6.5 practice the measure of the exterior of a triangle is equal to the sum of the remote interior angles?

Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.

To show that multiplication in M_n(R) is not commutative when n > 1, we need to find two matrices A and B in M_n(R) such that AB is not equal to BA.

Let's consider two matrices A and B in M_n(R) such that:

That is, A is the n x n identity matrix, and B is the matrix with 1's on the anti-diagonal and 0's elsewhere.

Now let's compute AB and BA:

AB = [c_ij], where c_ij = Σ_k=1^n a_ik * b_kj

If i+j = n+1, then b_kj = 1 only if k = i, and a_ik = 1 only if k = j.

Therefore,

c_ij = a_i1 * b_1j + a_i2 * b_2j + ... + a_in * b_nj = a_ii * b_jj = 1 * 1 = 1

If i+j ≠ n+1, then b_kj = 0 for all k, and hence c_ij = 0.

Therefore, AB is the matrix with 1's on the anti-diagonal and 0's elsewhere, just like B.

Now let's compute BA:

BA = [d_ij], where d_ij = Σ_k=1^n b_ik * a_kj

If i=j, then a_kj = 1 only if k = i, and b_ik = 1 only if k = i. Therefore,

d_ij = b_i1 * a_1j + b_i2 * a_2j + ... + b_in * a_nj = b_ii * a_jj = 1 * 1 = 1

If i ≠ j, then a_kj = 0 for all k, and hence d_ij = 0.

Therefore, BA is the matrix with 1's on the diagonal and 0's elsewhere, just like A.

Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.

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The inequality that represent how many laps she can do is "number of laps < 8.4".

Claire can jog a maximum of 8 laps in 42 minutes.

Since Claire can jog one lap in 5 minutes, we can use division to find how many laps she can complete in 42 minutes:

= 42 minutes / 5 minutes per lap

= 8.4 laps

However, since Claire cannot jog a fractional number of laps, we need to round down to the nearest whole number of laps. This is because she will have only completed a fraction of a lap by the time she reaches the end of the 42 minutes, and we want to know how many whole laps she completes. Therefore, we can write the inequality as "number of laps < 8.4".

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The translation rule for these circles is (x+2),(y+3).

This translation involves shifting the points of the original figure without rotating or reflecting it.

In the given transformation, circle A has been transformed to circle B.

Thus, the transformation rule is the x and y-coordinates of the points of the original figure added with certain values to obtain the coordinates of the points in the transformed figure.

In the given case, the x-coordinates of all the points of the circle A have been increased by 2 units, while the y-coordinates of all the points of the circle A have been increased by 3 units.

Thus, the translation rule for these circles is (x+2),(y+3).

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The slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.

The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).

The slοpe οf the graph οf Pt is the rate οf change οf the pοpulatiοn with respect tο time.

Specifically, it tells us hοw much the pοpulatiοn is changing fοr every unit change in time.

Since t represents the number οf years since 1975, the slοpe οf Pt can be interpreted as the annual rate οf change in pοpulatiοn. Fοr example, if the slοpe οf Pt is 100, then the pοpulatiοn is increasing by 100 peοple per year.

Therefοre, the slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.

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I think that the answer is 40 degreee

The required measure of section x on the circle is 95°.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.

Here,
From the given we have,
a = 40,
c = x
b = 15

Now, put this value in the given formula,
a = c-b / 2

So,
40 = x - 15/2
x -15 = 80
x = 95°

Thus, the required measure of section x on the circle is 95°.

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Answer:

Opposite, addition, division, inverse

Step-by-step explanation:

The answer of the given question is (3) the length of the run of the Mighty Drop ski slope is approximately 181.8 feet. (4) the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.

A slope typically refers to the angle of an incline or ramp, or the ratio of vertical change to horizontal change of a straight line or curve on a graph. For an incline or ramp, the slope is the angle between the surface and the horizontal plane. It is defined as the ratio of the vertical rise to the horizontal run of the ramp.

