If s< 0, then 152 is equal to the opposite of s.
O A. True ?
O B. False ?
​

Matrix A = xd\(x^{-1}\) is \(\left[\begin{array}{cc}4/\sqrt{17} &2/\sqrt{5} \\1/\sqrt{17} &1/\sqrt{5} \end{array}\right]\) \(\left[\begin{array}{cc}0 &0 \\0 &-2 \end{array}\right]\) \(\left[\begin{array}{cc}1/\sqrt{17} &-2/\sqrt{85} \\-1/\sqrt{17} &4/\sqrt{85} \end{array}\right]\) .

For the matrix A =

[ 2 -8 ]

[ 1 -4 ]

we need to find x and d such that A = xd\(x^{-1}\).

First, we find the eigenvalues of A:

det(A - λI) = (2 - λ)(-4 - λ) - (-8)(1) = λ*λ + 2λ = λ(λ + 2) = 0

So, the eigenvalues are λ1 = 0 and λ2 = -2.

Next, we find the eigenvectors associated with each eigenvalue:

For λ1 = 0:

(A - λ1I)x = 0

[ 2 -8 ] [x1] [0]

[ 1 -4 ] [x2] = [0]

Solving for x gives x = \([4,1]^{T}\).

For λ2 = -2:

(A - λ2I)x = 0

[ 4 -8 ] [x1] [0]

[ 1 -3 ] [x2] = [0]

Solving for x gives x = \([2,1]^{T}\).

We normalize the eigenvectors to get x1 = \([4/\sqrt{17},1/\sqrt{17} ]^{T}\) and x2 = \([2/\sqrt{5},1/\sqrt{5} ]^{T}\) .

Now, we can find d:

d = [λ1 0; 0 λ2] = [0 0; 0 -2]

Finally, we can find \(x^{-1}\):

\(x^{-1}\)  = \(\left[\begin{array}{cc}4/\sqrt{17} &2/\sqrt{5} \\1/\sqrt{17} &1/\sqrt{5} \end{array}\right]^{-1}\) =  \(\left[\begin{array}{cc}1/\sqrt{17} &-2/\sqrt{85} \\-1/\sqrt{17} &4/\sqrt{85} \end{array}\right]\)

Therefore, we have:

A = xd\(x^{-1}\)  = \(\left[\begin{array}{cc}4/\sqrt{17} &2/\sqrt{5} \\1/\sqrt{17} &1/\sqrt{5} \end{array}\right]\) \(\left[\begin{array}{cc}0 &0 \\0 &-2 \end{array}\right]\) \(\left[\begin{array}{cc}1/\sqrt{17} &-2/\sqrt{85} \\-1/\sqrt{17} &4/\sqrt{85} \end{array}\right]\)

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Answer:

yes they are equivalent. if you simplify -21/-56 by dividing it by 3 you will get -7/-21 which equals to 7/21

The sets that have no members are: B and F.

Given are 6 sets we need to determine which of them do not have any members in it,

Considering the sets B and F first,

B. The set of all days whose name does not end in the letter Y.

Explanation: There are no days that do not end in Y, such as Monday, Tuesday, Wednesday, Thursday, and Friday. Therefore, this set has no members.

F. The set of all even prime numbers larger than 27.

Explanation: There are no even prime numbers larger than 2. Therefore, this set has no members.

The sets A, C, D, E, G all have members:

A. The set of all odd numbers between 100 and 110 that are a multiple of 3.

105, is an odd multiple of 3 between 100 and 110.

D. The set of states in the United States that have a common border with Massachusetts has members such as New Hampshire, Vermont, New York, Connecticut, and Rhode Island.

E. The set of all negative integers larger than 16 has members such as -17, -18, -19, and so on.

G. The set of all fractions between 1 and 2 has members such as 1/2, 3/4, 7/8, and so on.

Hence the sets with no member are B and F.

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Using algebraic manipulation, we can prove that (x+y)⋅(x+7)=x is not true. By expanding the equation, we get x^2 + 7x + xy + 7y. This expression cannot be simplified to x, indicating that the given equation is incorrect.

