The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1 using synthetic division is x³ + 2x² - 2x + 7 and the remainder is 13
Finding the quotient and remainder using synthetic divisionFrom the question, we have the following parameters that can be used in our computation:
x⁴ - 3x³ + 9x + 6 ÷ x + 1
The synthetic set up is
-1 | 1 3 0 9 6
|__________
Bring down the first coefficient, which is 1 and repeat the process
-1 | 1 3 0 9 6
|__-1_-2_-2_7____
1 2 -2 7 13
This means that the quotient is
x³ + 2x² - 2x + 7
And the remainder is 13
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Complete question
Find the quotient and remainder using synthetic division.
x^4-3x^3+9x+6/x+1
The quotient is
The remainder is
Answer:
Step-by-step explanation:
To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.
So we have:
Dividend: x^4 - 3x^3 + 9x + 6
Divisor: x + 1
We can represent the divisor as (x + 1) and set up the synthetic division table as follows:
-1 | 1 -3 9 0 6
| -1 4 -13 13
|___________________
| 1 -4 13 -13 19
The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.
The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.
We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.
The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:
x^3 - 4x^2 + 13x - 13
And the remainder is:
13
Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.
I NEED HELP SOLVING THIS MATH PROBLEM PLEASE.
The ball's height is 11 meters after approximately 6.83 seconds and 0.17 seconds.
The height of the ball after t seconds is given by the equation h = 1 + 30t - 5t^2. To find all values of t for which the ball's height is 11 meters, we need to solve the equation [tex]1 + 30t - 5t^2 = 11[/tex].
[tex]30t - 5t^2 - 10 = 0[/tex]
[tex]t^2 - 6t + 2 = 0\\\\t = (6 \pm \sqrt{6^2 - 4(1)(2)}) / 2\\\\\t = (6 \pm \sqrt{32}) / 2\\\\t = (6 \pm 4\sqrt2 / 2\\\\t = 3 \pm 2\sqrt2[/tex]
Therefore, the values of t for which the ball's height is 11 meters are approximately 6.83 seconds and 0.17 seconds.
Rounding to the nearest hundredth, we get:
t ≈ 6.83 or t ≈ 0.17
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You have a cylinder with a height of 8 centimeters and a radius of 3 centimeters. What is the volume. If you get the answer please add a explantion.
Answer:
The exact volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.
Step-by-step explanation:
The volume of a cylinder can be calculated using the formula:
[tex]\boxed{V = \pi r^2 h}[/tex]
where:
V is the volume.r is the radius.h is the height.Given values:
r = 3 cmh = 8 cmSubstitute the given values into the formula and solve for V:
[tex]\begin{aligned} \implies V&=\sf \pi \cdot 3^2 \cdot 8\\&=\sf \pi \cdot 9 \cdot 8\\&=\sf 72\pi \;cm^3\\&= \sf 226.19\; cm^3\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.
Write an equation to solve for X.
Step-by-step explanation:
The sum of the interior angles of a n-gon is equal to ( n-2)(180) degrees
for this 6-gon the sum is (6-2) * 180 = 720 degrees
(145 + 165 + 58 + 130 + 125 + x ) degrees = 720 degrees
x = 97 degrees
O is the center of the regular decagon below. Find its area. Round to the nearest tenth if necessary. 14
The area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex]
To find the area of a regular decagon, we need to know either the side length or the apothem (the perpendicular distance from the center to a side). In this case, you have provided the radius of the decagon, which is 14 units.
For a regular decagon, the apothem (a) is related to the radius (r) by the formula:
[tex]a = r * cos(\pi/10)[/tex]
Let's calculate the apothem using the given radius:
[tex]a = 14 * cos(\pi/10) =12.149[/tex]
Now, we can calculate the area (A) of the regular decagon using the formula:
[tex]A = (5/2) * a^2 * tan(\pi/10)[/tex]
[tex]A = (5/2) * (12.149)^2 * tan(\pi/10) =195.7[/tex]
Rounding to the nearest tenth, the area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex].
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Is the relation a function? Explain.
A. No because for each input there is not exactly one output.
B. No because for each output there is not exactly one input.
C. Yes because for each input there is exactly one output.
D. Yes because for each output there is exactly one input.
The relation is a function because (d) Yes because for each output there is exactly one input.
