The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.
Which expression represents the correct form for the quotient and remainder?(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)
This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.
The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.
The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.The result is 4x².
Then, subtract 4x² from 8x²³ to get the remainder of 4x³.
Next, divide 4x² into 21².
The result is 33x.
Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.
Finally, divide 4x²-33x into 67x.
The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To learn more about partial fractions refer to:
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5) Which number is 10 times less than 45.3?
a) 453.0
b) 45.30
c) 4.53
d) 0.453
Answer: 4.53
Step-by-step explanation:
10 times less than 45.3 means that you will be looking for an answer that is the solution to 45.3 / 10, which equals 4.53.
Question 15 of 46
What identity can be used to rewrite the expression 4x² - 9?
A. Difference of Squares
B. Sum of Cubes
C. Difference of Cubes
D. Pythagorean Triples
SUBMIT
Answer:
A.
Step-by-step explanation:
4x² is a perfect square because it is (2x)²
9 is a perfect square with a value of 3
so if we factor 4x² - 9 we can use the difference of two squares to get:
(2x+3)(2x-3)
which part of the expression -2(3 +4) is the sum of two terms
The part containing the sum of two terms in the given expression can be found to be as (3 + 4) and (6 + 8) respectively.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
here, we have,
The given expression is 2(3 + 4).
It can be rewritten as follows,
2(3 + 4)
=2 × 3 + 2 × 4
=6 + 8
or, 2 × 7
Thus, in order to find the expression for sum of two terms in the given expression, there can be two possible ways, the first is (3 + 4) and the other is (6 + 8).
Hence, the sum of two terms in the given expression is found to be as (3 + 4) and (6 + 8) respectively.
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Which recursive sequence would produce the sequence 5, -17, 71, ...?
The recursive sequence that would produce the sequence 5, -17, 71, is by multiplying the previous term by -4 and adding 3.
What is a sequence?A recursive sequence is a sequence where each term is defined as a function of the preceding term(s).
Given the sequence 5, -17, 71, ..., we can see that the next term in the sequence is obtained by multiplying the previous term by -4 and adding 3.
Therefore, the recursive sequence that produces this sequence is:
a_1 = 5
a_n = -4a_{n-1} + 3 where n > 1
This means that the first term of the sequence is 5, and each subsequent term is obtained by multiplying the previous term by -4 and then adding 3.
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David wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 37 ft from the tree, and
David is standing 9.3 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
(The figure is not drawn to scale.)
6 ft
9.3 ft
37 ft
X
David's method to find the height of the tree is the use of the properties of similar triangles. The height of the tree is approximately 24 feet
Laws of ReflectionAccording to the laws of reflection, we have;
Angle of incidence of the light from the top of the tree = Angle of the reflected light ray David sees.
The possible values in the question are;
Distance of the mirror from the tree = 37 feet
Distance from where David is standing to the mirror = 9.3 ft.
Height of his eyes above the ground = 6 ft.
Required: Height of Tree
Therefore;
The triangle formed by David's height, the reflected ray from the mirror and his distance from the mirror is similar to the right triangle formed by the tree, which by the relationship of similar triangles, gives;
[tex]\frac{9.3}{37}[/tex] = [tex]\frac{6}{Height of the Tree}[/tex]
Height of the tree × 9.3 = 6 × 37
Height of the tree = [tex]\frac{6 X 37}{9.3}[/tex] = 23.87 ≅ 24 feet
Therefore, the tree is approximately 24 feet tall
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the area of a rectangle field is 7350m to the second power. if the length of the field is 98m, what is its width
Answer:
Step-by-step explanation:
The formula of the area of a triangle is equal to Length multiply by Width[A = L * W]
Therefore:7350m[tex]x^{2}[/tex] = 98 * W.7350m[tex]x^{2}[/tex] = 98W.7350m[tex]x^{2}[/tex]/98 = 98W/98.Thus: 7350 divided by 98 is 75 which is the width.W=75m .Given 450 grams of bacteria that decreases at a rate of 1/2 per year, what would be an appropriate range after 3 years?
The approximate range will be 56.25 gm. after the end of 3 years.
