T is on line segment SU. Given ST = 2x + 6, TU = 4, and SU = 4x, determine the numerical length of ST
Answers
Step-by-step explanation:
Point T is between Points S and U, where all 3 points are collinear.
Therefore ST + TU must be equal to SU.
(2x + 6) + 4 = 4x
2x + 10 = 4x
2x = 10
x = 5.
Hence, length of ST = 2(5) + 6 = 16.
The length of ST will be 16 units.
What is a line segment ?A line segment is basically a line with two end points.
two or more than two co-linear points is needed to form a line segment.
In the given question
Line segment is SU
Point T is in between point S and point U here all the points are co-linear
SU = ST + TU
4x = (2x + 6) + 4
4x = 2x + 10
2x = 10
x = 5
∴ The length of ST = 2x + 6 = (2×5) + 6 = 16 units
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Planes A and B both intersect plane S. Vertical plane S intersects horizontal plane A and horizontal plane B. Plane S and plane A intersect at line f. Line f contains points N and K. Plane S and plane B intersect at line g. Line g contains points P and Q. Line d intersects plane A at point L. Which statements are true based on the diagram? Select three options. Points N and K are on plane A and plane S. Points P and M are on plane B and plane S. Point P is the intersection of line n and line g. Points M, P, and Q are noncollinear. Line d intersects plane A at point N.
Answers
Answer:
Points N and K are on a plane A and plane S ( True )
Points P and M are on a plane B and plane S
Point P is the intersection of line n and line g ( True )
Points M, P, and Q are noncollinear ( True )
Line d intersects plane A at point N.
Step-by-step explanation:
Just took the test and got it right :)
The true are 1, 3, 4 and false are 2, 5.
To choose the statement are true or false.
What is plane?A surface in which if any two points are chosen a straight line joining them lies completely in that surface. A plane is a flat, two-dimensional surface that prolongs infinitely far.
Given that:
1. Points N and K are on plane A and plane S.
From that points N and K are on the plane A and on the plane S. Thus, this option is true.
2. Points P and M are on plane B and plane S.
From points P and M are on the plane B, but point M doesn't lie on the plane S. So, this option is false.
3. Point P is the intersection of line n and line g.
Point P lies on the line n as well as on the line g, therefore it is the point of intersection of these two lines. This option is true.
4. Points M, P, and Q are noncollinear.
It is true, because points M, P and Q do not lie on the same line at one time, that means they are noncollinear.
5. Line d intersects plane A at point N.
From the line d intersects plane S at point L, not at point N, then this option is false.
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Diagram is missing.
.000025 in scientific notation
Answers
Answer:
[tex]2.5 \times 10^{-5}[/tex]
Which number is an integer?
3
O
O 0
O 2.3
Answers
Answer:
3 is an integer
Step-by-step explanation:
intergers are numbers that are not a fraction.ie a whole number.
A mountain climber starts a climb at an elevation of 453 feet above sea level. At his first rest stop he has climbed 162 feet, and by his second rest stop he has climbed another 207 feet. It's getting late in the day, so the climber starts his way down. If the climber descends 285 feet, how much does he need to ascend or descend to return to the original starting point?
Answers
Answer:
cool!
Step-by-step explanation:
Answer:At the end of the day, he is [162 + 207 - 285] = 84 ft above his starting height
Step-by-step explanation:
anyone help please ?
Answers
Answer:
work is shown and pictured
The mathematical model C(x) = 500x + 100,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, how many items were produced if expenses were $250,000 in one month?
Answers
Answer:
300
Step-by-step explanation:
Fill in the given value and solve for x.
C(x) = 500x +100000
250000 = 500x +100000
500 = x + 200 . . . . . . divide by 500
300 = x
300 items were produced if the month's expenses were $250,000.
Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan
A according to the number of minutes used is shown in the table.
Monthly Charge for Plan A
Minutes used, X Monthly charge ($), y
0
14.45
3
14.84
6
15.23
9
15.62
12
16.01
Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total
monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that
represents the cost of plan B?
