what is the area of the scalene triangle shown (ABC), if AO=10cm,
CO=2cm, BC=5cm, and AB=12.20? (Triangle AOB is a right
triangle.)

Answers

Answer 1

Area of scalene triangle can be found using formula for area of triangle,is given by half product of base and height.Area of triangle ABC = Area of triangle AOB - Area of triangle BOC = 10 cm² - 12.20 cm² = -2.20 cm².

a) To find the area of triangle AOB, we can use the formula: Area = (1/2) * base * height. Substituting the values, we get: Area = (1/2) * 10 cm * 2 cm = 10 cm².

 

b) Now, to find the area of the scalene triangle ABC, we can subtract the area of triangle AOB from the area of triangle ABC. Given that AB = 12.20 cm and BC = 5 cm, we can find the area of triangle ABC by subtracting the area of triangle AOB from the area of triangle ABC.

Area of triangle ABC = Area of triangle AOB - Area of triangle BOC = 10 cm² - 12.20 cm² = -2.20 cm². Since the resulting area is negative, it indicates that there might be an error in the given values or construction of the triangle. Please double-check the measurements and information provided to ensure accurate calculations.

To learn more about scalene triangle click here : brainly.com/question/10651823

#SPJ11


Related Questions

how many 64kg to lbs

Answers

64 kilograms is equal to approximately 141 pounds. Kilograms and pounds are units of measurement for weight, with kilograms being part of the metric system and pounds part of the imperial system.

64 kilograms is a unit of weight that is part of the metric system. This unit of measurement is widely used around the world, particularly in scientific and medical applications. To convert kilograms to pounds, you can multiply the number of kilograms by 2.20462 which is conversion factor.

In this case, 64 kilograms is equal to approximately 141 pounds. Pounds, on the other hand, are part of the imperial system of units and are widely used in countries such as the United States. When converting between units of measurement, it is important to be precise and accurate to ensure that you obtain accurate results.

In many cases, you can use conversion tools such as calculators or charts to convert between units of measurement. However, it is also important to understand the basic conversion formulas so that you can perform the calculations manually if necessary.

To know more about conversion factor on the link below:

brainly.com/question/30166433#

#SPJ11

Part of the population of 6,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 9 of them are infected. How many elk are likely to be infected?

Answers

When the sample is given, the number of elk are likely to be infected is to be considered as the 1,215.

Calculation of the number of elk:

Since the population is 6,750.

The random sample is 50.

So here be like

\(6750\) ÷ \(50\) × \(9\)

= 1,215

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 1,215.

Learn more about sample here: https://brainly.com/question/24292263

Some cats have bobtails, which are short, stumpy tails that result from an inherited, recessive genotype (tt). Normal length tails are dominant in cats (TT, Tt). When a cat with a bobtail is crossed with a cat that is heterozygous for normal tail length, what is the likelihood that the offspring will have a bobtail?

75%
50%
25%
0%

I will give brainliest

Answers

Answer:

50%

Step-by-step explanation:

took the test and got it right

Answer:

Im sorry my post was removed, darn mods. it is 50%!

Step-by-step explanation:

I took the test a while ago and searched the same question, when i finished the quiz it said i was right! :)

HELP ME PLEASE SHOW THE WORK CORRECT ANSWER GETS BRAINLIEST

HELP ME PLEASE SHOW THE WORK CORRECT ANSWER GETS BRAINLIEST

Answers

The area of the polygon composed of rectangles and triangle is 405.5 ft²

What is area?

Area is the amount of space occupied by a two dimensional shape or object.

For the first rectangle:

length = 9 ft, width = 5 ft

Area of first rectangle = length * width = 9 ft * 5 ft = 45 ft²

For the second rectangle:

Length = 13 ft, width = (13 + 5) = 18 ft

Area of second rectangle = 13 ft * 18 ft = 234 ft²

For the triangle:

Base = (13 + 9) = 22 ft, height = 29.5 - 13 - 5 = 11.5 ft

Area of triangle = (1/2) * base * height = 0.5 * 22 * 11.5 = 126.5 ft²

Area of polygon = 45 + 234 + 126.5 = 405.5 ft²

The area of the polygon is 405.5 ft²

Find out more on area at: https://brainly.com/question/2972832

#SPJ1

Write 23/9 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Answers

Answer:

2.55555556

Step-by-step explanation:

Solve the inequality 9x + 5 < 77.

Answers

Answer:

x=8

Step-by-step explanation:

If X=8 then 9(8)+5=77

9x8= 72

72+5=77

77=77

Hope this helps

X=a so that should be the right one I did it on scratch paper

A ball is thrown straight up from the top of a 128 foot tall building with an initial speed of 32 feet per second. the height of the ball as a function of time can be modeled by the function below. how long will it take for the ball to hit the ground?

