Examples of permutation matrices are the identity matrices with a permutation in rows. Permutation matrices are invertible and the inverse is a permutation matrix as well.
A permutation matrix is a square matrix which contains exactly one 1 in each row and all other entries 0.
So a permutation matrix can be obtained by rearranging the rows or columns of an identity matrix. Identity matrix is also a permutation matrix with entry 1 exactly once in each row and all other entries 0.
Example of a permutation matrix:
[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]
A permutation matrix is invertible because an identity matrix is invertible [since det(I) = 1] and a permutation matrix is just got by exchanging rows or columns which does not change its determinant. So the determinant of a permutation matrix ≠ 0 and hence invertible.
The inverse of a permutation matrix is its transpose itself. The transpose is again a permutation matrix.
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Mason and Daisy are building towers. Each one of Masons blocks is 6cm tall. Each one of Daisys blocks is 8cm tall. They both build towers that are exactly the same height. What is the smallest height that their towers could be?Give your answer in cm
Reason:
GCF = greatest common factor
LCM = lowest common multiple
GCF of 6 and 8 = 2
LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24
We can list out the multiples of each to confirm this
multiples of 6 are: 6, 12, 18, 24, 30, ...multiples of 8 are: 8, 16, 24, 32, ...If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.
The smallest height that their towers could be 24 cm.
What is the lowest common factor?The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). The least Common Multiple and Least Common Divisor are other names for it (LCD). For instance, 12 is the least frequent multiple of 4 and 6.
GCF = greatest common factor
LCM = lowest common multiple
GCF of 6 and 8 = 2
LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24
We can list out the multiples of each to confirm this
multiples of 6 are 6, 12, 18, 24, 30, ...
multiples of 8 are: 8, 16, 24, 32, ...
If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.
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Jason is in the business of manufacturing phones. He must pay a daily fixed cost of $500 to rent the building and equipment, and also pays a cost of $150 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Total cost of phone in a day $650
What is Algebra ?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Total cost of rent in a day = $500
Total cost of per phone = $150
The equation which represents values in term of c:
150p + 500 = C
The total cost he had in a day :
= 150 + 500
= $650
Hence, the total cost throughout the day is $650
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translate the following into a equation: the product of five and a number is the quotient
(-) of six and the same number
The equation for the given sentence is 5x = 6/x
Given,
The product of five and a number is the quotient of six and the same number.
We have to translate this sentence into an equation:
Equation:
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So here,
The product of five and a number is the quotient of six and the same number
We can take the number as x.
Then,
5 × x = 6 ÷ x
5x = 6/x
Multiply x on both sides
5x × x = 6/x × x
We get,
5x² = 6
Divide both sides with 5
5x²/5 = 6/5
We get,
x² = 6/5
x = √6/5
That is, the equation for the given sentence is 5x = 6/x
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help me pls!
1. Which kind of model do you think best represents the profit for each business?
2. Find a function that models the profit you can expect, based on your projections, for each business. You can round your values to the nearest thousandth, as needed.
From the table given:
1. The type of function that best models each situation is:
D: Exponential.H: Linear.L: Quadratic.2. The functions are given as follows:
D: [tex]D(t) = 3.738 \times (1.749)^t[/tex]H: H(t) = 11.771t - 4.533.L: L(t) = -5.875t² + 30.582t + 116.9.Item 1For this problem, we have that each month, the amount increases, but the increase is approximately a factor of the previous amount, meaning that an exponential equation best models the data.
The points are given as follows:
(1, 5), (2, 12), (3, 23), (4, 50), (5, 62), (6, 80).
Using an exponential regression calculator, the equation is:
[tex]D(t) = 3.738 \times (1.749)^t[/tex]
Item 2For this problem, we have that each month, the amount increases, but the increase is approximately a constant from previous amount, meaning that an linear equation best models the data.
The points are given as follows:
(1, 11), (2, 19), (3, 29), (4, 38), (5, 50), (6, 73).
Using a linear regression calculator, the equation is:
H(t) = 11.771t - 4.533.
Item 3The amount initially increases, then it decreases, meaning that a quadratic model best represents the data.
The points are given as follows:
(1, 142), (2, 150), (3, 165), (4, 141), (5, 120), (6, 91).
Using a quadratic regression calculator, the equation is:
L(t) = -5.875t² + 30.582t + 116.9.
