Mathematics High School

find the standard matrix.
8. T: {R}^{2} → {R}^{2} first reflects points through the vertical x_{2} -axis and then reflects points through the line x_{2}=x_{1} .

Answers

Answer 1

The standard matrix for the transformation T, which reflects points through the vertical x2-axis and then reflects points through the line x2=x1, is:

[1 0]

[0 -1]

To find the standard matrix for the given transformation, we need to determine the images of the standard basis vectors in {R}^2 under the transformation T. The standard basis vectors in {R}^2 are:

e1 = [1 0]

e2 = [0 1]

First, we apply the reflection through the vertical x2-axis. This reflects the x-coordinate of a point, while keeping the y-coordinate unchanged. The image of e1 under this reflection is [1 0], and the image of e2 is [0 -1]. Next, we apply the reflection through the line x2=x1. This reflects the coordinates across the line.

The image of [1 0] under this reflection is [0 1], and the image of [0 -1] is [-1 0]. Therefore, the standard matrix for the given transformation T is obtained by arranging the images of the standard basis vectors as columns:

[1 0]

[0 -1]

This matrix represents the linear transformation that reflects points through the vertical x2-axis and then reflects them through the line x2=x1.

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Related Questions

Dilate ABC with A(-8, -4),
B(-4, 8) and C(2, 2) with a scale
factor of 2. What are the
coordinates of A', B' and c'?

Answers

Answer:

A' (-16, -8), B' (-8, 16), C' (4, 4)

Step-by-step explanation:

Because it is dilated by a scale factor of 2, you just multiply everything by 2.

Help im stuck on this problem

Help im stuck on this problem

Answers

Answer:

J.

\({ \bf{m \angle A}} = { \bf{180 \degree -48 \degree }} \\ { \tt{m \angle A = 132 \degree}}\)

a football team lost the same number of yards on each of three consecutive plays what is the total change in yards from where the team started

Answers

Answer:

-3x, where x is the number of yards lost on the first play.

Step-by-step explanation:

TUESDAY
SOLVE FOR X
8X5°
55°
(S.x - 25)
3x + 8°
X=

TUESDAYSOLVE FOR X8X555(S.x - 25)3x + 8X=

Answers

right angle x = 7 line x = 30

What does x equal in this question? 5 = -x/18

Answers

answer:

it equals 90

Step-by-step explanation:

1 = 18/18  to get 5 mulitply 18 x 5 = 90

so 5=90/18

Find the Volume of the Pyramid. Show your work.

Find the Volume of the Pyramid. Show your work.

Answers

Answer:

I think it's 62. volume is basically just adding the length, width, and height

The sum of two numbers is twenty-four. Four less than three times the
smaller is twelve less than twice the larger. Find the
two numbers.

can you please give me the equation for this tyyyy

Answers

With the help of two variable equations, the two numbers are 8 and 16.

How to solve the system of equations?

There are three ways to solve equations-

1. Substitution method

2. Elimination method

3. Graphing method.

Now, let the number be x and y.

Therefore, the sum of two numbers is twenty-four,  x+y= 24

Now, given that,

3x-4=2y-12

3x-2y=-8

2y-3x=8

Now, substituting the value of y in the equation

2(24-x)-3x=8

40=5x

x=8

Therefore, the two numbers are 8 and 16.

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Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?

Which ordered pair can be plotted together with these four points, so that the resulting graph still

Answers

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

Which ordered pair can be plotted together?

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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8) The sum of nine times a number and 13 is equal to seven times the number,

Answers

Answer:

-7.5=x

Step-by-step explanation:

9x+13=7x

13=-2x

-7.5=x

9x+13=7x
First, Subtract 9x on both sides to give you 13=-2x
Then divide -2 on both sides to give you -6.5

Consider the relation schema R(A,B,C,D,E) with the following functional dependencies F= {A->B, C->B, D->ABC, AC->D, D->E} Compute the candidate key for the given relation Compute the minimal cover of F.

Answers

The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

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What type of function is represented by the following graph?

What type of function is represented by the following graph?