Determining if the relation is a functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph can be represented as
x g(x)
-5 1
-2 0
-1 -1
0 2
1 3
5 1
The above table of values is a function
This is so because each output values have different input values.
i.e. it would pass the vertical line test when represented on a graph
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For a confidence level of 98% with a sample size of 32, find the critical t value.
The critical value for a confidence level of 98% with a sample size of 32 is given as follows:
t = 2.4528.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.
(df is one less than the sample size).
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.the diagonal of a picture frame is 18 inches the base of the picture frame is 12 what is the height of the picture frame rounded to the nearest tenth
After considering the given details we conclude that the height of the picture frame is 12, under the condition that the diagonal of a picture frame is 18 inches the base of the picture frame is 12.
The height of the picture frame can be evaluated applying the Pythagorean theorem. The Pythagorean theorem projects that in a right triangle, the square of the length of the hypotenuse (the diagonal of the picture frame) is equivalent to the summation of the squares of the lengths of the other two sides (the height and base of the picture frame).
Therefore , in this case, we have a right triangle with a hypotenuse of 18 inches and a base of 12 inches. We can evaluate for the height as follows:
height²+ 12² = 18²
height² = 18² - 12²
height² = 144
height = √(144)
height = 12
Hence, the height of the picture frame is 12 inches rounded to the nearest tenth.
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PLEASE HELP!!!!!!! URGENT!!!!!
Use Law of Cosines. Find length of X. (Round final answer to one decimal place as needed. Round all intermediate values to two decimal places as needed.)
Answer: 23.80
Step-by-step explanation:
[tex]\sqrt{19^2+18^2-2*19*18cos(80)}[/tex]
The pre image shown above is dilated by a scale factor of 1/2 about the center (1,-5). What is the location of the point C?
with scaling factor = 1/2 ,
the coordinate location of the dilated posit C is ( 2,-3)
Bookwork code: K27
,Calculator
allowed
A pendulum of length 18 cm is swinging from a fixed point, as shown.
Calculate the distance that the end of the pendulum travels when it swings
through an angle of 87°.
Give your answer in centimetres (cm) to 1 d.p.
87°
18 cm
The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm
Given data ,
A pendulum of length 18 cm is swinging from a fixed point
Now , it swings through an angle of 87°
So , Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
Now , D = ( θ/360 ) x 2πr
On simplifying , we get
D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )
D = ( 0.241667 ) ( 113.04 )
D = 27.3 cm
Hence , the pendulum travels a distance of 27.3 cm
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what is capital and revenue expenditure?
Answer:
Capital expenditures are typically one-time large purchases of fixed assets that will be used for revenue generation over a longer period. Revenue expenditures are the ongoing operating expenses, which are short-term expenses used to run the daily business operations.
4) Use the figure to answer the
following question.
The figure below is made up of two rectangular prisms.
Which answer below
*190
*170
*120
*70
The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.
How to Find the Volume of the Composite Solid that Involves Rectangular Prisms?Note that the formula for finding the volume of a rectangular prism is given as:
Volume of rectangular prism = length * width * height.
Find the volume of each rectangular prism and add them together:
Volume of prism 1:
length = 10 m
width = 4 m
height = 3 m
Volume = 10 * 4 * 3 = 120 m³
Volume of prism 2:
length = 10 m
width = 1 m
height = 7 m
Volume = 10 * 1 * 7 = 70 m³
Total Volume = 120 + 70 = 190 m³.
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Help me please for math
The total area of the composite figure is 17 square centimeters.
How to find the area of the figure?Remember that the area of a rectangle is equal to the product between its dimensions.
We can separate the figure into two rectangles, one of these rectangles is of 1cm by 2cm, then its area is:
A = 1cm*2cm = 2cm²
The other rectangle is of 3cm by 5cm, then its area is:
A' = 3cm*5cm = 15cm²
Adding that we get a total of:
total area = 2cm² + 15cm² = 17cm²
That is the area of the figure.
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BRAINLIEST
Write the equation for the translation of the graph of ( brackets = absolute value ) y=[2x+7] one unit to the left.
As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The function is given below:
y = |2x + 7|
The translated function is as follows:
y = |2(x - 1) + 7|
y = |2x - 2 + 7|
y = |2x + 5|
As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.
