Matrix A belongs to the permutation and Markov classes. A permutation matrix is a square matrix with exactly one 1 in each row and each column, and 0s everywhere else.
This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.
Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.
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HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
12π m²
Step-by-step explanation:
We are interested in calculating the area bounded by the given arcs .
we know that if [tex]\theta[/tex] is the angle subtended at the centre by the arc , then ; the area is given by ,
[tex]\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 \\[/tex]
here we have ,
[tex]\theta = 120^o[/tex][tex] r = 6m [/tex]Therefore on substituting the respective values, we have;
[tex]\longrightarrow Area =\dfrac{120^o}{360^o}\times \pi (6m)^2 \\[/tex]
Simplify,
[tex]\longrightarrow Area =\dfrac{1}{3}\times \pi \times 36m^2 \\[/tex]
[tex]\longrightarrow \underline{\underline{ Area = 12\pi \ m^2}} \\[/tex]
And we are done!
Answer: The result is 12π m²
Step-by-step explanation:To solve, we must find the Area of the circle, for this we must do the following:
[tex] \: \sf{Area} = \cfrac{ \sf{θ} }{360 {}^{ \circ} } * \sf{\pi r {}^{2} }[/tex]
Once having the above, we must extract the results that we have to put in the fraction, where:
[tex] \theta = 120 {}^{ \circ} [/tex][tex]\sf{r = 6m}[/tex]Once we have the above, we must substitute the respective values...
[tex] \sf Area = \cfrac{120 {}^{ \circ} }{360 {}^{ \circ} } * \pi(6m) {}^{2} [/tex]
Now to finish, let's simplify:
[tex] \sf{Area = \cfrac{1}{3}* \pi * 36m {}^{2} }[/tex]
[tex] \sf Area = 12 \pi \: m {}^{2} [/tex]
Rpt: The result is 12π m²
a student eats a dinner containing
[tex]8.0 \times 10 { }^{6} [/tex]
joules of energy. he wishes to do an equivalent amount of work in a nearby gym by lifting a 60kg object. how many times must he raise the object to expand this much energy? assume he raises it a distance of 2.0m each time
The number of times a student must raise the object to expand the given energy level is 6800 times.
What is work and energy?Work is defined as transferring energy into an object so that there is some displacement. Energy is defined as the ability to do work. Work done is always the same. Energy can be of different types such as kinetic and potential energy.
Here, W=8.0×10⁶, m=60 kg, g=9.8 ms⁻² and h=2.0 m
We know that, W=mghn
Now, n=W/mgh
n=8.0×10⁶/(60×9.8×2)
= 6800 times
Therefore, the number of times a student must raise the object to expand the given energy level is 6800 times.
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Plsss help and be legit I need help with this
On solving the provided question, we can say that the inequality we have ( -3, 2 ) => 2x - y>-8
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
here the inequality
we have ( -3, 2 )
y - 2 > 2(x+3)
y-2 > 2x +6
2x - y>-8
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True or False: Scale factors figures must be the same proportions on all sides from the original figure.
The statement is true, the scale factor maintains the proportions between the sides.
Is the statement true or false?We want to see if the statement "Scale factors figures must be the same proportions on all sides from the original figure." is true or false.
Suppose we have a polygon with N sides, such that the lengths of each side are:
{L₁, L₂, L₃,...}
If we apply a scale factor k, we just need to multiply each one of these lengths by k, then we will get:
{k*L₁, k*L₂, k*L₃,...}
Now, let's take the proportion between the new lengths for sides 1 and 2, we will get:
(k*L₁)/(k*L₂) = L₁/L₂
The scale factor disappears, then the proportions are maintained,
The statement is true.
