The remainder and quotient are written as the following partial fractions:
Quotient: [tex]4x + 1[/tex]
Reminder: [tex](18x - 3)[/tex]
Divide the leading term of the numerator by the leading term of the denominator to obtain the first term of the quotient:
[tex]\dfrac{8x^3} { 2x^2} = 4x[/tex]
Multiply the entire denominator by the first term of the quotient, then subtract it from the numerator:
[tex](4x)(2x^2 - x - 21) = 8x^3 - 4x^2 - 84x\\\\(8x^3 - 2x^2 - 67x - 24) - (8x^3 - 4x^2 - 84x) = 2x^2 + 17x - 24[/tex]
With the new numerator, repeat steps 1 and 2 [tex](2x^2 + 17x - 24)[/tex] and the original denominator [tex](2x^2 - x - 21)[/tex]:
[tex]\dfrac{2x^2} { 2x^2} = 1\\(1)(2x^2 - x - 21) = 2x^2 - x - 21\\(2x^2 + 17x - 24) - (2x^2 - x - 21) = 18x - 3[/tex]
The resulting numerator [tex](18x - 3)[/tex] is the remainder.
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What color is the condensed water, also called condensation, that collects on the inside of the top cup?
When the coloured water evaporates and condenses on the inside of the top cup, there is no colour in the water on the inside surface of the cup.
As water molecules in the air cool, they slow down and combine into tiny droplets of liquid water. This process is called condensation. This happens when water molecules in the air touch the outside of a cold mug exposed to air.
Water vapour in the air is extracted by several techniques, such as cooling the air below the dew point, exposing the air to a desiccant, using membranes that allow only water vapour to pass, collecting the mist, or pressurizing the air. I can do it.
Common examples are water forming on the outside of a cold mug, or moisture forming on a car window on a cool night.
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A cyclist travels 24 km from home to the park.
She leaves home at 13:05 and arrives at the park at 13:50.
What is her average speed in km/h?
Please Help. which of the following set notation describes the shaded region above?
B) X union Y complement
How should a set notation function be written?
The set of all functions f: X Y is denoted by the following notation: The set of all functions f: X Y is labeled Y X for any sets X and Y. Another helpful example of standard notation is as follows: Notation: The term |X|, or occasionally #X, is used to represent the number of elements in finite sets X.
In the above diagram we can see that the shaded region occupy the x and X ∩ Y so the correct option is B
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I’m confused on this question
The adjacents angles are ∠ RTL and ∠ ETL, The obtuse vertical angles are ∠ RTL and ∠ STE, the two supplementary angles are ∠ NTE and
∠ NTR and angles supplementary to ∠ RTS is ∠ RTL
What are angles?The two rays intersecting at a common point makes an angle.
Given is a figure,
Adjacent Angels =
The angles having one arm in common are called adjacent angles.
Here, adjacents angles are ∠ RTL and ∠ ETL
Vertical angles =
A pair of angles that have the same vertex and are on opposite sides of two intersecting rays makes Vertical angles
Here, vertical angles are ∠ RTL and ∠ STE
Supplementary angles =
When the sum of two angles is 180°, then they are supplementary angles.
Here, supplementary angles are ∠ NTE and ∠ NTR
We see that, the angle supplement to ∠ RTS is ∠ RTL
Hence, the correct answers are, adjacents angles = ∠ RTL and ∠ ETL, The obtuse vertical angles = ∠ RTL and ∠ STE, the two supplementary angles = ∠ NTE and ∠ NTR and angles supplementary to ∠ RTS is ∠ RTL
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A step that has a height of 6 inches. A ramp starts 5 feet away from the base of the step,making a 5.7 angle with ground. what can you say about the angle the ramp would make with the ground if the starts closer to the step?
Considering all the option and the question, We cannot determine anything about the angle is the right answer.
what is angle?An angle is a geometric shape that is formed by two rays that share a common endpoint, called the vertex.
what is vertex?The vertex of an angle is the common endpoint of the two rays that form the angle. The vertex is also sometimes called the "corner" of the angle.
It is not possible to determine whether the angle of the ramp will decrease or increase without more information. The angle of the ramp is determined by the slope of the ramp, which is the change in height divided by the change in distance. If the ramp starts closer to the step, it will have a different slope, and therefore a different angle, than if it starts 5 feet away from the base of the step.
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6. Find the area bounded by f(x) and the x-axis on the interval [0,pi]
f(x) = sin x + 1
The area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,pi]
What is a interval?
An interval is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbersGiven that:
x-axis on the interval [0,pi]
f(x) = sin x + 1
= integral 0 - integral π (sin x) dx + integral 0 - integral π (1) dx
= [- cos π + cos 0] + [π - 0]
= [-(-1) + 1 ] + π
= 2 + π
Therefore, the area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,π]
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Ayana is making 6 scarves that each require 114 yards of purple fabric and a certain amount of blue fabric. She will use 10 yards in all. Which equation can be used to determine how many yards of blue fabric, b, are needed for each scarf?.
each scarf's 0.4166 yards of blue scarf
What is the basic algebraic formula?
