(x³-15)+(x-1) Divide using synthetic division
Answers
The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.
What is synthetic division?
In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.
The divisor is x - 1.The dividend is (x³-15).
Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).
Step 2:Write down the first coefficient without changes:
Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum
Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.
We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)
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Related Questions
if a seed is planted, it has a 65% chance of growing into a healthy plant. if 12 seeds are planted, what is the probability that exactly 3 don't grow?
Answers
There is a 136.13 probability that 3 won't increase.
Only 0.65% of seeds will grow into robust plants.
There is a 0.35 probability that a seed won't grow into a robust plant.
In this case, n = 12 and r = 3.
11 seeds will sprout if 1 seed doesn't germinate. Raising 0.65 to the power of 11 and 0.35 to the power of 3 will result in the following: 11 seeds develop, and we use the 11th power; 3 seeds do not grow, so we use the power of 3:
So, the response is:
[tex]{}^{12}C_3[/tex] × [tex]{(chance of successful growth) }^{11}[/tex]x [tex](chance of Unsuccessful growth)^3[/tex]
= [tex]{}^{12}C_3[/tex] × [tex]0.65^{11}[/tex] × [tex]{0.35}^3[/tex]
= 362880 × 0.008750 × 0.042875
= 136.13
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question 4 while verifying cleaned data, a data analyst encounters a misspelled name. which function can they use to determine if the error is repeated throughout the dataset?
Answers
The function can they use to determine if the error is repeated throughout the dataset is " COUNTA ".
The given condition needs the following function;
Data Integration Error:
Data from a single source, obtained and entered in the same way across time is unusual to be present in a database of significant size and age. A database frequently comprises data that has been gathered over time from various sources using various ways. As an illustration, consider how the meaning of "affected" is evolving or changing as the crisis progresses and the number of people affected is tracked over time. In addition, many databases evolve in practice by joining together different pre-existing databases. Almost always, the databases involved in this merging effort include discrepancies involving various data units, measurement intervals, formats, etc. Any process that combines data from various sources has the potential to make mistakes. When two or more databases are combined, errors will be found where there are discrepancies between the databases as well as new errors will be produced (i.e. duplicate records). A few potential origins and types of errors in a big assessment are shown in Table 1 below, at three fundamental levels: after completing the survey, when adding information to the database, and when conducting the analysis.
So, we use " COUNTA "
The function can they use to determine if the error is repeated throughout the dataset is " COUNTA ".
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a bicycle wheel company packages each wheel in a square box. each wheel has a circumference of about 56.5 inches. what is the approximate length of each side of the box? a. 81 in b. 9 in c. 18 in d. 24 in
Answers
The approximate length of each side of the box is 18 inch.
Define circumference.The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian. The shortest path between any two points on a sphere called a geodesic. The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.
The circumference of a circle or other curved geometric object refers to its length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.
Given,
Circumference of circle = 56.5
c = π diameter
diameter = 3.14 × 56.5
diameter = 18
The approximate length of each side of the box is 18 inch.
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Hudson goes to a store an buys an item that costs a dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
Answers
An expression that represents the total amount (a) that Hudson paid is
a-a/10×2+{(a/10×2)/20}.
What do we mean by expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.So, the expression that represents the total amount Hudson paid:
We know that,
Hudson has a coupon for 20% off.A 5% tax is added to the discounted price.Then, the expression can be as follows:
a - (a/100×20) + {(a/100×20)/100 × 5}a - a/10 × 2 + {(a/10×2)/20}Therefore, an expression that represents the total amount (a) that Hudson paid is a - a/10 × 2 + {(a/10×2)/20}.
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Select the two values of x that are roots of this equation. x^2-5x+3=0
Answers
Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
Answers
Yes the diagram has enough information to prove that line segment JK is parallel to line segment ML
How to determine of line segment JK is parallel to line segment MLA rectangle is a polygon that has four sides. the two opposite sides are parallel to each other.
The given figure is a rectangle and according to the figure line LK is equal to line JM
This defines a parallel line which are lines that are equally spaced apart such that the lines will never meet
hence line segment JK is parallel to line segment ML since they are equally spaced, the spacing is achieved by line segment LK and line segment JM
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Find the unit rate. Round to the nearest hundredth, if necessary. $210 of 17 ft2
Can someone help me please it’s due today
Answers
The unit rate for $210 of 17 ft² rounded to the nearest hundredth is equal to 12.