Answers

Answer:

C. Absolute value is the answer

−9(4 − 3j)

A. 36 − 27j
B. 36 + 27j
C. −36 + 27j
D. 36 + j

Answers

Answer:

C

Step-by-step explanation:

-9×4

= -36

...

-9 × -3j = 27j

THEREFORE...

-36+27j

23.A chef ordered 400 pounds of potatoes in same-sized bags. Which expressions show
the number of bags and number of pounds of potatoes per bag the chef may have
ordered? Choose all that apply.
E 50 x 80
80 x 5
B 10 x 40
0 20 x 20
© 20 x 20

23.A chef ordered 400 pounds of potatoes in same-sized bags. Which expressions showthe number of bags

Answers

Answer:

10*40

80*5

20*20

Step-by-step explanation:

20*20=400

80*5=400

10*40=400

When should an accountant begin professional networking?
A. As soon as they decide to enter the profession
B. Once they start working in the field
C. After they finish their degrees
D. When they begin looking for a job

Answers

A is the right answer !!

Events A and B are independent.

P(A) = 0.48
P(A and B) = 0.3024
What is the probability of event B?

Answers

Answer:

A

Step-by-step explanation:

I think it's P(A)=0

In a kickball game, a ball is kicked and travels along a parabolic path. The height h, in feet, of the kickball t seconds after the kick can be modeled by the equation h(t) = −16 t2 + 24t .

a. A fielder runs a route that will allow him to catch the kickball at about 3 ft above the ground. Write an equation that can be used to find when the fielder will catch the ball.
b. Use graphing technology to find out how long the kickball has been in the air when the fielder catches it on its descent. Round to the nearest hundredth.

Answers

Answer:

(a) h(t) = 3

(b) time = 1.36 seconds

Explanation:

equation: h(t) = -16(t)² + 24t

Part A

If the fielder catches the ball at the height of about 3 ft.

equation: h(t) = 3

Part B

using graphing technology, graphed below. (height, y = 3)

Additional *solving part B algebraically*

-16(t)² + 24t = 3

-16(t)² + 24t - 3 = 0

using quadratic equation

\(\bold{x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ when \ ax^2 + bx + c = 0}\)

==================================

\(\sf t_{1,\:2}=\frac{-24\pm \sqrt{24^2-4\left(-16\right)\left(-3\right)}}{2\left(-16\right)}\)

\(\sf t=\frac{3-\sqrt{6}}{4}, \ t=\frac{3+\sqrt{6}}{4}\)

t = 1.36 seconds   and     0.14 seconds

The fielder shall catch the ball when the ball is falling, so time : 1.36 s

In a kickball game, a ball is kicked and travels along a parabolic path. The height h, in feet, of the

Answer:

See below ~

Step-by-step explanation:

a. Equation

In place of h(t), substitute 3 in its place3 = -16t² + 24tRearrange by bringing 3 to the other side-16t² + 24t - 3 = 0

b. Finding the duration of the kickball in air using graphing technology

Based on the graph (attached), the ball has been in the air for :1.5 seconds

In a kickball game, a ball is kicked and travels along a parabolic path. The height h, in feet, of the

What is the solution to in (x^2 - 16) = 0?
x ± square root of 17.
x = ±4.
x = ± square root of 32.

Answers

Answer:

x=+or-4...…............

Answer:

A

Step-by-step explanation:

got it right

Solving by Completing the Square
2x^2 - 2 - 3x = 0

Answers

Step-by-step explanation:

sorry..if it is wrong..I tried...........

Solving by Completing the Square2x^2 - 2 - 3x = 0

If you borrow $5.93 for nine years at an interest rate of 6%, how much interest will you pay? In terms of simple interest.

Answers

Answer: $3.20

Step-by-step explanation:

SI = p *r * t

= 5.93 * 0.06 * 9

= 3.20

Answer:

$3.20

Step-by-step explanation:

Using Simple Interest = (principal) * (rate) * (time), we get:

= 5.93 * 0.06 * 9

= $3.20

Hope this helps!

How many fl oz makes a liter?

Answers

33.814 fl oz make a liter

There are 33.814 fluid ounces in a liter, in unit of measurement.

What is unit of measurement?