In the context of a graph, slope refers to the steepness of a line or curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve. The slope of a line can be positive (if the line goes up from left to right), negative (if the line goes down from left to right), or zero (if the line is horizontal).

(3) . To solve for the length of the run of the Mighty Drop ski slope, we can use the trigonometric function tangent, which relates angle of elevation to ratio of opposite and adjacent sides of right triangle.

Let x be the length of the run. Then we have:

tangent(75°) = opposite/adjacent

tangent(75°) = 800/x

Solving for x, we get:

x = 800 / tangent(75°)

x ≈ 181.8 feet

Therefore, the length of the run of the Mighty Drop ski slope is approximately 181.8 feet.

(4) . To solve for the angle of elevation when little Judy looks at her red balloon, we can use the trigonometric function arctangent.

Let θ be the angle of elevation. Then we have:

tangent(θ) = opposite/adjacent

tangent(θ) = 2240/350

Taking the arctangent on  both sides, we will get:

θ = arctangent(2240/350)

θ ≈ 82.7°

Therefore, the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.

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Answer:

Step-by-step explanation:

we would cut it into small pieces and find their area,

Add three segments:

This will give us the following shapes:

You may find each area and add up to get the total area.

a. The probability that a real number between 3 and 5 is picked is

b. The probability that a real number between 3 and 7 is picked is

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space / total outcome

The sample space is the area between the real numbers and the total outcome is the total area

Total area = 0.12 + 0.56+ 0.32

= 1

a. The probability a real number between 3 and 5 is picked = 0.56/1

= 0.56

b. The probability a real number between 3 and 7 is picked is( 0.56+0.32)/1

= 0.88

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The similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°

The triangles RDS and ADB area similar thus the lines AB and RS are parallel to each other and the adjacent angles of m∠SRA and m∠BAR are supplementary, so their sum is equal to 180°.

m∠SRA and m∠BAR are supplementary so;

(6x + 8)° + (9x + 7)° = 180°

15x + 15 = 180°

15x = 180° - 15 {subtract 15 from both sides}

15x = 165

x = 165/15 {divide through by 15}

x = 11

m∠A = 9(11) + 7 = 106°

m∠R = 6(11) + 8 = 74°

m∠S = 4(11) + 14 = 58°

Therefore, the similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°

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Possible question:

Find the measure of the angles with the variable x for the similar triangles ∆RDS and ∆ADB.

Answer: The slope of y = -4 is 0.

Step-by-step explanation:

If the function is increasing to the left and falls to the right,

Leading coefficient of the function will be negative and the degree of the function will be Odd.

What is a polynomial's leading coefficient?

The term in a polynomial that has the highest power of x is the leading term. For instance, the leading term in the equation 7+x3x2 is 3x2. The coefficient of the first term is referred to as a polynomial's leading coefficient. The leading coefficient in the aforementioned example is 3.

Leading coefficient of the function will be negative and the degree of the function will be Odd.

Similarly, if the function is increasing to the right and falls to the left,

Leading coefficient of the function will be positive and the degree of the function will be Odd.

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Step-by-step explanation:

solving equipment step:

*SIMPLIFY THE EXPRESSION

- 12x² ÷(2x²²)

Rewrite

simply the equation

=12x² ÷ 2x²²

=-6x²÷x²²

Now cancel common factors

=-6x÷x^20

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Answer:

  A.  (2, 1)

Step-by-step explanation:

You want the solution to the system of equations represented by the given table and graph.

When we are given two functions and asked for "the solution to the system", we generally mean the value of x that satisfies f(x) = g(x). That will be represented on a graph as the point (x, f(x)), or (x, g(x)), where the function graphs intersect.

When you're looking for the solution in a table, you look for the row of the table where the value of f(x) is the same as the value of g(x). For the given table, we see that f(x) = g(x) = 1 on the last row of the table, where x=2. This means the solution is ...

  (x, f(x)) = (2, 1)

the solutions for a are:

a = n×π, π/4, or 7π/4, where n is any integer.

An integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.

tan²(a) - csc²(a) + 1 = 0

tan²(a) - (1/sin²(a)) + 1 = 0

(tan²(a)sin²(a) - 1 + sin²(a))/sin²(a) = 0

Simplifying the numerator:

(tan²(a) - 1)sin²(a) = 0

Using the identity tan^2(a) = sec²(a) - 1:

(sec²(a) - 2)sin²(a) = 0

Expanding and simplifying:

sec²(a)sin²(a) - 2sin²(a) = 0

sin²(a)(sec^2(a) - 2) = 0

So either sin²(a) = 0 or sec²(a) - 2 = 0.

If sin²(a) = 0, then a is an integer multiple of pi (i.e., a = n×π for some integer n).

If sec²(a) - 2 = 0, then sec²(a) = 2,

cos(a) = ±√(2)/2

So a can be π/4 or 7π/4.

Therefore, the solutions for a are:

a = n×π, π/4, or 7π/4, where n is any integer.

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Answer: Let's first calculate the number of users after one year:

Number of users after one year = 16 lakh + 50% of 16 lakh

= 16 lakh + 8 lakh

= 24 lakh

Now, we can calculate the number of users after two years by applying the same growth rate:

Number of users after two years = 24 lakh + 50% of 24 lakh

= 24 lakh + 12 lakh

= 36 lakh

Therefore, two years from now, it is expected that 36 lakh (3.6 million) students in India will be using Khan Academy.

Step-by-step explanation:

Answer:

36 Iakh Students

Step-by-step explanation:

Answer:

Fire animals = 36 * 1/4 = 9

Water animals = 36 * 1/6 = 6

Grass animals = 36 - (9 + 6) = 21

There are 21 - 9 = 12 more grass animals than fire animals

Step-by-step explanation:

colinear with P means they are in the same line as P.

that is K and N.

2 planes with J :

JKL (the ceiling) and JOKPN (the wall with J).

all the points that are in more than one plane : all of them, as they are all on an edge.

The solution to the system of equations is given as follows:

(1,9).

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The point of intersection on the graph means that the two functions have the same numeric value, hence on a table we must identify the point which the functions have the same numeric value.

From the table, function f(x) and g(x) both contain the point (1,9), hence this is the point of intersection of the two lines, and the solution is given as follows:

(1,9).

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In respοnse tο the given questiοn, we can state that This signifies that 3 equatiοn οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.

A algebraic equatiοn is a technique that links twο statements and utilises the equals sign (=) tο express equivalence. In algebra, an equatiοn refers tο the mathematical statement that prοves the equality οf twο fοrmulas. Fοr example, in the cοmputatiοn 3x + 5 = 14, a nοrmalise inserts a gap between the numbers 3x + 5 and 14. A mathematical fοrmula may be used tο explain the link between the twο phrases written οn either side οf a letter. The emblem and the prοgramme are usually the same. Fοr example, 2x - 4 equals 2.

Tο cοmpute prοpοrtiοns in arithmetic, yοu must first create a ratiο οf twο related numbers. Fοr example, if yοu want tο knοw what percentage οf all apples sοld were red, yοu wοuld put up a ratiο οf the number οf red apples sοld tο the οverall number οf apples sοld.

Assume that 200 apples were sοld in tοtal, with 60 οf them being red. Tο get the prοpοrtiοn οf red apples, use the fοllοwing fοrmula:

60 / 200 = red apples / tοtal apples

3/10 = red apples / tοtal apples

This signifies that 3 οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.

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Complete question:

Assume that 200 apples were sοld in tοtal, with 60 οf them being red.

What is proportion of red apples?

This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.

Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.

Here,

When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.

According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.

Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.

In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.

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The height οf the triangle is 15 inches. The diagram is attached belοw.

An isοsceles triangle therefοre has bοth twο equal sides and twο equal angles. The Greek wοrds isο (same) and skelοs are the sοurce οf the name. An equilateral triangle is οne with all three sides equal, and a scalene triangle is οne with nο equal sides.

Given that the length οf the base is 40 inches. The length οf equal sides is 25 inches.

The altitude οf an isοsceles triangle bisects the base.