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Determine the vertex and the zeros of the function: y = (x – 1)2 – 25. Question 1 options: A) Vertex: (–1,25); zeros: (–6,0), (4,0) B) Vertex: (–1,25); zeros: (6,0), (–4,0) C) Vertex: (1,–25); zeros: (6,0), (–4,0) D) Vertex: (1,–25); zeros: (–6,0), (4,0)
The vertex for the given function is (1, -25) and the zeros are (6, 0)(-4, 0).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
Given y = (x - 1)² - 25
converting the equation in form of y = ax² + bx + c
y = x² + 1 - 2x - 25
y = x² - 2x - 24
vertex of a quadratic equation is given by (-b/2a, -D/4a)
b = -2, a = 1, c = -24
D = b² - 4ac
D = (-2)² - 4(-24)
D = 4 + 96
D = 100
vertex is, -b/2a = -(-2)/2 = 1
and -D/4a = -100/4 = -25
vertex are (1, -25)
and for zeros put y = 0
y = x² - 2x - 24
x² - 2x - 24 = 0
x² - 6x + 4x - 24 = 0
x(x - 6) + 4(x - 6) = 0
(x - 6)(x + 4) = 0
x = 6 and x = -4
zeros are (6, 0)(-4, 0)
Hence option C is correct.
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factorise the following:
11a - 11a^
i think ^ is squared
The factorization of the provided question is basically -11a(a-1).
What exactly is factorization?The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring. You will mostly learn this idea in your lower secondary classes from grades 6 to 8.
A polynomial is an expression made up of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative exponents. Polynomials are commonly used in algebra and in various mathematical disciplines.
Given,
11a-11a²
Taking common terms
-11a(a-1).
by factorizing 11a-11a²
we get -11a(a-1).
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Liam has quarters, dimes, and nickels in his pocket. Liam says he has twice as many quarters as dimes and 3 more dimes than nickels. Liam also says he has the same amount of money in dimes as he has in quarters.
How many of each coin does Liam have in his pocket?
Liam has 5 quarters, 10 dimes and and 7 nickels.
What is quarter and dime?1 dollar is 100 cents - a full dollar, so 100 cents.
One dollar is written on one side of the coin, sometimes as "$1".
1 quarter dollar equals 25 cents - 1/4 of a dollar equals 25%, so 25 cents
On one side of the coin, a quarter dollar is written.
1 dime is 10 cents - 1/10th of a dollar, so 10%, so 10 cents, dime begins with d, decimal begins with, and decimal is base-10. One dime is written on one side of the coin.
1 nickel is 5 cents - made of nickel alloy, 1 cent/penny is possibly not made of nickel because it costs more than 1 cent, so it begins with 5 cents.
On one side of the coin, five cents are written.
Let d be the no. of dimes, n be the no. of nickels and q be the no. of quarters.
Given that
2q = d
n + 3 = d
money in dimes = money in quarters
10d = 25q
d can be written as
d = q/2
So
10(2q) = 25q
2q/q = 25/10
q = 2.5
as 2.5 cant be a number for quarter, lets double it
q = 5
d = 2q
d = 2(5)
d = 10
n = d - 3
n = 10 - 3
n = 7
Thus, Liam has 5 quarters, 10 dimes and and 7 nickels.
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Ronnie loaned her older brother $1500 and he offered to pay her 4% interest in three years. How much money will Ronnie have in three years when her brother pays her back
Answer: 1560
Step-by-step explanation:1500*1.04=1560
according to government data, 22 percent of children in the united states under the age of 6 years live in households with incomes that are classified at a particular income level. a simple random sample of 300 children in the united states under the age of 6 years was selected for a study of learning in early childhood. if the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (note: z represents a standard normal random variable.)
The probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.
What is the binomial distribution?
In a binomial distribution, the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.
To approximate the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level, we can use a normal approximation to the binomial distribution.
The sample size is n = 300 and the proportion in the population is p = 0.22. The standard deviation of the sample proportion is:
[tex]\sigma_{p}[/tex] = √(p(1-p)/n) = √(0.22(1-0.22)/300) = 0.0115
We can use the standard normal distribution to approximate the probability that the sample proportion is at least 0.27:
[tex]P(p_{hat} > = 0.27) \approx P( (p_{hat} - p) / \sigma_{p} > = (0.27 - 0.22) / 0.0115 )[/tex]
P(z >= 1.74)
where z is the standard normal variable.