Answers
Answer:B .17
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Edg
if the statement is a rewrite as a conditional statement in if-then form, which best describes the conclusion? A student who earns 85% earns a B
Answers
Answer:
Step-by-step explanation:
cdfbdfbf
Answer:
"then a student earns a b"
Step-by-step explanation:
7|12x+3|- 1=62 hhih
Answers
Answer:
a. x = ½, and x = -1
Step-by-step explanation:
Given the equation, 7|12x + 3| - 1 = 62, solve as follows:
Add 1 to each side of the equation
7|12x + 3| = 62 + 1
7|12x + 3| = 63
Remove the absolute value to create ± on the right side of the equation
7(12x + 3) = ±63
Solve the positive portion of the solution
7(12x + 3) = 63
84x + 21 = 63
Subtract 21 from both sides
84x = 63 - 21
84x = 42
Divide both sides by 84
x = 42/84
x = ½
Solve the negative portion of the solution
7(12x + 3) = -63
84x + 21 = -63
Subtract 21 from each side of the equation
84x = -63 - 21
84x = -84
Divide both sides by 84
x = -84/84
x = -1
The answer is: x = ½, and x = -1
Answer:
sorry i cant see i need a better pictureStep-by-step explanation:
Simplify the following expressions.
(x^-8/y^11)^-2
Please
Answers
Answer:
y ^22 x ^16
hope this helps
A landscaper installs 12 sections of trail he's his partner installs 12.5 sections of Trellis the neighbor installs $3.16 sections of Trellis.How much trailers do they install together?
Answers
Answer:
They installed 2 7 .6 6 trailers altogether
Step-by-step explanation:
Given that:
A landscaper installs 12 sections of trail
he's & his partner installs 12.5 sections of Trellis
the neighbor installs $3.16 sections of Trellis.
The number of trailers they install together can be calculated by finding the summation of all the value given.
i.e
The number of trailers they install together;
1 2 . 0 0
= + 1 2 . 5 0
3 . 1 6
2 7 .6 6
Multiply.
(+8)(-7/4)
Answers
Answer:
-14
Step-by-step explanation:
some of the apollo missions transported astronauts from earth to moon. the travel time was about 3 days and about 385,000 kilometers. what is the average speed of the trip in miles per hour
Answers
Ellie is 5 times as old as her sister Emma. In 2 years Ellie will be 3 times as Emma. How old is Emma now?
Answers
Answer:
8 years old maybe.
If your car can drive 433 miles on a full tank of gas, find the miles per gallon if your gas tank holds 17.2 gallons? How much does it cost to fill your tank if gas is $2.85 per gallon?
Answers
Answer:
-25.17 miles per gallon.
-It costs $49.02 to fill your tank.
Step-by-step explanation:
-To find the miles per gallon, you can use a rule of three:
17.2 gallons → 433 miles
1 gallon → x
x=(1*433)/17.2= 25.17
If your gas tank holds 17.2 gallons, you car can drive 25.17 miles per gallon.
-To find the cost to fill your tank, you have to multiply the price per gallon for the amount of gallons that the tank can hold:
$2.85*17.2=$49.02
It costs $49.02 to fill your tank.
Ruth borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Ruth paid for the book when
she returned it x days after
the due date:
2 + 0.25x
What does the second term of the expression represent?
The total late fee paid
The late fee per day for the book
The number of days the book was overdue
The fixed rental for the book
Answers
Answer:
The answer will be the fixed rental for the book
Step-by-step explanation:
Solve for b: r = (2x + b)/ a
Answers
Answer:
b=ra-2x
Step-by-step explanation:
You solve for b by simplifying both sides of the equation then isolating the variable.
Multi step inequality
-2b + 4 > -6
Answers
Answer:
b < 5
Step-by-step explanation:
-2b + 4 > -6 ⇒ subtract 4 from both sides
-2b > - 6 - 4
-2b > -10 ⇒ divide both sides by -2, it will change inequality sign to opposite
b < 5 ⇒ answer
Write 3•3•3•3 in exponential form
Answers
Answer:
[tex]3^4[/tex]
Step-by-step explanation:
There are four 3's
[tex]3\times 3\times3\times3 = 81\\\\3^4 = 81[/tex]
Answer: 3⁴
Explanation: Exponential form contains a base and an exponent.
The base is the number that is multiplied.
So in this case, 3 is the base.
Next we write the exponent which is the
number of times that the base is multiplied.
Since 3 is multiplied four times, the exponent is 4.
So in exponential form, 3 · 3 · 3 · 3 can be written as 3⁴.