The length οf BD = DC = 20 inches.

△ABD fοrms a right-angle triangle since AD is perpendicular tο BC.

Tο find the height apply Pythagοrean theοrem.

The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.

Cοnsider △ABD:

AB² = BD² + AD²

25² = 20² +AD²

625 = 400 +AD²

AD² = 625 - 400

AD² = 225

Take square rοοt οn bοth sides:

AD = 15

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The beetle crawled 1/15 of a yard farther than the spider.

What is the fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing a numerator(upper value) and denominator(lower value).

To find out how much farther the beetle crawled than the spider, we need to subtract the distance the spider crawled from the distance the beetle crawled.

The beetle crawled 2/3 of a yard, which can be written as a fraction with a common denominator of 15: 10/15.

The spider crawled 3/5 of a yard, which can also be written as a fraction with a common denominator of 15: 9/15.

Now we can subtract the distance the spider crawled from the distance the beetle crawled:

10/15 - 9/15 = 1/15

Hence, the beetle crawled 1/15 of a yard farther than the spider.

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The survey design that we have here is not an acceptable standard survey design for research.

This survey design has limitations and may not be the most optimal way to measure student interest in classroom topics. Here are some of the reasons why:

Limited response options: By only allowing four responses, the survey restricts the range of possible responses that students can give. For instance, some students may feel that a topic is somewhat interesting, but not interesting enough to warrant a score of 6. Similarly, some students may feel that a topic is not worth studying, but not to the extreme level of giving it a score of 1. This design does not account for such nuances in student opinions.

Lack of neutral option: The survey does not include a neutral option such as "no opinion" or "undecided". This means that students who do not have a strong opinion about a topic may be forced to pick a score that does not accurately reflect their level of interest.

Lack of context: The survey does not provide any context or information about the topics being evaluated. Without such information, students may base their scores on assumptions or incomplete knowledge about the topics, which may not accurately reflect their actual level of interest.

Lack of reliability and validity: The survey's reliability and validity may be questionable. The limited response options and lack of context may lead to responses that are not reliable or valid measures of student interest.

In conclusion, while this survey design may be simple and easy to administer, it has limitations that make it less than ideal for measuring student interest in classroom topics. A more comprehensive survey design that includes a wider range of response options and provides contextual information about the topics may provide more reliable and valid results.

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Based on the readings from the graph, the sequence has a next term of the 16

The missing information is attached

The readings on the graph can be represented as

1, 2, 4, 8, .....

We can see that multiplying 2 to the previous term to gives the next term

Using the above parameters, we have the following equation

Next term = 2 * Current term

The current term in the graph is 8

So, we have

Next term = 2 * 8

Evaluate

Next term = 16

Hence, the next term is 16

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Answer:

x = 9

Step-by-step explanation:

An equation for a vertical line is in the form:

x = anumber

The given information is the point (9,-10) this is in the form (x,y). So this gives us the information that x is 9. That is the equation!

x = 9

The equation of the vertical line through (9,-10) is

x = 9

Answer: C. (f+ g)(x) = 5x + 6

Step-by-step explanation:

C. (f+ g)(x) = 5x + 6

This is because when you add two functions together, you simply add their coefficients together and add the constants together. So, in this case, you add 3 and 2 to get 5 and add 10 and -4 to get 6. Therefore, the answer is 5x + 6.

Answer:

The correct answer is C. (f+ g)(x) = 5x + 6

Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to equation two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

The received power at a distance d is determined by:

Pr is equal to Pt, Gt, Gr, and (/4d)2.

where:

The transmitted power is Pt.

The transmitter antenna gain is Gt.

the receiver antenna gain, or Gr.

is the signal's wavelength.

Pr2 = (d1/d2)4 * Pr1

where:

At a distance of 325 m, Pr1 is the received power, which is specified as 25 W.

d1 is 325 metros away, while d2 is 1.3 kilometres away (i.e., 1300 m)

Inputting the values provided yields:

Pr2 = 25 W * (325/1300 m)4 = 25 W * 0.0625 = 1.5625 W

Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.

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