Answers

The time it will take for the ball to hit the ground can be found by solving the quadratic equation \(-16t^2 + 32t + 128 = 0\). One of the solutions will represent the time when the ball hits the ground.

The height of the ball as a function of time can be represented by an equation that considers the initial height, initial speed, and the effects of gravity. The equation takes the form of h(t) = \(-16t^2 + v0t + h0\), where h(t) represents the height at time t, v0 is the initial speed, h0 is the initial height, and -16t^2 represents the effect of gravity.

In this case, the initial height of the ball is 128 feet, the initial speed is 32 feet per second, and we want to find the time it takes for the ball to hit the ground (when the height is 0). We can set h(t) = 0 and solve the equation \(-16t^2 + 32t + 128 = 0\) for t.

By solving the quadratic equation, we can find the two possible values for t. One of the values will represent the time when the ball was thrown up, and the other value will represent the time when the ball hits the ground. We discard the negative value and consider the positive value as the time it takes for the ball to hit the ground.

Learn more about function here:

https://brainly.com/question/28278699

#SPJ11

Answer:

 It will take 4 seconds for the ball to hit the ground.

Step-by-step explanation:

I want to uderstand how to solve this
polynomial ƒ(X) = X³+X²-36 that arose in the castle problem Consider the in Chapter 2. (i) Show that 3 is a root of f(X)and find the other two roots as roots of the quadratic f(X)/(X − 3). (ii) U

Answers

3 is one of the roots of the given polynomial. The other 2 roots being -2 + 2i√2 and -2 - 2i√2.

We need to find its roots.  Step 1: Find out if 3 is a root of ƒ(X). If 3 is a root of ƒ(X), then ƒ(3) = 0. Let's see if 3 is a root of ƒ(X). ƒ(3) = (3)³ + (3)² - 36= 27 + 9 - 36= 0. Therefore, 3 is a root of ƒ(X).

Step 2: Find the other two roots. Let us perform the synthetic division with the root (X - 3) on the polynomial ƒ(X). By synthetic division, we get the quotient of ƒ(X)/(X - 3) to be X² + 4X + 12, which is a quadratic equation. We can solve this using the quadratic formula. The quadratic formula is, X = [-b ± sqrt(b² - 4ac)] / 2a. Let's substitute the values for a, b, and c from the quadratic equation we got above, which is, X² + 4X + 12= 0 a = 1, b = 4 and c = 12. Using the quadratic formula, X = [-4 ± sqrt(4² - 4(1)(12))] / 2*1 = [-4 ± sqrt(16 - 48)] / 2= [-4 ± sqrt(-32)] / 2 = -2 ± 2i√2.

Thus, the roots of the polynomial ƒ(X) = X³+X²-36 are:3, -2 + 2i√2 and -2 - 2i√2.

To know more about the roots of polynomials: https://brainly.com/question/2833285

#SPJ11

Lucy runs a day care center. There are 2 four-year-olds and 12 children of other ages.

What is the probability that a randomly selected child will be a four-year-old?

Write your answer as a fraction or whole number.

P(four-year-old) =

Submit

Answers

The probability of selecting a four-year-old child at random is 1/7.

Find the probability of a randomly selected child of four-year-old.

There are 2 four-year-olds and 12 children in total, so there are 2+12=14 children in Lucy's daycare center.

The probability of selecting a four-year-old child at random is the number of four-year-olds divided by the total number of children:

P(four-year-old) = 2/14

Simplifying this fraction, we get:

P(four-year-old) = 1/7

Therefore, the probability of selecting a four-year-old child at random is 1/7.

Learn more about The probability of selecting

brainly.com/question/28384133

#SPJ11

Noise in a quiet room is 500 times as intense as the threshold of sound. What is the decibel measurement for the quiet room? 20 decibels 28 decibels 200 decibels 280 decibels.

Answers

The intensity and the threshold of the noise are illustrations of rates

The decibel measurement of a quiet room is 28

How to determine the decibel measurement

From the graph that completes the question, we have the following point

(Decibel, Intense) = (28,500)

This means that, the decibel measurement is 28

Hence, the decibel measurement of a quiet room is 28

Read more about sound and noise at:

https://brainly.com/question/13741664

Answer:

B or 28

Step-by-step explanation:

edge 22

I need help I don’t understand this help can y’all help me pls

I need help I dont understand this help can yall help me pls

Answers

Break it up into three then add all areas
I need help I dont understand this help can yall help me pls

refer to the data of exercise 6.11. a potential criticism of analyzing these data as if they were two independent samples is that the measurements taken in 1996 were taken at the same sites as the measurements taken in 1982. thus, there is the possibility that there will be a strong positive correlation between the pair of observations at each site. a. plot the pairs of observations in a scatterplot with the 1982 values on the horizontal axis and the 1996 values on the vertical axis. does there appear to be a positive correlation between the pairs of measurements? estimate the correlation between the pairs of observations?