To prove the given equation using Venn diagrams, we need to represent the sets involved. However, Venn diagrams are typically used to illustrate relationships between sets, and not algebraic equations involving variables.

In this case, the equation (x+y)⋅(x+7)=x is an algebraic expression involving variables x and y, rather than sets or their relationships. Venn diagrams are graphical representations used to depict set operations, intersections, unions, and complements. They are not suitable for proving or disproving algebraic equations.

Therefore, it is not possible to utilize Venn diagrams to demonstrate the validity or invalidity of the given equation. Instead, we can rely on algebraic manipulation, as shown earlier, to determine that the equation is incorrect.

In summary, the equation (x+y)⋅(x+7)=x is not true, and Venn diagrams are not applicable for proving algebraic equations.

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Answer:

29n+1, I think

Step-by-step explanation:

P = 2(l + w)

P= 2(9.5n + 10 +5n-9.5)

p = 2(14.5n + 5)

P= 29n + 1

Since they didn't give you the value of n, I would leave it like that

The equation of the parallel line to y = 2x - 1, that passes through (-3, 1) is: y = 2x + 7.

Two lines that are parallel to each other would always have the same slope (m). In the slope-intercept form of the equation that represents a line, y = mx + b, the slope of the line is represented as "m", while the y-intercept is represented as b.

Given:

A point (-3, 1)

Equation, y = 2x - 1. The slope (m) = 2. Since parallel lines have the same slope (m), therefore, the line that passes through (-3, 1) also have a slope (m) = 2.

Substitute (x, y) = (-3, 1) and m = 2 into y = mx + b:

1 = 2(-3) + b

1 = -6 + b

1 + 6 = b

b = 7

To write the equation of the parallel line to y = 2x - 1, substitute m = 2 and b = 7 into y = mx + b:

y = 2x + 7.

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If 3x is the cost of x notebooks, we can find the cost of 24 notebooks by substituting x = 24:

3(24) = 72

Therefore, the cost of 24 notebooks is $72.

Answer:

66244.7

Step-by-step explanation:

70• 943.353 (1 liter into milliliters)=66244.7

Answer:

8sqrt2

Step-by-step explanation:

11.31 when rounded to the nearest hundreth

Answer:

sqrt (2) * sqrt(45) + sqrt (2) * sqrt (80)

45 = 9 *5 "9" is a perfect square so

sqrt (45) = 3 * sqrt (5) * sqrt (2)

sqrt (2) * sqrt (80)

80 = 16 * 5  "16" is a perfect square so

sqrt (2) * sqrt (80) = sqrt (2) * 4 * sqrt(5)

Adding both answers we get

3 * sqrt (5) * sqrt (2) = 3 * sqrt(10)

PLUS

4 * sqrt (10)

which equals

7 * sqrt (10)

SO, the value of a is 7

Step-by-step explanation:

Problem: A stick that is 24 feet long will be placed horizontally in the center of a wall that is 40 feet wide. How far will the stick be from each edge of the wall?

Solution:

Find half of the width of the wall:

Half of the width = 40/2 = 20 feet

Subtract the length of the stick from half of the wall width:

Distance from each edge = Half of the width - Length of the stick

= 20 - 24

= -4 feet (Note: The result is negative)

The negative result indicates that the stick will not fit within the wall width. In this case, it is not possible to place a 24-foot stick horizontally in the center of a 40-foot wide wall. Therefore, the given problem is not feasible.

So, the correct option is not (A) 16 feet, but rather that the given problem is not possible to solve as described.

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Answer:

x = 17deg

Step-by-step explanation:

angle DCE = angle ACB (vertically opposite angles)

therefore,

x + 100 = 4x + 49

3x = 51

x = 17deg

Answer:

X=

Step-by-step explanation:

First you have to divide the shape into to triangles. Triangle CED and triangle ACB.

Second you have to find what angle C is in the triangle ACB. For this you'll have to:

Find out which of the sides are which. For triangle ACB, side CB is the hypotenuse, CA and AB are adjacent.