A unit of measurement is a predetermined, acknowledged by law, and frequently used magnitude of a quantity that acts as a standard for evaluating other quantities of the same kind. A multiple of the measurement unit can be used to express any additional quantity of that type.

An example of a physical quantity is length. The word "metre" is a measurement that stands in for a particular, predetermined length, and it begins with the letter "M." A length is 10 times the precise, predetermined length known as "metre" when the term "10 metres" is used (or 10 m).

Human endeavour has relied on the definition, acceptance, and practical application of units of measurement from antiquity to the present.

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A
116°
27°
.Y
37°
Z
A. AZ
B. ZY
C. AY
D. ZW

A11627.Y37ZA. AZB. ZYC. AYD. ZW

Answers

Answer:

B.  ZY

Step-by-step explanation:

The longest side of any triangle will always correlate with the largest angle. Since m∠A = 116° and is biggest, the corresponding side ZY would be the largest side.

I would REALLY appreciate some help... :(
Evaluate the expressions 7-9

I would REALLY appreciate some help... :( Evaluate the expressions 7-9

Answers

Answer:

7. 64

8. -100000

9. 729

Step-by-step explanation:

Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options.

Answers

Answer:

6 feet by 5 feet by 4 feet

7 feet by 6 feet by 4 feet

Step-by-step explanation:

The surface are of rectangular prism = 140 ft²

Surface area of rectangular prism is given by :

A = 2(lw + lh + wh)

Using trial by error method :

6 feet by 2 feet by 3 feet

A = 2(6*2 + 6*3 + 2*3) = 72ft²

6 feet by 5 feet by 4 feet

A = 2(6*5 + 6*4 + 5*4) = 148 ft²

7 feet by 6 feet by 4 feet

A = 2(7*6 + 7*4 + 6*4) = 188ft²

8 feet by 4 feet by 3 feet

A = 2(8*4 + 8*3 + 4*3) = 136ft²

Your uncle wants to create a dog small enough to fit into a purse. Of the hundreds of dogs on his farm, he breeds only the smallest 10% of them. He then breeds only the smallest 10% of their offspring, and continues to breed only the smallest 10% of each generation. Over 20 years, he observes that his group of dogs did become smaller (though not small enough to fit into a purse). Which line of support does he have that his dogs have evolved?.

Answers

A kind of evolution through artificial selection is the practice of choosing creatures with desired features over several generations.

The mix of alleles found in an organism is known as its genotype. A phenotype is also the culmination of all the organism's discernible traits. In artificial selection, people choose animals or plants with favored phenotypic features for reproduction.

Since the phenotype is impacted by the genotype, the process of artificial selection alters allele frequencies throughout generations, resulting in the evolution of desirable features in offspring.

In conclusion, a kind of evolution through artificial selection is the practice of selecting creatures with desired qualities over several generations.

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Can anybody help!!!??? Pls

Can anybody help!!!??? Pls

Answers

Answer:

thanks for the points x

Step-by-step explanation:

thanks

help xxx
23421 x 230 = ? im not allowed to use a calc on this

Answers

Answer:

5,386,830

Step-by-step explanation:

The perimeter of a rectangle is $98,$ and the length of one of its diagonals is $41.$ Find the area of the rectangle.

Answers

Answer:

\(328units^2\)

Step-by-step explanation:

First off,  I do want to say that you could word this more easily.

98 is the perimeter. length is 41. width is 8.

the area is length*width for rectangles.

98-41=57

57-41=16

16/2=8

8*41=328 units^2

23. Graph the inequality x≤ 8.

Answers

The graph of the inequality is added as an attachment

How to determine the graph

From the question, we have the following parameters that can be used in our computation:

x≤ 8

The above expression is an inequality that implies that

The value of x does not exceed 8

Next, we plot the graph

See attachment for the graph of the inequality

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23. Graph the inequality x 8.

can anyone help me solve this?

can anyone help me solve this?

Answers

Step-by-step explanation:

a triangle,=180

so 68+35-180=77

then 77+68=145

What do variables and function have in common

Answers

A function is a mathematical relationship in which the values of a single dependent variable are determined by the values of one or more independent variables. Function means the dependent variable is determined by the independent variable(s)
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