What is a conversion factor?A conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal numerical value must be used when it is necessary to perform any mathematical conversion.
Conversion:
210 dollars = 17 square feet.
x dollar = 1 square feet.
Cross-multiplying, we have:
17x = 210
x = 210/17
x = 12.35 ≈ 12
Therefore, the unit rate is equal to 12.
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The number of computer security breaches is expected to increase at a yearly rate of
86%.
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
Answers
m = 1.053075265
The equivalent monthly rate of increase is 5.3%
A tank in the shape of a hemisphere has a radius of 14 feet. If the liquid that fills the tank has a density of 83.1 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Answer:
477,577 lb
Step-by-step explanation:
Volume of sphere:
V = (4/3)πr³
V = (1/2)(4/3)(3.14159)(14 ft)³ = 5,747.015 ft³
d = 83.1 lb/ft³
W = Vd
W = 5,747.105 ft³ × 83.1 lb/ft³
W = 477,577 lb
Alexa drive a motorcycle 200 kilometers in 3 hours. If she drove at this constant speed, how fat could she travel in 9 hours?
Answers
Answer:600
Step-by-step explanation:
i think
Use the number line to find the difference of 2 - (-4.5)
Answers
The value after solving the expression will be equal to 6.5.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtracting, multiplying, and dividing two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
From the data in the question,
The expression is,
2 - (-4.5)
⇒ 2 + 4.5
= 6.5
Therefore, the result for the expression is 6.5.
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Two cities are 45 miles apart train one is 70 mph train 2 is 60 mph
Answers
Answer:
Hi! I'm pretty sure the question is: Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two towns at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
I have had a similar question before, and I will answer yours. :)
Step-by-step explanation:
T1 - the time the trains are moving to each other.
For time T1, the first train will go the distance of 70*t.
The second train, for time t, will go the distance 60*t.
Both for time t1 - 70t+60(t1) = (70+60)*(t1).
45 - (70+60)*t is the distance between trains that left after t hours.
For the first time, they will be 10 miles apart when they are moving into each other
45 - (70+60)*t = 10
45-10 = (70+60)*t
35 = 130*t
t=35/130 h =7/26 h = 0.27 h
The train meets when distance = 0
45 - (70+60)*t = 0
45 = 130t
t =45/130 h = 9/26 h = 0.35 h when trains met.
Trains began to move apart from each other after 9/26 h moving,
After t2 time trains will be (70+60)*(t2) = 130*(t2) mi apart from each other.
130*(t2) = 10
t2 = 1/13h = 0.08h after they met, they are apart from each other 10 mi.
So after the beginning of the movement, it will be time when they met + time when they were moved 10 mi apart from each other
9/26 h+1/13h = 11/26 h = 0.42 h
bjorn is trying to estimate a difference in average sugar content in two different types of donut: one that is fat free, and one that is full fat. in order to do this, he collects 60 donuts to test: 22 donuts are fat free, 38 that are full fat. he says this satisfies his assumptions. is he right? if not what's wrong? (select all that apply)
Answers
The correct answers are His sample was not drawn at random ,he ought to purchase more fat-free donuts, he may look at the data's histogram to see whether it is roughly typical.
Given that, Bjorn is attempting to calculate the difference between the average sugar level of two distinct kinds of donuts: a fat-free kind and a full-fat variety.
He gathers 60 donuts to test in order to do this: There are 22 fat-free donuts and 38 full-fat donuts. The correct answers are A, D and E He did not get a random sample He should get more fat free donuts He could check the histogram of the data to see if it's approximately normal
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The mean temperature for the first 4 days in January was 3°C.
The mean temperature for the first 5 days in January was 1°C.
What was the temperature on the 5th day?
Answers
The temperature on the fifth day in January is -7°C.
What is mean?It should be noted that a mean simply means the average of a set of numbers that are given.
Since the mean temperature for the first 4 days in January was 3°C. The rural temperature will be:
= 4 × 3°C
= 12°C
The mean temperature for the first 5 days in January was 1°C. The total temperature will be:
= 5 × 1°C
= 5°C
The temperature of the fifth day will be the difference between the temperature. This will be:
= 5°C - 12°C
= -7°C
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Which expression represents "10 subtracted from the quotient of 3 and a number"?