We can use a standard normal table or calculator to find the probability for z >= 1.74 is about 0.04.
Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.
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Y=1+sinx/1-sinx find the derivative of this problem
The derivative of the problem is dy/dx = (2cosx)/(1-sinx)²
How to find the derivative of the function?The given function is Y=1+sinx/1-sinx
d/dx (u/v) = [u (dy/dx) - v (dv/dx) ] / v²or less formerly
(u/v) =[ [(v (du) = u(dv)] / v²
(Remember the rule in word; " vdu minus udv all over v squared)
So with Y=1+sinx/1-sinx then,
Let u = 1+sin x ⇒du/dx= cos x and
v = 1-sin x⇒dv/dx = -cos x
Then, [d/dx(u/v) = u(dy/dx) - u(dv/dx)] / v²
dy/dx = [(1-sinx)(cosx) - (1+sinx)(-cosx)] / (1-xin x)²
This implies that dy/dx =[ cosx - sin x +cosx +sin xcosx] / (1-sinx)²
Therefore, dy/dx = (2cos x)/(1-sinx)²
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HELP ASAP it is TIMED
Answer:24
Step-by-step explanation:
A store sells a package of 25 trading cards for $5.25.
The depth D in inches, of snow in my yard t hours after it started snowing this morning is given by D=1.5t+4 If the depth of the snow is 7 inches now, what will be the depth one hour from now?
If the depth of the snow is 7 inches now, the depth one hour from now is equal to 8.5 Inches.
How to determine the depth one hour from now?Based on the information provided above, a function which models the depth (D) in inches, of snow in a yard time (t) hours after it started snowing this morning is given by:
D = 1.5t + 4
where:
D represents the depth measured in inches.t represents the time measured in hours.When the depth (D) in inches is equal to 7 inches now, the time measured in hours would be given by:
D = 1.5t + 4
7 = 1.5t + 4
1.5t = 7 - 4
1.5t = 3
Time, t = 3/1.5
Time, t = 2 hours.
One hour from now, the time measured in hours would be given by:
Time, t = 1 hour + 2 hours
Time, t = 3 hours.
At time, t = 3 hours, the depth can be calculated as follows;
Depth, D = 1.5t + 4
Depth, D = 1.5(3) + 4
Depth, D = 8.5 Inches.
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Each cement block is 9 centimeters thick and each clay block is 5 centimeters thick. Xavier made a stack of 17 blocks that was 113 centimeters thick. How many of each type of block did Xavier use?
Using a system of equations, the number of each type of block Xavier used is as follows:
7 cement blocks10 clay blocks.What is a system of equations?A system of equations is two or more equations solved simultaneously or concurrently.
A system of equations is also described as simultaneous equations.
Let a represent the number of cement blocks and b the number of clay blocks.
9a + 5b = 113 ... Equation 1
a + b = 17 ... Equation 2
Multiply Equation 2 by 9:
9a + 9b = 153 ... Equation 3
Subtract Equation 1 from Equation 3:
9a + 9b = 153
-
9a + 5b = 113
4b = 40
b = 10
In Equation 2, substitute b = 10:
a + b = 17
a + 10 = 17
a = 7
Thus, Xavier used 7 cement blocks and 10 clay blocks to make the stack of 17 blocks that was 113 centimeters thick.
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Ina study, the sample is chosen by dividing the population into voting precincts, and sampling everyone in the precincts selected What is the sampling method? Simple Random Systematic Stratified Cluster Convenience
The sample is chosen by dividing the population into voting precincts, and sampling everyone in the precincts selected is cluster sampling.
As stated in the question statement, the sample was obtained by randomly selecting precincts from which to sample the entire population, which is known as cluster sampling.
A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the whole population.
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the length of a shadow of a tree is feet when the angle of elevation of the sun is . approximate the height of the tree.
The approximate height of the tree is feet.
The exact height of the tree cannot be determined without additional information. However, a rough estimate can be made using the following formula:
Height of Tree = Length of Shadow / Tan(Angle of Elevation of Sun)
In this case, the estimated height of the tree would be: Length of Shadow / Tan( ) = feet/tan( ).
The formula to calculate the height of a tree is:
Height of Tree = Length of Shadow * Tan(Angle of Elevation of the Sun)
In this case, Length of Shadow = feet and Angle of Elevation of the Sun
Therefore, the height of the tree can be calculated as follows:
Height of Tree = feet * Tan( )
Height of Tree = feet * 0.839
Height of Tree = feet
Therefore, By the angle of elevation the approximate height of the tree is feet.
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the data set shows the number of passengers on the flights leaving the columbus airport in the next hour. what is the median number of passengers on the flights? round answer to tenths place. if answer is a whole number then put a zero in your answer for the tenths place for it to be counted correct 39, 48. 25, 25, 53, 22, 70, 36
After rounding off the median of the given data would be 38.
What is the median?The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.
It could be referred to as "the middle" value for a data set.
The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.
So, calculate as follows:
22, 25, 25, 36, 39, 48, 53, 70
TErms are even: Average of two middle terms to get median.
Median = 36 + 39/2
Median = 37.5
Rounding off: 38
Therefore, after rounding off the median of the given data would be 38.
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Which of the following represents all solutions (x,y) to the system of equations created by the linear equation and the quadratic equation y=x^2+9
All solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).
To find all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9, we need to solve for the intersection of the linear equation and the quadratic equation. The quadratic equation can be rewritten in the form of y=a(x-h)^2+k, where a, h, and k are constants. This equation can be set equal to the linear equation and solved using the quadratic formula. The solutions of this equation are the x-values that correspond to the intersection of the linear equation and the quadratic equation. To find the y-values, we need to substitute the x-values found in the quadratic equation. Therefore, all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).
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i dropped a heavy cube the other day, creating a dent in my floor. the triangular hole in the surface of the floor has sides of lengths $68,$ $75,$ and $77.$ find the depth of the hole.
I recently dropped a large cube, leaving a dent in my floor. The floor's surface contains a triangular hole with sides that are $68, $75, and $77 long. The hole is about this deep: [tex]$d=12 \sqrt{6}[/tex]
What is meant by triangular?Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure. Triangle examples. Sandwiches, traffic signals, clothing hangers, and a billiards rack are a few instances of triangles in everyday life.
To start, you can determine the sides of the tetrahedron whose apex corresponds to the dent's deepest point. Three of its sides are previously known to be $68,75,77, and since we have perpendicular planes, if these side lengths are x, y, and z, then
[tex]$x^2+y^2=68^2, x^2+z^2=75^2, y^2+z^2=77^2$[/tex] and these three equations solve to
[tex]$x=12 \sqrt{15}, y=4 \sqrt{154}, z=3 \sqrt{385}[/tex]
When the origin of a coordinate frame is located at the point where three perpendicular planes cross and the axes are placed along the edges, the equation for the plane of the triangle hole is
[tex]$\frac{x}{12 \sqrt{15}}+\frac{y}{4 \sqrt{154}}+\frac{z}{3 \sqrt{385}}=1[/tex]
As a result, the distance from the origin, which is the hole's deepest point, to its plane is
[tex]$d=\frac{1}{\sqrt{\frac{1}{144(15)}+\frac{1}{16(154)}+\frac{1}{9(385)}}}[/tex]
Then we get,
[tex]$d=12 \sqrt{6}[/tex]
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Write the equation of the line that passes through the points (-3, 3) and (1, 2).
The equation of a line passing through the points (-3, 3) and (1, 2) is x + 4y = 9
What is line passing through the points?When two points in a plane are given, a line passing through them can be determined. It is the set of all points in the plane that are equidistant from the two given points.
These points form a straight line, which can be represented by an equation with two variables.
