How do I add the letters

AB = BA, the first pair of matrices does not satisfy \(AB \neq BA\).

AB = BA in general, even if A and B are both square. We say that A and B commute if AB = BA. We cannot argue that AB = AC provides B = C for a generic matrix A. (However, since A is invertible, we may multiply both sides of the equation AB = AC to the left by A1 to yield B = C.)

For matrices, A and B, the product AB is not necessarily equal to BA. In fact, matrix multiplication is not commutative in general. Therefore, we need to check each pair of matrices to see if their products are equal in order to determine which pair satisfies \($AB \neq BA$\).

\($$\begin{align*}AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 7 + 0 \cdot 3 & 1 \cdot 0 + 0 \cdot 4 \ 3 \cdot 7 - 2 \cdot 3 & 3 \cdot 0 - 2 \cdot 4\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}\)

\($$\begin{align*}BA &= \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \\\&= \left[\begin{array}{cc}7 \cdot 1 + 0 \cdot 3 & 7 \cdot 0 + 0 \cdot (-2) \ 3 \cdot 1 + 4 \cdot 3 & 3 \cdot 0 + 4 \cdot (-2)\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}\)

Since AB = BA, the first pair of matrices does not satisfy \(AB \neq BA\). We can proceed in the same manner to check the other pairs of matrices:

\($$\begin{align*}\\AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}8 & 0 \ 11 & -3\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 8 + 0 \cdot 11 & 1 \cdot 0 + 0 \cdot (-3) \ 3 \cdot 8 - 2 \cdot 11 & 3 \cdot 0 - 2 \cdot (-3)\end{array}\right] \\\&= \left[\begin{array}{cc}8 & 0 \ 2 & 6\end{array}\right]\end{align*}\)

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Answer:

D'G' = 52.5 units

Step-by-step explanation:

Since the dilatation is centred at the origin then multiply the original coordinates by the scale factor 3.5

D' = (1 × 3.5, 7 × 3.5 ) = (3.5, 24.5 )

G' = (- 8 × 3.5, - 5 × 3.5 ) = (- 28, - 17.5 )

Calculate D'G' using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = D' (3.5, 24.5) and (x₂, y₂ ) = G' (- 28, - 17.5)

D'G' = \(\sqrt{(-28-3.5)^2+(-17.5-24.5)^2}\)

       = \(\sqrt{(-31.5)^2+42^2}\)

       = \(\sqrt{992.25+1764}\)

        = \(\sqrt{2756.25}\)

         = 52.5 units

Answer:

What is the question?! I don't understand, sry?!

Step-by-step explanation:

Answer:

a 1,2.3,4,8,12 i think thats all

Answer:

24= 1, 2, 3, 4, 6, 8, 12 and 24.

c) is 12

Step-by-step explanation:

Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

The given categorical propositions and their forms are as follows:

(1) Some cats like turkey - Form: I:

Subject class: Cats,

Predicate class: Turkey

(2) There are burglars coming in the window - Form: E:

Subject class: Burglars,

Predicate class: Not coming in the window

(3) Everyone will be robbed - Form: A:

Subject class: Everyone,

Predicate class: Being robbed

In the first statement:

Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.

In the second statement:

There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.

In the third statement:

Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

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Answer:

True

Step-by-step explanation:

Answer: True

Step-by-step explanation:

We can plot the points (1,8), (2,6), (3,2), and (4,1) on a graph by using a coordinate plane and the x and y-coordinates of each point.

To plot these points, we will use a coordinate plane, which is a two-dimensional graph with an x-axis and a y-axis. The x-axis represents the horizontal position, and the y-axis represents the vertical position. We will use the x-coordinate to determine the horizontal position of the point and the y-coordinate to determine the vertical position of the point.

For the first point, (1,8), we will start at the origin of the graph, which is the point (0,0). We will then move 1 unit to the right along the x-axis and 8 units up along the y-axis to plot the point.

For the second point, (2,6), we will start again at the origin and move 2 units to the right along the x-axis and 6 units up along the y-axis to plot the point.

We will repeat this process for the remaining points, (3,2) and (4,1), to plot all four points on the graph. Once all four points are plotted, we can connect them with a line to visualize the pattern of the ball's bounces.

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Complete Question:

Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches.

The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1).

Plot the ordered points on the graph.

Answer:  The player runs 7 meters forward and then runs 7 meters in the opposite direction.

Step-by-step explanation:

Answer:

\( p = {8}^{7}\)

Step-by-step explanation:

\((8^9)p = 8^{16 } \\ \\ p = \frac{8^{16 } }{8^{9 } } \\ \\ p = {8}^{16 - 9} \\ \\ \huge \red{ \boxed{p = {8}^{7} }}\)

Answer:

are you lonly

Step-by-step explanation:

Answer:

vvv ahah hopefully it helps

Step-by-step explanation:

11.  pi is irrational number since you can't write it down as a non-infinite decimal

12. .5 is rational since its a terminating decimal

13. .3 repeating is rational b/c it's represented as a ratio of two integers

A vector space is an abstract mathematical concept that is used to describe a collection of elements, known as vectors.

Vector is a mathematical object that has both magnitude and direction. It can be represented graphically by a line segment with a starting point and an endpoint. Vectors are used in physics, engineering, and mathematics to represent physical quantities such as force, velocity, and acceleration. They can also be used to represent geometric figures such as lines, points, and planes. Vectors are important in many applications, such as navigation, graphics, and robotics.