The formula we use is \(a^{2} +b^{2} =c^{2}\).  a and b are adjacent and c is hypotenuse.

When you found what angle C is, you can go on and to the second triangle same theorem applies to the second triangle \(a^{2} +b^{2} =c^{2}\). At this stage you will already know two angles, 100 and c, so finding E using this formula will be easy

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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Answer:

the answer is 5 5/8

i think it's this

The cost described in the scenario is an example of a mixed cost.

A mixed cost consists of both fixed and variable components. In this case, the $10 per month base charge represents the fixed component of the cost. This charge remains constant regardless of the amount of electricity consumed. It covers the basic service and is not influenced by usage levels.

On the other hand, the additional charge of $0.08 per kilowatt-hour (kWh) of electricity used represents the variable component. This charge varies directly with the amount of electricity consumed. As more electricity is used, the variable cost increases proportionally.

By combining the fixed base charge and the variable charge per kWh, we get a mixed cost structure. The fixed component ensures a minimum cost for the service, while the variable component adds to the total cost based on actual usage. This combination of fixed and variable elements makes the cost a mixed cost.

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The output when the given pseudocode is executed with A = 5 and B = 3 will be "25, 16, 9, 4, 1".

The given pseudocode includes a loop that iterates as long as A is greater than or equal to B. In each iteration, the square of A is displayed, and A is decremented by 1. We are asked to determine the output when A is initially 5 and B is 3.

Step 1: Initialization

A is set to 5 and B is set to 3.

Step 2: Iteration 1

Since A (5) is greater than or equal to B (3), the loop executes.

The square of A (5²) is displayed, resulting in the output "25".

A is decremented by 1, so A becomes 4.

Step 3: Iteration 2

A (4) is still greater than or equal to B (3).

The square of A (4²) is displayed, resulting in the output "16".

A is decremented by 1, so A becomes 3.

Step 4: Iteration 3

A (3) is still greater than or equal to B (3).

The square of A (3²) is displayed, resulting in the output "9".

A is decremented by 1, so A becomes 2.

Step 5: Iteration 4

A (2) is still greater than or equal to B (3).

The square of A (2²) is displayed, resulting in the output "4".

A is decremented by 1, so A becomes 1.

Step 6: Iteration 5

A (1) is still greater than or equal to B (3).

The square of A (1²) is displayed, resulting in the output "1".

A is decremented by 1, so A becomes 0.

Step 7: Loop termination

Since A (0) is no longer greater than or equal to B (3), the loop terminates.

Therefore, The output generated by the code execution will be "25, 16, 9, 4, 1" as the squares of A (starting from 5 and decreasing by 1) are displayed in each iteration of the loop.

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The equation of the circle is (x - 2)²+ (y - 3)² = 169

A circle is a two-dimensional form that may be described as a collection of points that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.

The following is the equation for a circle with centres (a, b) and radius r:

(x - a)² + (y - b)² = r²

In this case, the center of the circle is A(2,3), and a point on the circle is B(7,15). The radius of the circle may be calculated using the distance formula:

r = √((7 - 2)² + (15 - 3)²) = √(5² + 12²) = 13

So the equation of the circle is:

(x - 2)² + (y - 3)² = 13²

(x - 2)²+ (y - 3)² = 169

Therefore, the equation of the circle is (x - 2)²+ (y - 3)² = 169

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Here we have a program written in C++ language. Each // symbol is a relative comment explaining the reason for each command line (and is not included during the program execution).