A 3n - 10
B 10 - 3n
C 10 - 3 over n
D 3 over n - 10
Answers
The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Let the number be n
The expression will be:
= 3/n - 10
Therefore, the correct option is D.
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Choose the correct description of the graph of the inequality x − 3 greater than or equal to 5. (5 points)
Open circle on 8, shading to the left.
Closed circle on 8, shading to the left.
Open circle on 8, shading to the right.
Closed circle on 8, shading to the right.
Answers
The correct description of the graph of the inequality x - 3 ≥ 5, is: D. Closed circle on 8, shading to the right.
How to Graph an Inequality?An inequality statement compares two unequal quantities. When plotting the graph of an inequality, if the inequality sign involve is "< or >", an open circle is used to mark the value of the variable on the number line, while a closed circle is used when the inequality sign involved is, "≤ or ≥".
Given the inequality, x - 3 ≥ 5, solve for x:
x - 3 ≥ 5
Add 3 to both sides
x - 3 + 3 ≥ 5 + 3 [addition property]
x ≥ 8
This means the possible values of x are greater than or equal to 8. The graph of the inequality would have a closed circle at 8, with the line shaded to the right on the number line.
The correct description is: D. Closed circle on 8, shading to the right.
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If the shared side between angles 1 and 2 has a measure of 2×+9 and the shared side between angles 3 and 4 has a measure of 9x+1, what is the value of X? Round your answer to the nearest hundredth.
Answers
Answer:
x = 1.14---------------------------
Given figure is a parallelogram since opposite sides are parallel.
Therefore the sides between angles 1 & 2 and 3 & 4 are of equal length:
2x + 9 = 9x + 19x - 2x = 9 - 17x = 8x = 8/7x = 1.14How many solutions can be found for the linear equation?
3(x + 4) = 3x + 4
Responses
A infinitely many solutionsinfinitely many solutions
B no solutionno solution
C two solutionstwo solutions
D one solution
Answers
Answer:
B No solution
Step-by-step explanation:
3(x+ 4) = 3x + 4 Distribute the 3
3(x) + 3( 12) = 3x + 4
3x + 12 = 3x + 4 There is not number that I can multiply by 3 and then add to 12 on one side and add to 4 on the other side of the equal sign to make a true statement, so the answer is no solution.
3x + 12 = 3x +4 Subtract 3x from both sides
12≠4. A false statement means no solution.
When the equation is simplified and the coefficient of the variable (the number before the letter) is the same on both sides of the equation and the constraints (the numbers without letters) are different, this will result in no solution.
Juan owns 8 pairs of pants 1 shirt 3 ties 1 jacket. How many different outfits can he wear to school if he must wear one of each item
Answers
He can wear 24 different outfits can he wear to school .
what is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.
Given:
Juan owns 8 pairs of pants, 1 shirt, 3 ties and 1 jacket
So, number of outfits can he wear to school is
= 8 x 1 x 3 x 1
=24
Hence, he can wear 24 different outfits can he wear to school .
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I need help like asap !!!
only numbers and decimal points
Answers
Answer:
b = 10.06 in
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (10.5)² = b² + (3)²
→ 110.25 = b² + 9
→ b² = 110.25 - 9
→ b = √101.25
→ [ b = 10.06 in ]
Hence, value of b is 10.06 in.
How many times larger is 9 x 10^5 than 5 x 10^3?? PLSSSSS HELP
Answers
Answer:
[tex]1.8 \times {10}^{2} = 180[/tex]
Step-by-step explanation:
[tex] \frac{9 \times {10}^{5} }{5 \times {10}^{3} } = \frac{9}{5} \times \frac{ {10}^{5} }{ {10}^{3} } = 1.8 \times {10}^{2} = 1.8 \times 100 = 180[/tex]
the price of popcorn is $0.50 per box and the price of peanuts is $0.25 per bag, and you have $10. the maximum number of bags of peanuts that you can purchase is: question 8 options: a) 20. b) 5. c) 10. d) 40.
Answers
Answer:
d is correct
Step-by-step explanation:
[tex].25p = 10[/tex]
[tex]p = 40[/tex]
So d is correct.
Pls help due today!!!!!
Answers
Write an equation of the line that passes through (1,6) and is parallel to the line shown.