The equation of the line can be found using the slope-intercept form or by solving a system of two equations.
The slope of the line is the ratio of the change in the y-coordinate of the two points over the change in the x-coordinate of the two points.
The y-intercept is the point where the line crosses the y-axis. The line can also be expressed in terms of its intercepts on the x and y-axes.
The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
We know that the equation of a line passing through the points (x1, y1) and (x2 , y2) is given by y - y1 = m (x - x1).
m is the slope given by the formula m = (y2 - y1) / (x2 - x1)
Hence on substituting the given points in the equation of a line, we get
y - 3 = m ( x - (-3) ) -------(1)
m = (y2 - y1) / (x2 - x1)
m = (2 - 3) / (1+3)
m = -1/4
Substituting value of m in equation (1), we get
y - 3 = -1/4 ( x + 3)
4(y - 3) = -x - 3
4y - 12 = -x - 3
x + 4y = -3 +12
x + 4y = 9
Therefore, the equation of a line passing through the points (-3, 3) and (1, 2) is x + 4y = 9
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question content area top part 1 describe the three methods used to represent a set. give an example of a set represented by each method.
The three methods which are used to represent a set are word description, roster method and set-builder notation.
What is a set?
The way that sets are represented by a person is always the same which is as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.
The three methods used to represent a set are as follows;
1. Word description
It is the method of representing a set under which we simply use words for describing the elements of the given set.
For example: A is the set of all natural numbers less than 8.
2. Roster method
It is the method of representing a set under which the elements of the set are listed by separating them with commas and in curly brackets.
For example: A = {1,2,3,4,5,6,7}
3. Set-builder notation
It is the method of representing a set under which only the property of the elements of the given set are written.
For example: A = {x ,x ∈ N and x<8}
Hence, the above stated methods are used to represent a set.
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Question 15
Divide £65 in the ratio 11:2
Questic
Divide
Answer:
55 and 10
I hope this helps
One factor of the function f(x) = x^3 - 6x^2 + 11x - 6 is (x-3)
The quotient of the polynomial division is x^2 - 3x + 2.
How to determine the quotient of the division?From the question, we have the following parameters that can be used in our computation:
f(x) = x^3 - 6x^2 + 11x - 6
Factor = (x-3)
One way to find the other factors of the function f(x) = x^3 - 6x^2 + 11x - 6 is to divide the polynomial by (x-3) and see what the quotient is.
To do this, we have
Quotient = f(x)/Factor
Substitute the known values in the above equation, so, we have the following representation
Quotient = (x^3 - 6x^2 + 11x - 6)/(x - 3)
Using a graphing calculator, we have
Quotient = x^2 - 3x + 2
Hence, the quotient is x^2 - 3x + 2
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Complete question
One factor of the function f(x) = x^3 - 6x^2 + 11x - 6 is (x-3)
Determine the quotient of the polynomial and the factor
The functions f and g are such that
f(x) = 6x+7 /2
g(x) = 3x - 5
Find the value of x that makes f^-1 g ^-1 (x) = 0.
Give your answer as an integer or as a decimal.
Using the inverse function method, the value of x should be x = 7/2 or x = -5
From the case, we know that:
f(x) = (6x + 7) / 2
g(x) = 3x - 5
f⁻¹.g⁻¹(x) ?
First, we need to find the inverse function of each given functions. We assume that:
f⁻¹(x) = p
g⁻¹(x) = q
f⁻¹(x) = (6x + 7) / 2
p = (6x + 7) / 2
2p = 6x + 7
2p - 7 = 6x
x = (2p - 7) / 6
f⁻¹(x) = (2x - 7) / 6
g⁻¹(x) = 3x - 5
q = 3x - 5
q + 5 = 3x
x = (q + 5) / 3
g⁻¹(x) = (x + 5) / 3
Next, we will try to find the value of x
f⁻¹.g⁻¹(x) = 0
(2x - 7) . (x + 5) = 0
6 3
(2x² - 7x + 10x - 35) = 0
15
2x² +3x - 35 = 0
(2x -7) (x+5) = 0
x = 7/2 ∨ x = -5
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When the function f(x) is divided by 2x + 3, the quotient is 2x² + 7x - 8 and the
remainder is-7. Find the function f(x) and write the result in standard form.