It is an important concept in linear algebra, and is used to describe the behavior of linear equations and systems.

A vector space is made up of a set of vectors, which can be seen as elements of the space. Each vector is a combination of scalar numbers, called components, and the space is made up of all possible combinations of these components. The components can be real numbers, complex numbers, or even functions.

The vector space is defined by certain operations, called vector addition and scalar multiplication. Vector addition is the process of adding two vectors together, and scalar multiplication is a process of multiplying a vector by a scalar number. Using these operations, the vector space can be used to solve linear equations and systems of equations.

The vector space is also used to describe the geometry of the space. It is used to describe dimensions, angles, and distances between vectors. It is also used to describe shapes and objects within the space, and to describe how they interact with each other.

Finally, the vector space is used to represent linear transformations, which are important in physics and engineering. A linear transformation is a process of mapping a vector to another vector, and is used to describe the behavior of physical systems. This can be used to solve complicated equations and systems of equations.

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In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

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The width of the playground when the city is building a fence around a rectangular playground is 19 feet.

It should be noted that the perimeter of a rectangle is calculated as:

Perimeter = 2(length + width)

In this case, the city is building a fence around a rectangular playground. If the perimeter of the playground is 94 feet and the length of one side of the fence is 28 feet.

Perimeter = 2(length + width)

94 = 2(28 + width)

94 = 56 + 2w

Collect like terms

2w = 94 - 56

2w = 38

Divide

w = 38/2

w = 19

The width is 19 feet.

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Answer:

.......................

Step-by-step explanation:

a) x=14°

b) x=23°

the initial expression is:

Answer:

640\(\pi\)

Step-by-step explanation:

Answer:

640π

Step-by-step explanation:

The formula for a cone volume is

\(V = \pi r^{2} \frac{h}{3} \\\\V = \pi 8^{2} \frac{30}{3} \\\\V = \pi 64 * 10 \\\\V = 640\pi\)

The length and width of this rectangular picture frame are 99 inches and 24 inches respectively.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

Since the length of the rectangular picture frame is 3 inches more than the four times the width, we have:

L = 4W + 3

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

246 = 2L + 2W

246 = 2(4W + 3) + 2W

246 = 8W + 6 + 2W

246 = 10W + 6

W = 24 inches.

For the length, we have:

L = 4W + 3

L = 4(24) + 3

L = 99 inches.

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The slope of the any line parallel to the line y-5 = 25/2(x+4)  is equal and its value is 25 /2 .

We have given equation y-5 = 25/2(x+4) .

On simplifying , we get

      y - 5 = 25 x/2 +50

       y = 25 x /2 +55

On comparing the above equation with slope intercept form y = mx + b ,

we get m = 25 / 2

All the lines which are parallel to any other line have equal slope.

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Answer: 24/28

Step-by-step explanation:

Answer:  It A. 6 ÷ 3/5 is 10

Step-by-step explanation:

I wasnt sure how to do number line i just did it in my head but hope this helps!

Answer: 10

Step-by-step explanation:

3/5 ÷ 6/1= 3/30

to get 3/30 you do cross multiplication

30÷3=10

I hope this helps you let me know if it did!!

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

2×3=6

Have a nice day!

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Answer:

here you go! :))

n= 2

m=3

a= 10

q= 50

The solution for w in terms of x equation is w = -x/2 + 3.

Let's solve the equation :

8w - 8 = -4x + 16

To solve for either variable,  start by isolating one of them. Let's isolate w:

8w = -4x + 16 + 8

8w = -4x + 24

Now, divide both sides of the equation by 8 to solve for w:

w = (-4x + 24) / 8

w = -x/2 + 3

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Answer:

\(\mathsf {\frac{17}{10}}\)

Step-by-step explanation:

\(\mathsf {2\frac{2}{3} + \frac{14}{5} + ? = \frac{43}{6} }\)

\(\mathsf {\frac{8}{3} + \frac{14}{5} + ? = \frac{43}{6} }\)

Take the LCM (common denominator) to be 30.

\(\mathsf {\frac{80}{30} + \frac{84}{30} + ? = \frac{215}{30} }\)

Bring the known values to the RHS.

\(\mathsf {? = \frac{215}{30} - \frac{164}{30} }\)

\(\mathsf {? = \frac{51}{30}}\)

\(\implies \mathsf {\frac{17}{10}}\)

Let that be x

Now

\(\\ \rm\rightarrowtail \dfrac{8}{3}+\dfrac{14}{5}+x=\dfrac{43}{6}\)

\(\\ \rm\rightarrowtail \dfrac{40+42}{15}+x=\dfrac{43}{6}\)

\(\\ \rm\rightarrowtail \dfrac{82}{15}+x=\dfrac{43}{6}\)

\(\\ \rm\rightarrowtail x=\dfrac{43}{6}-\dfrac{82}{15}\)

\(\\ \rm\rightarrowtail x=\dfrac{215-164}{30}\)

\(\\ \rm\rightarrowtail x=\dfrac{51}{30}\)

\(\\ \rm\rightarrowtail x=\dfrac{17}{10}\)

\(\\ \rm\rightarrowtail x=1\dfrac{7}{10}\)

Answer:

Below

Step-by-step explanation:

Divide 3 into all of the coefficients

16         +       12         -  9           now divide 'w' into the variables

16 w^2   + 12  w   - 9      Done.

Answer: C

Step-by-step explanation: