the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.
What is Diagonalizable matrix?
If there is an invertible matrix P and a diagonal matrix D such that
P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.
If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.
The given statement is false.
If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.
Hence, the given statement is false.
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During one particular sales day, 75% of the store's customers paid with credit cards. If there were 60 customers that day, how many used a credit card? A. 15 B. 30 C. 45 D. 50 HINT Method 1: Set up a proportion and cross multiply. Method 2: Convert the
45 people used credit card on that particular day , this could be found out using simplified multiplication.
What is proportion?
A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.
A proportion is Associate in Nursing equation within which 2 ratios ar set up to one another.
Main body:
We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.
To find the number of people, who used credit card, we will find 75% of 60.
The number of people who used credit card = (75 / 100 )* 60
The number of people who used credit card = 0.75 *60
The number of people who used credit card = 45
Therefore, 45 people used credit card on that particular day.
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2x+2y=10 slope intercept equation
Answer:
y = -x + 5
Step-by-step explanation:
2x+2y=10 slope intercept equation
2x+2y=10
subtract 2x from both sides:
2y = 10 - 2x
rearrange right side:
2y = - 2x + 10
divide all terms by 2:
y = -x + 5
Answer:
Step-by-step explanation:
5 over 2
Liz dives 10 feet below the surface of the water. Then she returns to the surface. Use the drop-down menus to write an expression that represents her overall change in depth.
The expression that represents her overall change in depth is given as follows:
-10 + 10.
How to represent the changes in depth?The changes in depth are represented using integer numbers, as follows:
Movement in the direction below the surface: negative value.Movement in the direction above the surface: positive value.Liz dives 10 feet below the surface of the water, hence the integer number is of:
-10.
Then she returns to the surface, that is, moving 10 feet in the direction of the surface, hence the integer number is given as follows:
10.
Then the addition operation that represents her overall change in depth
-10 + 10.
Which has a result of zero, as she finished at the same place that she started.
Missing InformationThe problem is given by the image shown at the end of the answer.
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identify features of graphs and tables for linear and nonlinear relationships (example: coordinates of points; x/y intercept)
If you graph a linear characteristic you may get a immediately line. There also are nonlinear functions. If you graph the coordinates of a nonlinear characteristic you may now no longer get a immediately line.
One of the very best ways (however now no longer the handiest way) to differentiate among a linear and a nonlinear characteristic is to have a take a observe the graph of the characteristic.
A linear equation is an equation with variables whose graph is a line. The graph of the linear equation is a hard and fast of factors withinside the coordinate aircraft that every one are answers to the equation. If all variables constitute actual numbers you can graph the equation via way of means of plotting sufficient factors to understand a sample after which join the factors to encompass all factors.
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Subtract expression 2 from expression 1
Expression 1: -9x + 8y
Expression 2: -8x - 2y
Question What is the best approximation of the solution to the system to the nearest integer values? Responses (3, 2) begin ordered pair 3 comma 2 end ordered pair (2, 3) begin ordered pair 2 comma 3 end ordered pair (3, 4) begin ordered pair 3 comma 4 end ordered pair (1, 3) begin ordered pair 1 comma 3 end ordered pair Graph of a system of linear equations. Equation 1 is 5 x plus 2 y equals 16. Equation 2 is x plus 3 y equals 12.
The best approximation to the solution of the system of equations is (2, 3)
How to determine the best approximation to the solution?From the question, we have the following parameters that can be used in our computation:
Equation 1 is 5 x plus 2 y equals 16.
Equation 2 is x plus 3 y equals 12.
Rewrite the equations properly
So, we have the following representation
5x + 2y = 16
x + 3y = 12
Make x the subject in the second equation
So, we have
x = 12 - 3y
Substitute x =12 - 3y in the equation 5x + 2y = 16
So, we have
5(12 - 3y) + 2y = 16
Open the brakects
This gives
60 - 15y + 2y = 16
Evaluate the like terms
-13y = -44
Divide both sides by -13
y = 3.39
Substitute y = 3.39 in x = 12 - 3y
x = 12 - 3 * 3.39
Evaluate
x = 1.83
Approximate the solutions
x = 2 and y = 3
Hence, the solution is (2, 3)
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Suppose that f(3)=2 and g(-2)=6 explain how f(x) and g(x) cannot be inverse funtions of one another
If f{g(x)} = g(x) and g{f(x)} = f(x)
That means they cannot be inverse functions of one another.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given that f(3) = 2 and g(-2) = 6.
From the expression, f⁻¹(2) = 3 and g⁻¹(6) = -2
So now we take the composition,
f{g(-2)} = f (6) = y (let)
Then f⁻¹(y) = 6 = g (-2) , which is given.
Now, f{g(-2)} = g (-2).
And similarly g{f(3)} = g (2) = k (let)
g⁻¹(k) = 2 = f (3)
Now, g{f(3)} = f (3)
Therefore, if f{g(x)} = g(x) and g{f(x)} = f(x)
That means they cannot be inverse functions of one another.
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Please Help!!
It's urgent somebody
2) Write a word problem using the information from the given equation and inequality. Be sure to include all seven parts and an appropriate question requesting a solution for the unknown (variable).
The seven parts of a one-variable equation are as follows:
1 – correct variable term for the left side expression
2 – correct constant term for the left side expression
3 – correct operation between the terms of the left side expression
4 – correct equal sign or inequality symbol
5 – correct variable term for the right side expression
6 – correct constant term for the right side expression
7 – correct operation between the terms of the right side expression
Inequality: 58x+170>42x+320
The solution for the variable is that the variable should be greater than 9.375
How to write a word problem using an inequality?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: the inequality 58x+170 > 42x+320. The unknown variable is x
In word problem, we can write:
When a variable x is multiplied by 58 and then 170 is added. The result is greater than variable x multiplied by 42 with 320 added
Solution for the unknown
58x+170 > 42x+320
58x-42x > 320-170
16x > 150
x > 150/16
x > 9.375
Thus, the solution for the unknown is that the unknown should be greater than 9.375
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Four students were given paint supplies for an art project. The table shows the amount of paint used by each student.
Student 1 Student 2 Student 3 Student 4
seventeen twentieths 1 and one fourth 65% 0.20
Which student used the least amount of paint for their art project?
Student 1
Student 2
Student 3
Student 4
Student 4 used the least amount of paint for the art project
How to determine which student used the least amount of paint?Given:
Student 1 used seventeen twentieths => 17/20
Student 2 used 1 and one-fourth => 1 1/4 = 5/4
Student 3 used 65% = 65/100
Student 4 used 0.20 = 20/100
Since the amount of paint used for the art project has been expressed in fractions. Find the LCM:
17/20, 5/4, 65/100, 20/100
The LCM of 20, 4 and 100 is 100
Student 1: 17/20 = 85/100
Student 2: 5/4 = 125/100
Student 3: 65/100
Student 4: 20/100
Thus, student 4 used the least amount of paint
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Answer: Student 4 (d)
Step-by-step explanation:
Brainliest?
please help. A camper drove 80 miles to a recreational area and then hiked 4 miles into the woods. The rate of the camper while driving was 10 times the rate while hiking. The total time spent hiking and driving was 3 hours. Find the rate at which the camper hiked
Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.
Given that,
A camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods. The camper's speed while driving was ten times that of the hiker. Three hours were spent driving and hiking together.
We have to determine the camper's hiking speed.
We know that,
Let x represent the increasing rate and 10x represent the driving rate.
Time equation is
80/10x+4/x=3
Simplify
8/x+4/x=3
12/x=3
x=12/3=4
Therefore, Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.
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If a = -2 and b = 3, what is the value of -3a²b?
Answer:
-36
Step-by-step explanation:
-3[tex]a^{2}[/tex]b Substitute -2 for a and 3 for b
-3[tex](-2)^{2}[/tex](3)
-3(4)(3)
-36
Answer:
= -36
Step-by-step explanation:
-3a²b
if:
a = -2
b = 3
Then:
= -3*-2²*3
= -3(-2*-2) * 3
= -3*4*3
= -36
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
x = 13
x = 1
Step-by-step explanation:
The (x – 7)2 = 36 gives the value of x as 25.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
(x – 7)2 = 36
Now, dividing both side by 2
(x – 7)2/2 = 36 /2
(x – 7) = 18
Now, add 7 both side
x- 7+ 7= 18 + 7
x = 25
Hence, the value of x is 25.
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What is the domain of the function graphed?
A. {x:x > -4}
B. {x:x < -4}
C. {x:x ≥ -4}
D. all real numbers
(If you have the time, please give an explanation because I completely forgot how to solve these problems)
The correct option is D .
This is a parabola with domain all real numbers D .
Write an expression that is equivalent to 4^4
Answer:
[tex]\sqrt[4]{256}[/tex]
Step-by-step explanation:
1. simplify the expression
4^4 = 256
2. calculate the fourth root of 256 because we used the power of 4
[tex]\sqrt[4]{256}[/tex] = 4
Shirley bought 20.8 pounds of bird seed at a bargain store. She wants to fill her feeder 100 times with an equal amount. How much seed should she put in the feeder each time?
Part A
Which expression represents the problem?
20.8 ÷ 100
20.8 + 100
20.8 × 100
100 ÷ 20.8
Part B
When solving Part A, how is the decimal point moved?
3 places to the right
3 places to the left
2 places to the right
2 places to the left
Part C
How much seed should she put in the feeder each time?
pound(s)
Answer: Part A 20.8 divided Part B 2 places to the left Part C 0.208
Step-by-step explanation:
Part A the question ask each time and when it ask each time it means dividing Part B when dividing you move to the left and their are two 0s and moving the decimal two places to the left would get you 0.208 so, therefor the answer is 0.208
How many gifts total in 12 Days of Christmas?; How many gifts were given in total?; How many gifts were given on the 12th day?
With the help of "The Twelve Days of Christmas” song 364 is the total gifts in 12 days of Christmas.
Total 364 Christmas gifts were given in total.
Total 78 gifts were given on the 12th day.
"The Twelve Days of Christmas”: is one of the most famous and most often sung Christmas carols of all.
So, how many presents are there altogether?
Partridges: 1 × 12 = 12
Doves: 2 × 11 = 22
Hens 3 × 10 = 30
Calling birds: 4 × 9 = 36
Golden rings: 5 × 8 = 40
Geese: 6 × 7 = 42
Swans: 7 × 6 = 42
Maids: 8 × 5 = 40
Ladies: 9 × 4 = 36
Lords: 10 × 3 = 30
Pipers: 11 × 2 = 22
Drummers: 12 × 1 = 12
i) we have to calculate how many gifts total in 12 days of Christmas.
We observe from above that we have the same number of partridges as drummers (i.e 12) ; doves and pipers (i.e 22 ); hens and lords (i.e 30 ) etc. So the simplest way to count our gifts is to add up to the middle of the list and then double the result = (12 + 22 + 30 + 36 + 40 + 42) × 2 = 364.
ii)How many gifts were given in total :
On day one this is simple; just the one gift.
On day two, we get 1 + 2 = 3 gifts.
On day three, we get an additional three gifts on top of day two's three. We receive 3 + 3 = 6 gifts.
On day four, we add four to the previous day's total getting 6 + 4 = 10.
similarly, as we going on words the
we find out that total gifts were given are 364.
iii) The formula which is used to determine the how many gifts given on each day is
n x (n+1) ÷ 2 where n -->a particular day
we have to calculate total gifts were given on 12th day.
So, n x (n+1) ÷ 2 = 12(12+1)/2 = 13× 6 = 78
Hence, total received gifts on 12 days of Christmas is 364.
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evaluate the expression 2x−yz , where x=34 , y=−0.2 , and z = 6. responses 0.3 0.3 1.95 1.95 2.7 2.7 i don't know.
the evaluation of the expression 2x−yz is 69.2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all arithmetic operations that are possible, however division by variables is not one of them. The polynomial x2+x-12 is an illustration of one with one variable. Three terms—x2, x, and -12—are included in this case.
the expression 2x−yz , where x=34 , y=−0.2 , and z = 6.
So putting the value of x,y and z.
2(34)- (-0.2*6) = 68+1.2
=69.2
Hence the evaluation of the expression is 69.2.
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Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?
Answer:
[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]
Step-by-step explanation:
There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.
There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.
The only option that satisfies this is Option 1.
The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the polynomial equation be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )
The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.
The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.
Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.
Hence , the graph of the function is plotted
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1) 9x² + 4y² - 36x + 8y + 4 = 0
Write the standard form equation of each ellipse
A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.
The number of tiles in the bag of 10 that are yellow in colour are; 5 tiles
How to find the probability of selection?We are given;
Total number of tiles in bag = 10 tiles
Now, we are told that in the bag, the tiles are either blue, green, red, or yellow.
Now, after selecting a tile, we are told that it is put back and as such we have after 100 selections that we have 24 blue tiles, 12 green tiles and 12 red tiles. Thus;
Number that will be yellow = 100 - 24 - 12 - 12 = 52 yellow tiles
Thus, it means that the probability of selecting a yellow tile is;
52/100
Thus, number of tiles out of the 10 in the bag that are yellow =
(52/100) * 10 = 5.2
Approximately 5 yellow tiles
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Complete question is;
How many yellow tiles are most likely in the bag? Enter the answer in the box. A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.
please help i need it!
thank you!!
Find the equation of parabola
(i) having focus at (0,-3) its directrix is y = 3.
(ii) having end points of latus rectum (5,10) and (5,10) and which opens towards right.
(iii) having vertex at origin and focus at (0,2)
Answer:
somone in my class is literally a new York rat
Step-by-step explanation:
Chris and Layla bought new fish for their home aquariums. Chris bought 4 guppies and 3 platys for a total of $25.80. Layla bought 4 guppies and 2 platys for a total of $22.92. Find the price of a guppy and the price of a platy.
Solving system of equations we get price of the guppy is $4.29 and platy is $ 2.88.
How to Find the price of a guppy and the price of a platy ?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.Let
price of guppie = x
price of platy = y.
Chris bought 4 guppies and 3 platys for a total of $25.80.
i. e.
4x + 3y = 25.80-----------1
Layla bought 4 guppies and 2 platys for a total of $22.92.
4x + 2y = 22.92-----------------2
equation 1 - 2
then we get
y = 2.88
put y = 2.88 in to equation 1
4x + 3 ( 2.88) = 25.80
then we get
X = 4.29
price of the guppy is $4.29.
price of the platy is $ 2.88.
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there is a real number n such that numerical values of sum of the edge lengths and surface area of a cube with side length n are equal. find n?
Answer:
Given:
Sum of edge lengths = TSA of cube
there are 12 edges in a cube
[tex]12n = 6 {n}^{2} \\ 6 {n}^{2} - 12n = 0 \\ 6n(n - 2) = 0 \\ 6n = 0 \\ n = 0 \\ n - 2 = 0 \\ n = 2[/tex]
n ≠ 0 (since length can't be 0)
therefore n=2
I just need the answer for part a, please help! You just need a graphing calculator and with the data table, find the logistic regression from my understanding
The logarithmic function that models the data is given as follows:
y = 1.0994 + 5.6403 ln(x).
Why is the logarithmic function used, and how to define it?The logarithmic function is used as from the table, the data has a initial fast increase and then the rate of the increase decreases, as the graph reaches it's horizontal asymptote.
The function is defined using a logarithmic regression calculator, inserting the points of the data-set.
From the table, the points are given as follows:
(0, 0.5), (1, 1.4), (2, 4.1), (3, 7.6), (4, 9.1), (5, 10).
(as x represents the number of years after 2005).
Inserting these points into the logarithmic regression calculator, the equation is given as follows:
y = 1.0994 + 5.6403 ln(x).
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The vertex form of the quadratic function f (x) = x² + 8x + 7 is
f(x)= a(x-h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?
Answer:
Step-by-step explanation:
The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.
To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:
h = -8 / 2(1) = -4
Therefore, the value of h is -4.
Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:
k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9
Therefore, the value of k is -9.
Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:
f(x) = a(x - h)² + k
x² + 8x + 7 = a(x - (-4))² + (-9)
We can then distribute the squared term and simplify the equation to get:
x² + 8x + 7 = a(x² - 8x + 16) + (-9)
x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)
We can then collect like terms to get:
x² + 8x + 7 = a(x²) - 8ax + 16a - 9
Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.
Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.
How to multiple fractions with different denominators?
Please explain step by step to get picked brainliest!!
To multiply fractions with multiple denominators, you have to change the fraction to get the same denominator.
For example, if you have 1/3 * 1/2, you will have to find the least common multiple of 3 and 2, which is 6. Then, multiply the numerator by the same number that you multiplied the denominator to get 6.
1/3 * 1/2
LCM = 6
[tex]\frac{1*2}{3*2} *\frac{1*3}{2*3} =\frac{2}{6} *\frac{3}{6}[/tex]
Then, multiply across the numerator
[tex]\frac{2}{3}*\frac{3}{6} =\frac{6}{6}=1[/tex]
TRUE/FALSE american television programs that cross cultural and linguistic frontiers are successful because they appeal to basic human values.
Answer: True
Step-by-step explanation:
They appeal to how humans are empathetic towards others who may not speak their language. Also, they are more inclusive and may talk about things considered "taboo".
Hope this helps! :)
Answer:
False
Step-by-step explanation:
factor this expression 9x^2 - 18x
factor this expression 4x^2 - 9
Answer:
9 x (x - 2) and (2 x - 3) (2 x + 3)
Step-by-step explanation:
Factor the following:
9 x^2 - 18 x
Factor 9 x out of 9 x^2 - 18 x:
Answer: 9 x (x - 2)
Factor the following:
4 x^2 - 9
4 x^2 - 9 = (2 x)^2 - 3^2:
(2 x)^2 - 3^2
Factor the difference of two squares. (2 x)^2 - 3^2 = (2 x - 3) (2 x + 3):
Answer: (2 x - 3) (2 x + 3)
A total of 50 people play darts.
Each player is given 3 darts to try and
hit the bullseye. If 21 of the darts hit
the bullseye, then what percent of
the darts hit the bullseye?
The percentage of the darts hit the bullseye will be 14%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A sum of 50 individuals plays darts. Every player is given 3 darts to attempt to stir things up around town. Assuming 21 of the darts hit the bullseye.
The total number of dart is calculated as,
Total dart = 50 x 3
Total dart = 150
The percentage is given as,
P = (21 / 150) x 100
P = 0.14 x 100
P = 14%
The percentage of the darts hit the bullseye will be 14%.
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