The function f(x) is 4x³ + 20x² + 5x - 31.
What is a function?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each part of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here, we have
Given: function f(x) is divided by 2x + 3, the quotient is 2x² + 7x - 8 and the remainder is -7.
When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:
f(x) = d(x)q(x) + r
Now putting values of d(x) = 2x+3, q(x) = 2x² + 7x - 8 and r = -7, we get
f(x) = (2x+3)(2x² + 7x - 8) - 7
f(x) = 4x³ + 14x² - 16x + 6x² + 21x - 24 - 7
f(x) = 4x³ + 20x² + 5x - 31
Hence, the function f(x) is 4x³ + 20x² + 5x - 31.
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f (x) = log(x-1) +1
g(x) = log
What shifts occur for f(x)?
Answer:
f(x) shifts for log(DWX)
Step-by-step explanation:
can someone pleaseeeee help me???????
Answer:
Hello the vertex point is (4, -6)
this parabola opens upwards because the coefficient of x is positive.
The answer is B, good luck!
In baseball, a ".300 hitter" gets a hit 30% of the time. (For those of you not well-versed in spiritual things like baseball: hitting .300 is pretty good.) Suppose a player has five times at bat in a game.
a) What is the probability of getting at least one hit in a game?
b) What is the probability of getting at least one hit, in ten consecutive games?
The answers are 0.8319, 0.1588, but I don`t understand how the textbook got them.
Step-by-step explanation:
a) The probability of getting at least one hit in a game can be found by using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
In this case, the event of getting at least one hit in a game is the complement of getting no hits in a game.
To get no hits in a game, the player must get 0 hits out of 5 at bats.
The probability of getting no hits in a game is (1-.3)^5 = 0.168.
Therefore, the probability of getting at least one hit in a game is 1 - 0.168 = 0.832
b) The probability of getting at least one hit in ten consecutive games is found by multiplying the probability of getting at least one hit in one game by itself ten times.
So it would be (0.832)^10 = 0.1588
Alternatively, we could use the binomial distribution formula, where probability of getting a hit k times out of n trials is given by
P(k) = (n choose k) * p^k * (1-p)^(n-k)
If we want to find the probability of getting at least one hit in ten games, we need to find the probability of getting 0 hits in all ten games and subtract it from 1.
1 - (1 - 0.832)^10 = 0.1588
So the probability of getting at least one hit in ten consecutive games is 0.1588.
Writing and solving radical equations: Mastery Test
PLEASE HELP
The equation has 2 valid solutions; no extraneous solutions.
What are functions?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.
What is factorization and radicals?Factorisation : The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.
Radicals :In the same way that addition is the opposite of subtraction in mathematics, a radical, also known as a root, is the opposite of an exponent. The square root, denoted by the symbol is the smallest radical.
The given equation is:
First, we determine the solutions
Add 5 to both sides
Square both sides
Expand
Collect like terms
Expand again
Factorize
Factor out x - 2
Split
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
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Armando's workouts consist of kickboxing and swimming. While kickboxing, he burns 10 calories per minute and he burns 9 calories a minute while swimming. He wants to burn at least 450 calories each day.
a) If
x
is the number of minutes that Armando will kickbox and
y
is the number of minutes he will swim, write an inequality that would help Armando create a workout for today.
The inequality that models this scenario is given as 10x + 9y ≥ 450
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let x represent the number of minutes that Armando will kickbox and y represent the number of minutes he will swim.
Kickboxing, he burns 10 calories per minute and he burns 9 calories a minute while swimming. He wants to burn at least 450 calories each day, hence:
10x + 9y ≥ 450
The inequality is given as 10x + 9y ≥ 450
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