This problem can be solved using a straightforward algebraic equation. For each scarf, Ayana requires many yards of blue cloth.
When solving a straightforward equation, visualize the equals symbol (=) as the fulcrum or center of a balance.
What three sorts of equations are there?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
In order to answer this question, let's say that each scarf needs x square inches of purple fabric and y square inches of blue fabric.
A total of six scarves are reportedly required. It is assumed that a total of 10 yards of fabric—the combined amount of the purple and the blue fabrics—will be utilized.
So that we may solve this equation.
We use x and y as 6x and 6y as 6 scarves are needed.
10 yards of cloth were used in total (6x + 6y).
Next up It goes without saying that 1 yard of purple cloth is required for each and every scarf.
Therefore, a total of 6 * 1(1/4) yards is required for 6 scarves.
As a result, 6x becomes 6 * 1/4 yards.
This equates to 6 yards of purple material
We now solve for the required amount of blue cloth.
6y = 10 -30/4 = 40-30/4 = 10/4
However, the yards are for six scarves, therefore we need to divide it by six to obtain the amount of material for one scarf.
Each scarf needs 0.4166 yards of blue fabric, or y = (10/4)/6 =10/4 *1/6 =10/24 = 5/12 yards.
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A point at (−3,−2) is transformed in two steps.
It is reflected about y = x.
It is translated 3 units right and 2 units up.
What is the location of the transformed point?
The location of the transformed point will be at the coordinate (0,4).
What is translation?In mathematics, a translation moves a shape left, right, up, or down but does not turn it. The translated (or picture) shapes appear to be the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.
Given that a point at (−3,−2) is transformed in two steps. It is reflected in y = x. It is translated as 3 units right and 2 units up.
The translated point will be,
(−3,−2) ⇒ (-3,2)
Translation of the point,
(-3,2) ⇒ (-3+3, 2+2) ⇒(0,4)
Therefore, the location of the transformed point will be at the coordinate (0,4).
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Which fraction has the same value as 55.5¯%?
Answer: 55.5 as a fraction is 111/2.
Answer:
55.5/100 or 111/200 in its simplest form
Step-by-step explanation:
55.5 (per)cent) - means every 100
55.5/100= 111/200
If u + t = 5 and u-t=2, what is the value of
(u-t) (u²-1²)?
The value based on the given equation is 22.5
What is an equation?
In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
According to given info.
u + t = 5 ------(1)
u - t = 2 ------(2)
adding equation 1, 2 ;we get
2u = 7
u = 7/2
using value of u in any equation,
7/2 - t = 2
t = 3.5 - 2
t = 1.5
we need to find value of
(u-t) (u²-1²)
(3.5 - 1.5) (3.5² -1²)
2*(12.25 - 1)
2*(11.25)
22.5
Hence the value of the function is 22.5
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Find the slope of each line.
66) pls answer
Answer: The slope is 5/6
Answer:
5/6
Step-by-step explanation:
I need help to solve this!
Answer:
C. neither B. exponentialStep-by-step explanation:
You want to know the nature of the sequences ...
1, 4, 9, 161/3, 1, 3, 9, 27DifferencesTo determine if a sequence is linear, you look at the differences between terms. If they are all the same, then the sequence is linear.
Here, the differences are ...
3, 5, 72/3, 2, 6, 18Neither sequence is linear
Common factorA sequence that is exponential will have adjacent terms with the same ratio.
Here, the ratios are ...
4/1, 9/4, 16/93, 3, 3, 3The first sequence is not exponential. The second sequence is.
The sequences can be characterized as ...
neitherexponential__
Additional comment
You may have noticed that the differences of the first sequence have a common difference of 2. This constant 2nd difference means the sequence can be described by a 2nd-degree (quadratic) polynomial. In fact, each term is the square of its term number.
Please Hurry
Complete the algebraic proof by identifying the reason for each statement.
In mathematics is an expression which is made up of variables and constants, along with algebraic operations
What is algebra explain with example?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.An algebraic equation is a mathematical sentence, when two algebraic expressions are related with an equality sign (=). For example, 3x+6 = 1 is an algebraic equation.Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.There are many laws which govern the order in which you perform operations in arithmetic and in algebra. The three most widely discussed are the Commutative, Associative, and Distributive Laws.Commutative Rule of Addition.Commutative Rule of Multiplication.Associative Rule of Addition.Associative Rule of Multiplication.Distributive Rule of Multiplication.x = 1
3(5x+1) = 13x + 5
3(5x) + 3(1)
15x + 3 = 13x + 5
-13x -13x
2x + 3 = 5
__-3__-3____
2x = 2
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the ftoli (fundamental theorem of line integrals) says: (select all correct answers) group of answer choices none of these the work done by a gradient vector field is always zero. the work done by any vector field is independent of path. the line integral of a gradient vector field depends only on the initial and terminal points of the path. the work done by a gradient vector field is independent of path.
Fundamental Theorem of Line Integral, also called the Gradient theorem, tells us that line integrals through gradient fields are path independent and depend only on the initial and final values. correct answer is option 4 and 5
What does the Line Integrals Fundamental Theorem teach us?
In general, this theorem, like the Fundamental Theorem of Calculus, states that if we integrate a "derivative-like function" (f′ or f), the outcome depends only on the values of the original function (f) at the endpoints.
It is referred to be a conservative vector field if a vector field F is the gradient of a function, F=f.
The line integral of a gradient vector field depends only on the initial and terminal points of the path.
The workdone by gradient vector field is independent of path..
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the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. the thickness of the rind is always one tenth of the radius. the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week. assume that the radius is initially zero.
The volume of a sphere is V = 4/3 x pi x r^3 .
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
V' equals (4 pi x r' x r'2) (4 pi x (.9 3) x r2 x r')
This equation expresses how quickly the rind volume changes over time.
As stated in the issue, r' = 2.
Additionally, the radius will be r = 2 * 5 = 10 after 5 weeks.
V' equals (4 pi x 102 x 2) (Pi x (.93) x 10 x 2) = -
V' is equal to (800 pi) - (800 pi x (.729)).
V' = (800 x pi) (1 - .729) (1 - .729)
V' = (800 x pi)(.271) (.271)
681.09 cubic centimeters make up V'.
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need help on this! thank you in advance!
The value of the angle x will be equal to 36°.
What is an arc of the circle?A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be created by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.
Given that the minor arc is 144. The value of angle x will be calculated by the ratio of the difference between the major arc and the minor arc to the 2.
The angle x will be calculated as,
x = ( Major arc - Minor arc) / 2
x = ( 360-144-144) / 2
x = 72 / 2
x = 36
Therefore, the value of the angle x will be equal to 36°.
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Lin family travels 235 miles to reach her grandmothers.how far have they traveled when they have completed 72% of the trip distance.I’m so stuck I can’t figure out
Answer:
72% of the trip is 169.2 miles
Step-by-step explanation:
[tex]\frac{235}{100} =\frac{y}{72}[/tex]
y · 100 = 235 · 72
100y = 16920
100y ÷ 100 = 16920 ÷ 100
y = 169.2
If false explain why. |-7| is greater than -7
Answer:
True
Step-by-step explanation:
|-7| (absolute value) removes the negative sign, and 7 is greater than -7 so the statement is true.
Without graphing, answer the questions for the system of equations below.
2x+y = 7
x+6y= 30
Are the graphs of the given equations identical lines, parallel lines, or lines intersecting at a single point?
Identical lines
Parallel lines
Intersecting lines
Answer:
intercepting lines
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. Y = x2, y = 5 x2 + 4.
The graph of the equation Y = x² and the 5x² + 4 is attached below.
Equation:
Equation is the combination of variables, numbers and constants.
Given,
Here we have to sketch the region enclosed by the given curves for the equations, Y = x² and Y = 5x² + 4.
Here we have to take some sample value for x to find the value of equations.
And then by using the values, we have to plot the graph through this.
x = -2, -2, 0, 1, 2
Then the corresponding value of y is calculated as,
=> x = -1 => y = 1
=> x = -2 => y = 4
=> x = 0 => y = 0
=> x = 1 => y = 1
=> x = 2 => y = 4
Similarly, the value of Y for the next equation is,
=> x = -2 => y = 24
=> x = -1 => y = 9
=> x = 0 => y = 4
=> x = 1 => y = 9
=> x = 2 => y = 24
Then the graph of the given equation is drawn as.
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or According to his running log, Zachary averaged 4 miles per week last month and 25% less this month. How much did he average this month?
Answer:3
Step-by-step explanation:
George i 89. 99 cm tall. Alex i 72. 44 cm tall. How much taller i George than Alex?
George is 17.55 cm taller than Alex. By simply subtracting the heights of the two, we get the required change between them.
How to do decimal subtraction?Decimal subtraction is as similar to normal number subtraction. Here the subtraction starts from the decimals or the digits after the decimal point.
Calculation:It is given that,
The height of George is 89.99 cm and the height of Alex is 72.44 cm.
Since 89.99 cm > 72.44 cm; George is taller than Alex.
To know how much he is taller, we just simply subtract the height of Alex from the height of George.
I.e., 89.99 cm - 72.44 cm = 17.55 cm
Therefore, George is 17.55 cm taller than Alex.