Answers

The size of the decrease in mean PCB content from 1982 to 1996, based on the study, is estimated to be approximately 45.5, with a 95% confidence interval of (38.4, 52.6).

To calculate the confidence interval, we multiply the standard error by the appropriate critical value from the t-distribution. Since we do not know the exact sample size, we will use a conservative estimate and assume a sample size of 10. This allows us to use the t-distribution with n-1 degrees of freedom.

Using a t-distribution table or statistical software, the critical value for a 95% confidence interval with 10 degrees of freedom is approximately 2.228.

Confidence Interval = Mean Difference ± (Critical Value × Standard Error)

= 45.5 ± (2.228 × 3.2)

= 45.5 ± 7.12

Therefore, the 95% confidence interval for the size of the decrease in mean PCB content from 1982 to 1996 is approximately (38.4, 52.6).

To know more about confidence interval here

https://brainly.com/question/24131141

#SPJ4

Complete Question:

PCBs have been in use since 1929, mainly in the electrical industry, but it was not until the 1960s that they were found to be a major environmental contaminant. In the paper “The ratio ofDDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data” [appearing in the Journal of Great Lakes Research 24 (1): 12–31, 1998], researchers report on the following study. Thirteen study sites from the five Great Lakes were selected. At each site, 9 to 13 herring gull eggs were collected randomly each year for several years. Following collection, the PCB content was determined. The mean PCB content at each site is reported in the following table for the years 1982 and 1996.

Site         1982                    1996                      Differences

1               61.48                    13.99                           47.49

2              64.47                     18.26                           46.21

3                45.5                     11.28                             34.22

4                59.7                      10.02                           49.68

5             58.81                       21                                  37.81

6              75.86                   17.36                                 58.5

Estimate the size of the decrease in mean PCB content from 1982 to 1996, using a 95% confidence interval.

Find the volume 10 2/5cm 3cm 8 1/3cm​

Answers

Answer:

260

Step-by-step explanation:

Multiply all of the numbers together

what does 134 x-7 equal?

Answers

Answer:

What does 134 x-7 equal?

134 x -7

= -938

Step-by-step explanation:

You're welcome.

If you buy three ice creams and the total is $26.94, how much does each ice cream cost?

If you buy three ice creams and the total is $26.94, how much does each ice cream cost?

Answers

Answer:

$8.98

Step-by-step explanation:

Divide 26.94 by 3

Answer: $8.98

Step-by-step explanation:

26.96/3= 8.98

The non-profit organization you volunteer for is throwing a fundraiser cookout. You are in charge of buying the hamburgers, which cost $3 per pound, and hot dogs, which cost $2 per pound. The meat budget you are given totals $600 dollars. The inequality 3x + 2y ≤ 600 represents the possible combinations of pounds of hamburgers (x) and hot dogs (y) you can buy.

Answers

Answer: 7

Step-by-step explanation:

7

Answer:

Whatever point that is in the shaded region.

Step-by-step explanation:

Hope this helps!

If not I am sorry.

7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = { vt ++3 dt Jo Answer 8. g(x) = {* In (1+tº) dt

Answers

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

To know more about Fundamental Theorem of Calculus:

https://brainly.com/question/30761130

#SPJ4

____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

harold must write a 2000 word composition for a history assignment of 480 words fill 3 pages how many pages will harlod have to write to complete the assingment

Answers

The answer is : 12 pages

Please help! I will mark as brainliest. <3

Please help! I will mark as brainliest. &lt;3

Answers

that’s called a slope , i think it would be like y = mx + b if i’m wrong let me know<3

Answer:

\(y = \frac{5}{2}x +\frac{1}{2}\)

Step-by-step explanation:

in this graph we know two points whose values are certain which are, (1,3) and (-1,-2) we can find the equation of this line from these two points.

first we need to find slop which is m.

y2-y1/x2-x1 = m

y2 = 3( highest y value will always be y2) and y1 = -2

x2 = 1( counterpart of y2) and x1 = -1

3--2/1--1 = 5/2 ( -- is +)

so m = 5/2

now we can find the equation of line.