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What is d to the power of 6 and d to the power of 0 equal together?
The value of d to the power of 6 and d to the power of 0 equal together is d^6.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
The information given regarding the power is illustrated thus:
d^6 + d^0
In this case, the addition of the power will be 6 + 0 = 6. Therefore, the value is d^6.
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Given m||n, find the value of x.
Answer:
kt
49
O
xº
Submit Answer
x° = 49°
What are alternate angles?Alternate interior angles are formed when two parallel lines are cut by a transversal and the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal. These angles are equal.
Pairs of alternate angles around the transversal are equal to each other. Angles can either be alternate interior or exterior angles. Sum of the angles formed on the same side of the transversal of the two parallel lines is equal to 180°.
Given , ∠t = 49°,
Therefore angles x° will also 49° because alternate angles are equal when two parallel lines are cut by a transversal.
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If you wanted to take a simple random sample for a study on screen time in elementary school students in your town, which describes the sample you would ask?
twenty students from one elementary class in your town
twenty students from each elementary school in your town
twenty students that are friends from an elementary school in your town
twenty students that are friends from each elementary school in your town
The option that describes the sample you would ask is A. twenty students from one elementary class in your town.
What is a simple random sampling?It should be noted that a simple random sampling simply means a form of sampling whereby everybody has an equal chance of being selected.
In this case, it should be noted that the person wanted to take a simple random sample for a study on screen time in elementary school students in the town. Therefore, twenty students can be chosen to illustrate this.
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6. There are 45 cans of mixed nuts. Each
can has 338 nuts. Below is Mary's work
to find the total number of nuts.
The total number of nuts is 15210 and the missing number is 5
Number of cans of mixed nuts = 45 cans
Number of nuts in each can = 338 nuts
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.
Finding the total number of nuts we get:
Total number of nuts = Number of cans*Number of nuts in each can
[tex]338\\*45\\= 1690\\+ 13520\\= 15210[/tex]
So, the missing number is 5
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What is the domain of the relation(x,y):y=x(x-3) / (x+4)(x-7) ?
{ x : x = R, x -4, x 7}
{ x : x R, x = -4, x 7}
{ x : x R, x -4, x 7}
{ x : x R, x -4, x 7}
The domain of the relation as given in the task content; (x,y): y = x(x-3) / (x+4)(x-7) is the set of all real number values except; -4 and 7 and hence is represented as; { x : x R, x ≠ -4, x ≠ 7}.
What is the domain of the relation given; { x : x R, x -4, x 7}?It follows from the task content that the domain of the relation given in the task content be determined.
On this note, since the domain of a relation or function simply refers to the set of all possible input values of such function.
Since the relation in this scenario is a rational function, it follows that the domain is the set of all real number values except that which renders the relation undefined.
Therefore, since the values which render the relation undefined, render the denominator equal to 0; we have;
(x+4)(x-7) = 0.
x = -4 OR x = 7.
Ultimately, the domain of the relation is the set of all real numbers except; x = -4 and x = 7.
Therefore, when represented by set builder notation; we have; { x : x R, x ≠ -4, x ≠ 7}.
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How do you solve this?
The value of x are 4 and 2.4 after simplifying and applying the quadratic formula.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The equation is:
4/(x - 2) + 3/(x - 3) = 5
4(x - 3) + 3(x - 2) = 5(x -2)(x - 3)
4x - 12 + 3x - 6 = 5x² - 25x + 30
5x² - 32x + 48 = 0
After solving the above quadratic equation by the formula:
[tex]\rm x = \dfrac{-(-32) \pm\sqrt{(-32)^2-4(5)(48)}}{2(5)}[/tex]
x = 4
x = 2.4
Thus, the value of x are 4 and 2.4 after simplifying and applying the quadratic formula.
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In 1992, a postage stamp cost $0.25. In 2004, a postage stamp cost $0.37. What is the average rate of change in postage cents per year?
Answer: 0.01 (One cent per year)
Step-by-step explanation:
We need to find the price the stamp increased per year.
The difference in years is 12.
2004 - 1992 = 12
The difference in price is 0.12.