The Program:

#include <iostream>

//c++ build in library

using namespace std;

//main code body starts here

int main()

{

 //declare variable to store phone numbers,its area code, prefix and line    number.

long pnumber;   //declare long variable

int ac, prefix, lnumber;

 //declare integer variables, where ac: Area Code and lnumber is the Line Number

cout<<"Enter a 10-digit Phone Number: "<<endl;

 //cout command prints on screen the desired message

 cin>>pnumber;

 //cin command enables the user to interact with the programm and enter information manually

//main body to obtain the desired output starts below

 //each 'division' is used to allocate the correct value at the correct

 //since prefix is used to get the desired output of ( )    -

 ac = pnumber/10000000;

 prefix = (pnumber/10000)%1000;

 lnumber = pnumber%10000;

 //main body ends here

 cout<<"Based on your 10-digit number"<<endl;

 cout<<"below you have (AreaCode), Prefix, and - line number "<<endl;

 cout<<"("<<ac<<")"<<""<<prefix<<"-"<<lnumber<<endl;

 //Prints on screen the desired output of the long 10 digit Number

 return 0; //ends program

}

-------------------------------------------------------------------------------------------------------

The Output Sample:

Enter a 10-digit Phone Number:

8019004673

Based on your 10-digit number

below you have (Area Code), Prefix, and - line number

(801) 900-4673

....Programm finished with exit code 0

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Answer:

Step-by-step explanation:

30/10x = 3x

Answer:

\(30\div10x\)

Step-by-step explanation:

Using x for the unknown number, "the quotient of thirty and ten times a number" is written as:

\(30\div10x\)

Answer:

\(-2x^2 + 8x - 8\)

Step-by-step explanation:

To make \(-4 - x^2 + 4x - 4 - x^2 + 4x\) into standard form, we want to combine like terms to get a simplified expression.

In standard form, the highest exponent term always comes first, which here is the \(x^2\) term.

\(-x^2 - x^2 = -2x^2\)

Next comes the b term (bx).

\(4x + 4x = 8x\)

Then comes the constant (c).

\(-4 - 4 = -8\)

So in total we have \(-2x^2 + 8x - 8\).

Hope this helped!

Answer:

\( \frac{2}{3} n - 11 \geqslant 17\)

\(n \geqslant 42\)

Explanation:

difference equals -

two-thirds equals 2/3

a number n equals variable of n

and 11 equals 11

at least equals _> (but like those together)

For solving equations just use photomath

The solution to the expression is n ≥ 42

An equation, statement of equality between two expressions consisting of variables and/or numbers

An equation is a mathematical expression that contains an equals symbol.

Equations often contain algebra.

Algebra is used in maths when you do not know the exact number in a calculation.

Translating the equation

\(\rm \dfrac{2}{3} \;n-11 \geq 17\)

\(\rm \;n \geq (17 + 11)\times\dfrac{3}{2}\\\\\\ n \geq 42\)

Therefore the solution to the expression is n ≥ 42

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Answer:

-2

Step-by-step explanation:

-2 is greater than -4 because on number line the numbers on the left of zero are negative numbers and the numbers which are very close to zero on left side are greater. So -2 is more close to zero than -4 . Hence answer will be

Nachelle needs to score 110 on Exam B in order to do equivalently well as she did on Exam A.

Given data: Nachelle earned a score of 725 on Exam A that had a mean of 700 and a standard deviation of 50.

She is about to take Exam B that has a mean of 100 and a standard deviation of 20.Let x be the score on Exam B that Nachelle needs to do equivalently well as she did on Exam A.

According to the Z-score formula, Z = (x - μ) / σ where Z is the standard score, x is the value of the element, μ is the population mean, and σ is the standard deviation.

Let's calculate the Z-scores for Nachelle's scores on Exams A and B.

Z-score for Nachelle's score on Exam AZ1 = (725 - 700) / 50 = 0.5

Z-score for Nachelle's score on Exam BZ2 = (x - 100) / 20 = (x - 100) / 20

Now, if Nachelle has to do equivalently well on Exam B as she did on Exam A, then the Z-scores for both exams should be equal.

Hence,0.5 = (x - 100) / 20Solving for x,x - 100 = 0.5 × 20 = 10x = 100 + 10 = 110.

Therefore, Nachelle needs to score 110 on Exam B in order to do equivalently well as she did on Exam A.

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Step-by-step explanation:5 times 2=10 but 6 times 2=12 not 15 so 5/6 is proportional to 10/12 not 10/15