choose any of the two points from above to find the equation. ill choose (1,3)

y-3/x-1 = 5/2

\(y-3 = \frac{5}{2} (x-1)\\\\y = \frac{5}{2}x -\frac{5}{2} +3\\\\y = \frac{5}{2}x +\frac{1}{2}\)

PLEASE HELP WILL GIVE BRAINLIEST AND I WILL LOVE YOU FOREVER

PLEASE HELP WILL GIVE BRAINLIEST AND I WILL LOVE YOU FOREVER

Answers

Answer:

Step-by-step explanation:

PLEASE HELP WILL GIVE BRAINLIEST AND I WILL LOVE YOU FOREVER

determine the value of such that the matrix is the augmented matrix of a linear system with infinitely many solutions.

Answers

The value of such that the matrix is the augmented matrix of a linear system with The system has an infinite number of solutions if $k=-1$.

To find out the value of $k$ that results in the matrix being the augmented matrix of a linear system with infinitely many solutions, you need to reduce the matrix to row echelon form and check the conditions. If you get a row of all zeroes but the last entry in that row is not zero, then there is no solution. If you get a row of all zeroes including the last entry in that row, then there are infinitely many solutions. Therefore, the value of $k$ that leads to the augmented matrix of a linear system with infinitely many solutions is $k=-1$.

A system of linear equations has an infinite number of solutions if and only if its augmented matrix, after being transformed to row-echelon form, has at least one free variable column.

The matrix in question is given as:

\($$\begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix}$$\)

To find the value of $k$, we need to convert it to a row-echelon form.

\($$ \begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix} \overset{R2\rightarrow R2+\frac{3}{2}R1}{\longrightarrow} \begin{bmatrix}2 & -2 & 4 \\ 0 & 0 & 0 \\ 1 & -1 & k\end{bmatrix} $$\)

Notice that the second row of the matrix is all zeros, so the system either has no solution or has an infinite number of solutions. Therefore, we need to determine the value of $k$ to figure out which of the two cases apply. Since the third row is independent, we can choose to work with it only.

\($$1a - 1b = c \rightarrow c = a - b$$\)

We can also write it as a linear combination of $a$ and $b$:

\($$\begin{aligned} c &= a - b \\ &= a(1) + b(-1) \end{aligned}$$\)

Therefore, it follows that if $k$ equals -1, we can rewrite the last row as a linear combination of the first two rows.

for such more question on infinite number

https://brainly.com/question/30304852

#SPJ11

Susan paid $240. to have her house decorated. The materials
used to decorate the house cost $115, and service was
charged at $5 an hour. How many hours was the house
worked on?
hours :
=

Answers

Answer:

2 hours

Step-by-step explanation:

$115 + $5 = 120

120 x 2 = 240

Answer:

25 hours

step-by-step explanation:

240-115=125/5=25 pog

-1/5 divided by 20







































Help please

-1/5 divided by 20Help please

Answers

Answer:

-0.01

Step-by-step explanation:

So, answer is -1/100

Calculate each quotient
1. 2/5 ÷ 3 1/10

2. 4 1/3 ÷ 4/7

3. 3 1/6 ÷ 9/10

4. 5/8 ÷ 2 7/12

Please answer all of these questions.

Answers

Answer:

1.2/5÷3 1/10=

2/5÷31/10=

2/5×10/31=

20/155=

4/31

2.4 1/3÷4/7=

13/1÷4/7=

13/1×7/4=

91/4 then simplify it

3. 3 1/6÷9/10=

18/6÷9/10=

18/6×10/9=

180/54 then simplify it

4.5/8÷2 7/12=

5/8÷31/12=

5/8×12/31=

60/248=

15/62

Am done please mark me the brainliest and give me more points

Ravi works as a tutor for an hour and as a waiter for an hour. This month, he worked a combined total of hours at his two jobs. Let be the number of hours Ravi worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answers

The expression for his total earnings can be derived by multiplying the number of tutoring hours by the tutoring rate and adding it to the product of the number of waiter hours and the waiter rate.

Let's assume the hourly rate for Ravi's tutoring job is "t" dollars and the hourly rate for his waiter job is "w" dollars.

Since Ravi worked as a tutor for "x" hours this month, he earned a total of x * t dollars from his tutoring job.

Similarly, as he worked as a waiter for 1 hour each day this month, he earned a total of 1 * w dollars from his waiter job.

To calculate the combined total dollar amount he earned this month, we can express it as x * t + 1 * w, which represents the earnings from his tutoring job plus the earnings from his waiter job.

This expression provides the total dollar amount Ravi earned based on the given hourly rates and the number of tutoring hours.