As per the question,
We have, the value of the weight of the bacteria = 450 gm
As the rate of bacteria is decreasing with rate of 1/2
So, after 1 year the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 1 year will be = 450 *(1/2)=225
As the rate of bacteria is again decreasing with the rate of 1/2
So, after 2 years the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 2 years will be = 225 *(1/2)=112.5
As the rate of bacteria is decreasing with the rate of 1/2
So, after 3 year the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 3 years will be = 112.5*(1/2)=56.25
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Help I can’t find the answer. Which math expression means "the product of 33 and 18"?
О A. 33 • 18
О B. 33 ÷ 18
O C. 33 + 18
• D. 33 - 18
Answer:
A. 33 • 18
Step-by-step explanation:
Product means multiplication
There are different symbols that are used for denoting multiplication and the dot (•) symbol is one of them
So 33 • 18 is same as 33 x 18 which is the product of 33 and 18
Solve the quadratic equation using the square root method:
-108 = (x-11)^2 +13
Answer:
[tex]\sf x=11+11i\\x=11-11i[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]\sf -108=(x-11)^2+13[/tex]
Subtract 13 from both sides:
[tex]\implies \sf -108-13=(x-11)^2+13-13[/tex]
[tex]\implies \sf -121=(x-11)^2[/tex]
Switch sides:
[tex]\implies \sf (x-11)^2=-121[/tex]
[tex]\textsf{For $(g(x))^2=f(a)$ the solutions are $g(x)=\pm\sqrt{f(a)}$}[/tex]
[tex]\implies \sf x-11=\pm \sqrt{-121}[/tex]
Rewrite -121 as 11² · -1 :
[tex]\implies \sf x-11=\pm \sqrt{11^2 \cdot-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sf x-11=\pm\sqrt{11^2} \sqrt{-1}[/tex]
[tex]\implies \sf x-11=\pm11\sqrt{-1}[/tex]
[tex]\textsf{Apply\;imaginary\;number\;rule}:\quad \sqrt{-1}=i[/tex]
[tex]\implies \sf x-11=\pm11i[/tex]
Add 11 to both sides:
[tex]\implies \sf x=11\pm11i[/tex]
Therefore, the solutions are:
[tex]\implies \sf x=11+11i[/tex]
[tex]\implies \sf x=11-11i[/tex]
on two tosses of a coin, what is the probability of head on 1st toss or head on 2nd toss (assume all outcomes are equally likely)
As an alternative, we could contend that the probability of the first coin coming up heads or tails is 1/2, the probability of the second coin coming up heads or tails is 1/2, and so on for the third and fourth coins.
This would reduce the probability of any given sequence of heads and tails to (1/2)x(1/2)x(1/2)x(1/2)=(1/16).
The curve achieves its greatest value for N=2 heads, which is the case where the outcome is most likely. This is exactly what you would anticipate: if each coin has an equal chance of landing heads or tails, then in four flips, half of the results should be heads, making N = 4x(1/2) = 2 the most likely result.
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There are 875 hotel rooms in Edwin's city. During a convention, 16% of the hotel rooms were occupied. How many occupied hotel rooms were there during the convention?
The number of occupied rooms is 140 rooms
What is percentage?Percentage can be defined as a ratio or number that is expressed as a fraction of the number, 100.
It is denoted the the percent sign, "%"
Percentage is known as a dimensionless number. This means that is it has no unit of measurement.
They can also be represented in fraction or decimal forms, like 0.3%, 0.5%, etc
From the information given, we have that;
875 hotel rooms were avaliable16% of the rooms were occupiedThe number of occupied rooms is;
= 16/100 × 875
Find the fraction
=0. 16 × 875
multiply the values
= 140 rooms
Hence, the value is 140 rooms
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70%
60%
50%
40%
30%
20%
10%
0%
Federal Government Funding of Stem Cell Research
55%
58%
52%
Should fund
41% 39%
44%
Should not fund
4%
Total
Men
Women
3% 4%
No opinion
1. There are about 117,000,000 adult American men. About how many of these men
think the federal government should fund stem cell research?
Based on the given percentages, the number of adult American men who think the federal government should fund stem cell research is 67,860,000.
What is the percentage?The percentage is the ratio of a value in relation to another.
The percentage is determined as the quotient of the numerator divided by the denominator, multiplied by 100.