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the diagram shows a right triangle and the lengths of two of its sides in 11.9in and 7.9 and d what measurement is closest to the value of d inches
The measurement is closest to the value of d inches is 14. 28
How to determine the valueIt is important to note that the Pythagorean theorem is stated as;
The Pythagorean theorem states that the square of the longest leg or hypotenuse side of a triangle is equal to the sum of the squares of the other two sides.
This is represented as;
x²= y²+ z²
Now, substitute the values, we get;
x² = 11. 9² + 7.9²
Find the square values, we have;
x² = 141. 61 + 62. 41
add the values, we have;
x² = 204. 02
Now, find the square root of both sides, we get;
x = √204. 02
x = 14.28
Know that d = x = 14. 28
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Is this figure a polygon? Explain.
a series of lines, connected randomly
Based on the information and the image, we can infer that it does correspond to a polygon.
What is a polygon?A polygon is a term used in geometry to refer to a closed plane figure made up of three or more line segments called sides. Polygons are classified according to the number of sides they have. For example:
A triangle is a three-sided polygon.A quadrilateral is a polygon with four sides.A pentagon is a polygon with five sides.Based on the above information, we can infer that the image corresponds to an irregular polygon with 20 sides.
Note: This question is incomplete. Here is the complete information:
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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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QUESTION 8 1 POINT
.
Find the GCF of the following three monomials:
21x³y5
63x5y²
45x¹y³
The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²
How do i determine the greatest common factor (GCF)?The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:
First, we shall determine the factors of each monomials. This is illustrated below:
21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y
63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y
45x¹y³ = 3 × 3 × 5 × x × y × y × y
Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:
3 × x × y × y = 3xy²
Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²
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Find the median and mode of the data.
3, 414, 334, 5, 212, 4, 823, 212
Median: 212
Mode: 212
The median and mode of the data set are 273 and 212 respectively.
What is the median?The median is the value that splits the mathematical numbers or expressions in half. The median value is the middle number of data points. To find the median first arrange the data points in ascending order.
To find the median, we need to arrange the numbers in order from least to greatest:
3, 4, 5, 212, 212, 334, 414, 823
There are 8 numbers in total, so the median is the average of the two middle numbers, which are 212 and 334.
Median = (212 + 334)/2 = 273
To find the mode, we need to identify the number(s) that occur most frequently. In this case, 212 appears twice, so it is the mode.
Mode = 212
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Find the probability that a randomly
selected point within the square falls in the
red-shaded square.
1
1
3
P = [?]
3
Enter as a decimal rounded to the nearest hundredth.
The probability that a randomly selected point within the square falls in the red-shaded square is 0.11
Finding the probabilityFrom the question, we have the following parameters that can be used in our computation:
Red square of length 1White square of length 3The areas of the above shapes are
Red square = 1² = 1
White square = 3² = 9
The probability is then calculated as
P = Red square/White square
So, we have
P = 1/9
Evaluate
P = 0.11
Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11
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See photo how to use distributive property of multiplication to simplify the expression.
The simplest form of the expression by the use of the distributive property is;
[tex]12x^2 + 24x + 9[/tex]
What is the distributive property?In mathematics, the distributive property, which explains how multiplication interacts with addition or subtraction, is a fundamental concept. By allocating or multiplying a number or term to each term enclosed by a set of parenthesis, it enables you to simplify expressions.
The distributive property is frequently employed in algebraic expressions, equation simplification, and polynomial operations. By spreading out the multiplication over addition or subtraction, it aids in simplifying complex statements and makes calculations easier to understand.
We know that;
[tex]3(4x^2 + 8x + 3)\\12x^2 + 24x + 9[/tex]
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4. What is the mean absolute deviation of the data below to the nearest hundredths?
(13, 16, 16, 17, 20, 20, 20, 21, 22)
Answer:
Exact form: 2.5185185185185
Simplified form: 2.52
Fraction form: 63/25
Step-by-step explanation:
I'm giving the brainiest to the correct answer.
Answer:
$15,200
Step-by-step explanation:
You want to know the amount deposited at 1.5% that will earn the same simple interest in a year as $12,000 deposited at 1.9%.
InterestThe interest amount is given by the formula ...
I = Prt
For the two accounts, the interest and the time are the same, so we have ...