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Jared also gathered data from a competing real estate broker's office. The competitor's sales were equal to the average
number of sales 8 months before Jared began gathering data and again 2 and 6 months after he began gathering data.
The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.
Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.
Real estate is any immovable property of this kind that has a stake in a piece of land, a building, or housing in general. It also includes the natural resources on the land, such as water, crops, minerals, and minerals.
How does this occur?
from a company real estate broker's office. The competitor's sales were equal to the average number of sales 8 months before jured began gathering data and again 2 and 6 months after he began gathering data. The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.
Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.
Graph is given below in Image.
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Mike had $201.58 in his bank account. He paid some bills and now his account balance is -$57.18 Which equation can be used to find x, the amount of his bill payments?
A) 201.58 + x = -57.18
B.) 201.58 - x = -57.18
C.) -201.58 - x = -57.18
D.) 201.58 - x = 57.18
The equation that can be used to find the amount of bill payments Mike makes, from the $201.58 and the balance in the account of -$57.18, after making the payments is specified in option B.
B.) 201.58 - x = -57.18
What is a mathematical equation?An equation in mathematics is a mathematical statement that joins two expressions, with an 'equals to' mathematics symbol.
The initial amount in Mike's account = $201.58
The money in Mike's account after paying his bills = -$57.18
The amount of Mike's bill payment = x
Therefore;
The initial amount of money in Mike's account less the amount Mike paid as bills = The amount Mike has remaining in his account (his account balance)
Plugging in the values of the variables, we get;
The initial amount = 201.58
The amount of bill payments Mike makes = x
The balance in the account = -57.18
The equation, by plugging in the values becomes:
201.58 - x = -57.18The correct option is therefore, option B
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The equation 201.58 - x = -57.18 with option B is the best equation Mike can used to find the amount of bill payments from his bank account of $201.58 and that of -$57.18, after making the payments is specified in
How to find the equation of Bank balance?An equation is a mathematical model stating the equality of two sides.
The given parameters are
The initial balance = $201.58
Balance after paying bills = -$57.18
Mikes payment = x
The equation, by plugging in the values becomes:
201.58 - x = -57.18
The correct option is therefore, option B
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Here is a shaded parallelogram inside a rectangle.
2x
5
12
W
The area of the parallelogram is (10x +50) cm².
Work out the length of the base of the parallelogram.
Answer:
8
Step-by-step explanation:
Select the correct answer.
Which statement about the inequality 2 1/5< 2 3/5 is true?
A. On the vertical number line, 2 1/2 is located below 2 3/5
B. On the vertical number line, 2
3/5 is located below 2 1/5 C. On the vertical number line, 2 3/5 and 2 1/5 are located at the same point
D. On the vertical number line, 2 1/5 and 2 3/5 are both located
is located below 0
Answer: A.
Step-by-step explanation: On the vertical number line, 2 1/5 is located below 2 3/5.
To compare the values of 2 1/5 and 2 3/5, you need to first convert them to fractions with a common denominator. For example, you can convert 2 1/5 to a fraction with a denominator of 5 by multiplying the numerator (1) and the denominator (5) by 2: 2 1/5 = (2 * 1)/(2 * 5) = 2/10 = 1/5.
Then, you can add the fractions to get a common denominator: 2 1/5 + 2 3/5 = (2 + 2) + (1/5 + 3/5) = 4 + (4/5) = 4 4/5.
Since 4 4/5 is greater than 4, it follows that 2 3/5 is greater than 2 1/5. Therefore, on the vertical number line, 2 3/5 is located above 2 1/5.
has one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
What is eigenvalue?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
a) -4
b) 1
c) 1
Step-by-step explanation:
a) The matrix A is given by:
[tex]A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\[/tex]
where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:
[tex]A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right][/tex]
and by taking the determinant:[tex]\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}[/tex]
and the roots of this polynomial is:
[tex]\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}[/tex]
hence, the real eigenvalue of the matrix A is -4.
b) The multiplicity of the eigenvalue is 1.
c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)
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Complete Quetion
The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.
PLSS HELP! I'LL GIVE BRAINLIEST!!
Answer:
20.625
Step-by-step explanation:
a=− 3263i/24 + 1/12 ≈0.083333333−2.380111459i, b= 165/8 =20.625
Hope this helps
Answer:
1.1
Step-by-step explanation:
Here is the answer. Have a good day!
(y + 1)^5 divided by (y + 1)^2
Answer:
(y+1)³
Step-by-step explanation:
(y+1)⁵/(y+1)²
=(y+1)(y+1)(y+1)(y+1)(y+1)/(y+1)(y+1)
=(y+1)(y+1)(y+1)
=(y+1)³✓✓
If PS ≅ WX, then PS= WX
F. Reflexive
G. Symmetric
H. Definition of congruent segments
J. Transitive