Answers
Answer:
[tex]y=2x+4[/tex]
Step-by-step explanation:
The slope of the given line is [tex]\frac{-2-4}{-2-1}=2[/tex].
Parallel lines have the same slope, so the equation is:
[tex]y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4[/tex]
v = u + at
u = 2 a = -5 t = 1/2
Work out the value of v
Answers
Explanation:
Substitute values
V=2+-5(1/2)
V=2-5/2
V=-1/2
Answer:
-.5
Step-by-step explanation:
u=2+-2.5=.5
the expressions 9x+7 and 7+9x are equivalent or not equivalent? The equation has_____
Answers
Answer:
Equivalent
Step-by-step explanation:
The equation is equivalent because they are just written the other way around although if you were to rewrite them both they would both be 9x+7
Expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.
What is Expression?An expression is combination of variables, numbers and operators.
The expressions 9x+7 and 7+9x are equivalent because they have the same terms, although the order of the terms is different.
Let us check their equivalence.
9x+7 = 7+9x (commutative property of addition)
9x = 9x (subtract 7 from both sides and subtract 9x from both sides)
Both expressions simplify to the same thing, which means they are equivalent.
In terms of an equation, if we set these two expressions equal to each other, we get:
9x+7 = 7+9x
Simplifying this equation gives:
9x - 9x = 7 - 7
0 = 0
This means that the equation has an infinite number of solutions, since any value of x will satisfy.
Hence, expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.
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Square root five as a decimal 
Answers
To get the answer go to desmos
Answer:
2.2360679775 or 2.24
suppose for a particular week, the forecasted sales were $4,000. the actual sales were $3,000. what is the value of the mean absolute percentage error?
Answers
The mean absolute percentage error is 33.3%
The mean absolute percentage error measures the forecast accuracy by determining how well a particular forecasting method is able to reproduce the time series data that are already available.
This method is referred to as the forecasts of accuracy, which help to measure the number of errors that are in a former forecast.
Then this would factor these errors into a new forecast while making adjustments to the new forecast.
Forecasted sales were $4,000
Actual sales were $3,000
Absolute error = |Actual sales - Forecasted sales|
= |3,000-4,000|
= 1000
Mean Absolute error percentage = (Absolute error / Actual sales) *100%
=(1000/3000)*100
= 33.33%
Hence, The Mean Absolute error percentage is 33.3%
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for a thin piece of 30 inches by 30 inches cardboard, square corners are cut out so that the sides can be folded up to make a box. what dimensions will yield a box of maximum volume? what is the maximum volume?
Answers
Dimensions 5in x 10in x 10in will yield a box with a max. volume of 500 cubic inches.
Volume = height x length x width
Considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.
Square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x
Therefore,
V = x (30-2x) (30-2x) --------------------------------- (1)
V=( 30x - 2x²) (30-2x)
V= 900x- 60x² - 60x² + 4x³
V= 4x³ - 120 x²+ 900x
Taking derivative with respect to x:
dV /dx = 12x² - 240 x +900
dV/dx = 4 (3x² - 60x +225)
For maximum dV/dx, make it equal zero
dV/dx = 0
⇒ 4 (3x² - 60x +225)=0
⇒ 3x² - 60x+225=0 (taking 3 common)
⇒ x² - 20x + 75 =0
Solving this quadratic equation, we get,
x² - 15x -5x + 75 =0
x(x-15) - 5(x-15) =0
Either (x-15)=0
x=15
Or, x-5=0
x = 5
If we substitute x = 15 in equation (1), volume becomes zero.
Therefore, x cannot be 15
When x= 5, putting in the equation (1)
V = 5 (30-2(5)) (30-2(5))
V= 5 (10) (10)
V= 500 cubic inches,
Therefore, Dimensions 5in x 10in x 10in will yield a box with a max. volume of 500 cubic inches
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f(x) = x + 2
g(x) = 3x
Work out the value of gf (4).
Answers
The value of gf(4) is 18
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given,
f(x) = x + 2
g(x) = 3x
Now we need Function of a function
i.e. g[f(x)]
Then on g(x) we have to replace the x with f(x)
Thus,
g[f(x)] = 3(x + 2)
= 3x + 6
Now by evaluating at
x = 4 i.e.
gf(4) = 3(4) + 6
gf(4) = 12 + 6
gf(4) = 18
Hence, The value of gf(4) = 18
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