P1·r1 = P2·r2
12000·1.9% = P2·1.5% . . . . . . . . . . . equate interest amounts for t=1
P2 = 1.9/1.5·12000 = 15200 . . . . . . divide by 1.5%
Ruth deposited $15,200.
<95141404393>
4x+4=4x-4 what dose x equal
The value of the variable is equal to 0
What are algebraic expressions?Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.
These algebraic expressions are also composed of arithmetic operations, such as;
AdditionBracketParenthesesMultiplicationDivisionSubtractionFrom the information given, we have that;
4x+4=4x-4
To determine the value of x, take the steps;
collect the like terms, we have;
4x - 4x = -4 - 4
subtract the values, we have;
0 = -8
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help 30 pts if your right
The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].
Option D is the correct answer.
We have,
The expression:
2/5 - 15 + 8 - 1/5 + 3
Now,
To make the simplification easier,
We combine the fraction and like terms together.
So,
[2/5 + (-1/5)] + [8 + 3 + (-15)]
This can be seen as applying the properties of commutative and associative.
Thus,
The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].
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please help thank you !!
Answer:
[tex]\left \{ {{R + L = 27} \atop {1.99*L+1.29*R=43.23}} \right.[/tex]
Step-by-step explanation:
If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
OC) 3 years
D) 308 years
Answer:
31 years
Step-by-step explanation:
A = P(interest rate)^number of years (n)
if the money is to quadruple, A = 4 X 22,000 = 88,000.
P = investment amount = 22,000.
interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.
n is number of years.
22,000 (1.045)^n = 88, 000
divide both sides by 22, 000:
(1.045)^n = 4
take logs for both sides:
log (1.045)^n = log 4
simplify using log laws (by bringing down the n):
n log (1.045) = log 4
divide both sides by log (1.045):
n = (log 4) / log (1.045)
= 31.49 (31 years to nearest year)
1,6,9,1,6,9 what is a rule for the pattern?
The piecewise rule for the pattern is given as follows:
f(n) = 1 if n % 3 = 0.f(n) = 6 if n % 3 = 1.f(n) = 9 if n % 3 = 2.What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The pattern for this problem is given as follows:
1,6,9,1,6,9.
The period of the pattern is given as follows:
3 units.
The pattern of the function is constant, meaning that all the outputs for an input that is a multiple of 3 are of 1, if the remainder of the division is of 1 the output is of 6, and if the remainder of the division is of 2 the output is of 9.
Hence the pattern is defined as follows:
f(n) = 1 if n % 3 = 0.f(n) = 6 if n % 3 = 1.f(n) = 9 if n % 3 = 2.More can be learned about piece-wise functions at brainly.com/question/19358926
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jeremiah spends at least $14.50 on dinner everyday. Write an inequality to repersent the amount jeremiah spends. then write two examples of amounts jeremiah might spend. Please help
The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.
1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.
2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.
3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.
4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.
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The sine of an angle 0 in the third quadrant is -0.5. What is the value of cos(0)?
The value of cos(θ) value of cos(0) when the sine of the angle is -0.5 in the third quadrant is -sqrt(0.75).
To solve this problem, we need to use the fact that the sine and cosine functions are related through the Pythagorean identity: [tex]sin^2[/tex](0) + [tex]cos^2[/tex](0) = 1.
Since we know that the sine of angle 0 in the third quadrant is -0.5, we can use the unit circle to find the corresponding x-coordinate (cosine value) of the angle.
In the third quadrant, the angle is between 180 and 270 degrees, which means that the x-coordinate (cosine value) is negative.
We can draw a right triangle with the hypotenuse on the unit circle and the angle in the third quadrant, and use the Pythagorean theorem to find the length of the adjacent side (the x-coordinate).
The hypotenuse has a length of 1 because it is on the unit circle, and the opposite side (the y-coordinate) has a length of -0.5 because we know that the sine of the angle is -0.5. Using the Pythagorean theorem, we can solve for the length of the adjacent side (the x-coordinate):
[tex]cos^2[/tex](0) + (-0.5)2 = 1
[tex]cos^2[/tex](0) + 0.25 = 1
[tex]cos^2[/tex](0) = 0.75
Taking the square root of both sides, we get:
cos(0) = +/- sqrt(0.75)
Since we know that the cosine value is negative in the third quadrant, we can take the negative square root:
cos(0) = -sqrt(0.75)
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