The percentage of men who approve of stem cell research = 58%
The percentage of men who do not approve of the research = 39%
The percentage of men who have no opinion on the research = 3%
The estimated number of adult American men = 117,000,000
Thus, based on the percentage of men who approve of stem cell research, the number is 67,860,000. (117,000,000 x 58%).
Federal Government Funding of Stem Cell Research
Total Men Women
Should fund 55% 58% 52%
Should not fund 41% 39% 44%
No opinion 4% 3% 4%
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The dot plots below show the number of students present in Mr. King's first and second period classes each day in April.
2 dot plots showing the number of students present in Mr. King's first and second period. X axis is labelled number of students present.
The mean absolute deviation for each class period is 1.4. The difference between the mode number of students present for each class period is how many times the mean absolute deviation?
A.
6
B.
5
C.
7
D.
4
The mode of each data-set is given by the input that has the most dots in the dot plot.
After obtaining the mode, the difference is obtained subtracting the mode from the MAD of 1.4 for each data-set.
How to obtain the modes and the difference?A dot plot shows the number of times that each observation appears in the data-set.
The mode of a data-set is the observation that appears the most times in the data-set, hence it will be given by the observation with the most dots in the dot plot.
The mean absolute deviation is of 1.4, then for each data-set the mode is subtracted by 1.4.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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An architect is designing a new windmill with four sails. In his sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails, point Upper R,
has coordinates (2,-4).
He wants to make another sketch that shows the windmill after the sails have rotated 180 degrees about their center of rotation. What would be the coordinates of Upper R prime ?
The coordinates of Upper R prime would be ______?
The coordinates of upper R prime are (-2, 4).
Now, According to the question:
Rotation describes the circular motion of an object around its center. There are different ways things can rotate. Rotation of the Earthre. A very familiar kind of rotation is when a spherical, three-dimensional object turns around an invisible line inside its center.
The sails center of rotation is the origin (0,0)
The top of one sails point R(2, -4).
A 180 degree rotation make you turn (x, y) into (-x, -y),
So, the point turn (2,-4 ), into (-2, 4).
Therefore the coordinates of R are (-2, 4).
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Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank.
Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent. What is the total price he has to pay for the clothes?
Step 1: (Original Price)(Tax Percent) = Amount of Tax
Step 2: Original Price + Amount of Tax = $
The total price he has to pay for the clothes is 27.83
What is Percentage ?
Percentage can be defined as the product ratio of given value, total value and hundred.
Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank.
Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent.
If Darrien spends 26.50, multiply that by 0.05 (26.50×0.05)
which is 1.325 which rounds to 1.33. $1.33 is the amount of tax he has to add. For the full price you would do 26.50+1.33 to get 27.83.
Therefore, The total price he has to pay for the clothes is 27.83
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What expression and quotient does the diagram model?
Answer:
The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.
Which expression and quotient is depicted by the diagram model as in the task content?
It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).
Additionally, the dividend in the quotient by observation is the sum of terms as follows;
x² + x +x -x -1 -1 = x²+x -2.
Ultimately, the result of the division according to the model is; (x +2).
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Step-by-step explanation:
if you are driving from vegas to los angeles, how fast would you need to drive to make it there in 3.5 hours?
You need to drive 122.86 km/ h to driving from Vegas to los Angeles in 3.5 hours
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
v = x /t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 430 km (distance from Vegas to los Angeles)t = 3.5 hoursv = ?Applying the velocity formula, we get:
v = x /t
v = 430 km / 3.5 h
v = 122.86 km/ h
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given f(x) = 3x^2 - 9, find f(1)
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionSolution is in attached photo, this question is testing on function substitution. (Substituting an input to get an output.)
You have a recipe that indicates to use 7 parts of sugar for every 6 parts of milk. You use 28 cups of sugar. How much milk do you need?
7/6 = 28/x
To solve for x, you can cross-multiply:
7 * x = 6 * 28
Simplifying:
x = 6*28/7
x = 24
So, you would need 24 cups of milk.
Answer:
28 cups of sugar / 7 parts of sugar = 4 cups
If 4 cups is 1 part, 6 parts of milk would be 4 x 6
4 x 6
= 24
You would need 24 cups of milk.
Hector's net pay, after a $122.00 automatic savings withdrawal, is $1,413.00. Determine the percent of Hector's net pay that is automatically withdrawn for savings. a 7.9% b 8.0% c 9.1% d 9.5%\
The percent of Hector's net pay that is automatically withdrawn for savings is 7. 95 %
How to find the percentage ?To find the percentage of Hector's net pay that is being withdrawn for savings in an automatic manner, the formula is:
= Amount withdrawn for savings / Pay before amount is withdrawn x 100 %
Amount withdrawn for savings = $ 122
Pay before amount is withdrawn :
= 1, 413 + 122
= $ 1, 535
The percentage withdrawn is :
= 122 / 1, 535 x 100%
= 7. 95 %
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Lawrence worked 12 days for a total of 112.8 hours. How many hours did he average per day?
Answer:
112.8 hours / 12 days
112.8/12 = average of 9.4 hours per day
True or false
The following graph represents a maximum:
f(x)=3x^2+2
Answer:
False
Step-by-step explanation:
Answer come only two
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow. Therefore, option D is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, a spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Here,
Probability of landing on orange is 1/8
Probability of landing on purple is 2/8 =1/4
Probability of landing on yellow is 2/8 =1/4
Probability of landing on blue is 3/8
Therefore, option D is the correct answer.
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Sheng drives at a constant speed for 0.2
hours to get to the train station. He then boards a train that takes him 35
miles to downtown. His whole trip is 42
miles long.
How can Sheng determine his driving speed?
The train travels an average 12 miles/hr
We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.
12 miles / 60 min = 0.2 miles/min
Complete the table and write the question
A linear equation representing the data in table is t(n) = 12x + 23.
The missing values in table should be completed as follows;
n t(n)
4 71
5 83
How to write the equation and complete the table?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.
x and y are the data points.
Next, we would determine the linear equation representing the data in table which passes through the points (1, 24) and (2, 36) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 24 = (36 - 24)/(2 - 1)(x - 1)
y - 24 = 12(x - 1)
y = 12x - 1 + 24
y = t(n) = 12x + 23
When the value n = 4, the value of t(n) can be calculated as follows;
t(4) = 12(4) + 23
t(4) = 71.
When the value n = 5, the value of t(n) can be calculated as follows;
t(5) = 12(5) + 23
t(5) = 83.
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from a (western) standard 52-card deck, how many ways are there to draw two cards such that the first card is a spade and the second card is a queen?
So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.
In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).
To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.
There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.
There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.
To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.
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What is equal to 4 pencils every 2 students
A camera has a listed price of $653.99 before tax. If the sales tax rate is 8.5%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$709.58
Step-by-step explanation:
The total cost is 100% plus the tax rate of 8.5%, it will be 108.5%
To find the cost of the camera with the sales tax included, we take
$653.99 divided by 100, then times 108.5 = $709.58
So, the cost of the camera with sales tax is $709.58
x^-4/x^3 times x^-7 in equivalent expression
x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴
What are index forms?The index form of a number can be defined as the number that is written as an exponential expression.
It is also seen as the single number that is raised to another number.
The rules of index forms are;
Multiplying the index forms when they have the same base, add the exponents or powersDividing indices, in dividing, they must have the same base so subtract the powers Brackets with indices. When there is a power outside the parentheses, then multiply the powersFrom the information given, we have that;
x⁻⁴/x³ × x⁷
Since the denominators are of the same base, add the powers
x⁻⁴/x³⁺⁷
Add the values
x⁻⁴/x¹⁰
Now, subtract the powers
x⁻¹⁴
Hence, the value is x⁻¹⁴
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The table shows the decrease in the amount of chicken feed in a farmer's barn over a seven-month period. Let x represent the number of months since March. Write a linear regression equation for the data. Explain what does the linear regression equation for the data represents in the problem situation.
This data's linear regression equation is y = mx + b, where y is the quantity of chicken feed, x is the number of months since March, m is the line's slope (or the rate at which y changes with respect to x), and b is the y-intercept (or the value of y at x = 0).
The pace at which the amount of chicken feed has been decreasing over time is seen by the slope of the line. The beginning quantity of chicken feed in the barn in March is represented by the y-intercept.
Based on the rate of reduction and beginning quantity for each month since March, the linear regression equation may be used to forecast the amount of chicken feed in the barn in the issue situation.
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