0.37 - 0.25 = 0.12
So to find price increase per year we do the following:
$0.12/12 = 0.01
$0.01 is one cent per year.
what is (x squared -4x+3)-(3x squared -3x -5)
Need help with this pls
Answer:
Step-by-step explanation:
Please help asap, I will give brainliest
Answer:
the answer is A
Step-by-step explanation:
To check your answer, move 4 units to the right and 3 units up
I don’t understand my check of solution for the equation ^4√x+12=15 with x=81 and how it becomes 15 if √81 is 9
Find the x- and y-intercepts of the graph of x+y=18. State each answer as an integer or an improper fraction in simplest form
The x- and y-intercepts of the graph of x + y = 18 both have the values of 18
What is the x-intercept of the function?The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0
How to determine the x- and y-intercepts of the graph?The equation of the graph is given as
x + y = 18
To calculate the x-intercept, we set the value of y to 0
This is represented as
y = 0
So, we have the following equation
x + 0 = 18
Evaluate the like terms
x = 18
To calculate the y-intercept, we set the value of x to 0
This is represented as
x = 0
So, we have the following equation
0 + y = 18
Evaluate the like terms
y = 18
This means that the x-intercept has a value of 18 and the y-intercept has a value of 18
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Which postulate could we use to prove that the angles
Answer:
PWP (Part Whole Postulate)
Step-by-step explanation:
Supplementary angles add up to 180 degrees. The part whole postulate states that two angles make up a whole.
Answer:
Supplement postulate
Step-by-step explanation:
Supplement Postulate:
If two angles form a linear pair, then they are supplementary.
James and Lucas are eating a pizza. James ate 2/3 of the pizza and Lucas ate 1⁄4 of pizza. Who ate more pizza and by how much?
Answer: James ate more pizza by 5/12 parts.
Step-by-step explanation:
To solve let us takes the lcm of the denominators 3 and 4
which is 12.
James ate 2/3 * 4/4 = 8/12 parts
Lucas ate 1/4*3/3= 3/12 parts
now, we can see 8/12>3/12
Therefore, James ate more pizza by 8/12-3/12= 5/12 parts.
Write an equation of the line that passes through the points. (2,8), (-2,10)
Explanation.
The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)
To do this, we can use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]In our case, we have
[tex]\begin{gathered} x_1=2 \\ y_1=8 \\ x_2=-2 \\ y_2=10 \end{gathered}[/tex]We will simply put all the values above into the formula to get the equation of the line
[tex]\frac{10-8}{-2-2}=\frac{y-8}{x-2}[/tex]Simplifying further
[tex]\begin{gathered} \frac{2}{-4}=\frac{y-8}{x-2} \\ \\ -\frac{1}{2}=\frac{y-8}{x-2} \end{gathered}[/tex]Cross multiplying
[tex]\begin{gathered} y-8=-\frac{1}{2}\left(x-2\right) \\ y-8=-\frac{1}{2}x+1 \\ y=-\frac{1}{2}x+1+8 \\ y=-\frac{1}{2}x+9 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=-\frac{1}{2}x+9[/tex]Choose the answer that best completes the sentence.
-2 - √3i is a known root not a possible root, option 4 will be the correct answer.
What are real and imaginary roots ?
A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.
In other words real roots can be represented in a number line where as imaginary roots can not.
Here, the given root is -2 + √3i :
It is known that the complex roots comes in pairs that is in form a ±ib, where, a is real part of imaginary root and b is imaginary part.
Therefore, the other root will be -2 - √3i.
So, -2 - √3i is a known root not a possible root, option 4 will be the correct answer.
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Is the equation a true statement when x = 3? In other words, is 3 a solution to theequation?7x – 5 = 23 + 10A. Yes, 3 is a solution.B. No, 3 is not a solution.
SOLUTION:
Case: Simple equation
Given:
7x – 5 = 23 + 10
Required:
Is the equation a true statement when x = 3?
Method:
Step 1: Rewrite the equation
7x – 5 = 23 + 10
Step 2: Plug the value x= 3 into the equation
7x – 5 = 23 + 10
7(3) - 5 = 33
21 - 5 = 33
16 is not equal to 33
Final answer:
B. No, 3 is not a solution.
Which could not be the number of snowballs Penn has?
From the question, we have:
P(n) = P(n - 1) + n²
P1 = Po + 1² = 0 + 1 = 1
P2 = P1 + 2² = 1 + 4 = 5 (This is option C)
P3 = P2 + 3² = 5 + 9 = 14 (This is option B)
P4 = P3 + 4² = 14 + 16 = 30 (This is option D)
Therefore the number of snowballs cannot be 25.
So, the correct option is A, which is 25.
there are 3 sides to a triangle 1 measures 115 and the other 2 are x what is x. write and solve an equation
If one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each, then the equation to be solved to obtain the value of "x" is [(115 + 2x) = 180] and the value of "x" will be 32.5°.
As per the question statement, one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each.
We are required to determine a Linear equation of singular value that can describe our concerned situation, and solving which, we will be able to obtain our desired value of "x".
To solve this question, we need to know about one basic yet very important property of a triangle, that is, the sum of all the three interior angles of a triangle is equal to 180 degrees.
Here, the three angles measure 115°, x° and x°.
Therefore, our required equation will [(115 + x + x)° = 180°]
or, [(115 + 2x)° = 180°]
Now solving the above mentioned equation to obtain the value of "x", we get, [(115 + 2x)° = 180°]
Or, [2x = (180 - 115)°]
Or, (2x = 65°)
Or, x = (65/2)°
or, x = 32.5°
Equations: In Mathematics, an equation is a statement that expresses the relation of equation between two separate expressions (of numbers and/or variables) connected by an "equal to" sign.To learn more about Equations, click on the link below.
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Work out the missing numbers:
b) 10.2 +
= 0.8
Answer: -11
Step-by-step explanation:
Gabriella enlarged the size of a painting to a width of 78 cm. What is the new height if it was originally 6 cm wide and 19 cm
tall?
After using substitution method - The new height of the painting will be 247cm.
What is the substitution method?
To solve many simultaneous linear equations, use the substitution method in algebra. As implied by the name, this strategy involves replacing a variable's value from one equation with another.
we are given the original width of the painting to be 6cm and the original height to be 19cm.
after enlarging the size of the painting the new and enlarged width becomes 78cm
and we assume the new and enlarged height of the painting to be xcm.
we now the ratios
original height : original width = enlarged height : enlarged width ,
will remain equal,
Hence substituting the numerical values in the ratios we get
19/6 = x/78
19 * 78 = 6x
1482/6 = x
247cm =x
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Your hotel has been reviewed on yelp 10 times you received the following ratings 4,5,5,3,5,4,2,3 what is your overall rating
The overall rating is 31 and the average rating is 3.8.
What is average?A large number of data points are reduced into a single value using averages. It is a visual depiction of all the data set's available numbers. The average is derived by adding up all the data values and dividing them by the total number of data points.
The word "average" is used in many different contexts in daily life. The average is computed and a single value is used to represent the values for quantities with fluctuating values.
Overall rating = 4+5+5+3+5+4+2+3
Overall rating = 31
Average rating = Overall rating/ Total number of ratings
= 31/8
= 3.8
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Find the equation of the line that passes through (-3,1) and is parallel to
y
=
4
−
3
x
.
Leave your answer in the form
y
=
m
x
+
c
Answer:
y=3x-5
Step-by-step explanation:
parallel lines have the same slope
Find g(x), where g(x) is the translation 2 units right of f(x)=x.
Write your answer in the form mx+b, where m and b are integers.
The image of the function f(x) = x , after the translation is g(x) = x -2 .
In the question
it is given that
the function f(x) = x ,
and f(x) has to be translated 2 units to the right means subtract 2 from the function .
which means g(x) = f(x) - 2
substituting f(x) = x , we get
g(x) = x - 2
the answer in the form of mx+b is g(x) = x - 2
(can refer to the graph given below)
Therefore , The image of the function f(x) = x , after the translation is g(x) = x - 2 .
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three times the sum of a number and seven is greater than five times the number less thirteen in a equation
The function f(t)=16t2 represents the distance (in feet) a dropped object falls in t seconds. The function g(t)=s0 represents the initial height (in feet) of the object. A necklace is dropped from a height of 64 feet. After how many seconds does the necklace hit the ground?
By solving a quadratic equation, we will see that the necklace hits the ground 2 seconds after it is dropped.
After how many seconds the necklace hits the ground?We know that the function:
f(t) = 16*t^2
Represents the distance that an object falls down in t seconds.
If the necklace is dropped from a height of 64 feet, the necklace will hit the ground when the distance that an object falls down in t seconds is equal to 64 feet, so we just need to solve the quadratic equation:
f(t) = 64
16*t^2 = 64
t^2 = 64/16 = 4
t = √4 = 2
The necklace will hit the ground after 2 seconds.
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