To learn more about tutoring rate click here: brainly.com/question/29289802

#SPJ11

What is 8 to the square root of 3 time square root of 3

Answers

Answer:

531441

Step-by-step explanation:

The square root of 3 times 3 ^8

Determine whether the following equence i an arithmetic or geometric progreion. Give a reaon for your anwer. 100p,50p,25p,

Answers

Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

X/6 -5 = -2 please help ASAP

Answers

Answer: x = 18

Step-by-step explanation:

rewrite the following integral using the indicated order of integration and then evaluate the resulting integral. ∫01∫01−x2∫01−x2 dy dz dx to dz dy dx

Answers

The integral, when rewritten using the indicated order of integration, is ∫₀¹ ∫₀¹-y² ∫₀¹-x² dz dy dx, and the value of the resulting integral is 2/3.

To rewrite the given integral in the indicated order of integration, we integrate with respect to 'z' first, then 'y', and finally 'x'. The given integral is triple nested, and each integral has specific limits.

integrate with respect to 'z':

∫₀¹ ∫₀¹-y² (z ∣₀¹-x²) dy dx

∫₀¹ ∫₀¹-y² (1-x²) dy dx

integrate with respect to 'y':

∫₀¹ (y ∣₀¹) (1-x²) dx

∫₀¹ (1-x²) dx

(x - x³/3) ∣₀¹

evaluate the result:

(1-1/3) - (0-0) = 2/3

Thus, the integral rewritten and evaluated using the indicated order of integration is 2/3. However, this is not the final answer as we still need to perform one more integration with respect to 'y':

∫₀¹ (2/3) dy = (2/3) * (y ∣₀¹) = 2/3 * (1 - 0) = 2/3

Thus, the final result after evaluating all integrals is 2/3 * 1 = 2/3.


To know more about integration, refer here:

https://brainly.com/question/31744185#

#SPJ11

Please help ASAP it’s all I ask for to help me. It’s supposed to be turned in tomorrow. Please help.

Please help ASAP its all I ask for to help me. Its supposed to be turned in tomorrow. Please help.

Answers

Answer:

you would need to find the price before tax of the game. (B)

Answer:

V= video game $

.50V=.75

Now divide,

.75 divided by .05=15= V

So the video game wquals $15.

Now Check your answer

15 times (x) .05= .75

There you go :)

Step-by-step explanation:

Other Questions
What are derivatives? Different types of derivatives ? What are Forward contracts ?What are Futures contracts ? Features and benefits of derivatives ? The existence of Hindu Indian communities in places such as Guyana (South America), Fiji (Oceania), and South Africa is the result of which of the following?Relocation diffusionRural to urban migrationReligious conversionColonial-era labor migrations Need help asap! HDTV screens usually have a width-to-height ratio of 16:9. Which screen dimensions are in the same proportion? 26in by 19in, 48cm by 27cm, 4ft by 3ft,28in by 21in A car of mass 2000Kg is following a curve of radius 300 m at a speed of 50.0 m/s find the coefficient of static friction between the car and the road?0.1270.090.840.79 Which of the following statements about fire antsin the United States is TRUE?A They reproduce slowly.B_They are a native species of the United States.C They are an invasive species. D They do not compete with other ant species. Calculating Volume of a Composite Figure 2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units. Which statements about the composite figure are true? Check all that apply. The composite figure consists of two rectangular pyramids. The composite figure can be broken down into rectangular prisms. The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5). The total volume is 45 units3. The total volume is 90 units3. when the superposition theorem is applied to a circuit containing a current source, the current source is replaced by an open circuit when solving for the other sources. why the hundred days refers to the enormous amount of legislation enacted during the What did the Supreme Court say in Terry v. Ohio and why is it important?. does anyone mind helping me on this question? (the question is shown on the picture). Calculate the energy needed to climb to the top of a large hill from the start of the trail up a large hill (1300 feet up, 3 miles long), compared to what a typical person (like Dr. Burkholder) exercising moderately vigorously for an hour would burn There is the energy of just walking, plus the added gravitational potential energy. if your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound? Explain your rationale using a cost and portion argument What is the answer to this question mozarts symphony no. 40 is unique because intentionally breaking a law (and insisting that it be enforced) is characteristic of ) Let SL(2, R) be the set of 2 x 2 matrices with entries in R and determinant +1. Prove that SL(2, R) is a group (called the special linear group) under matrix multiplication in the following steps:(a) Show that SL(2, R) is closed under matrix multiplication. That is, if A and B are inSL(2, R), then AB SL(2, R).(b) Verify that SL(2, R) has an identity element I. Show that I SL(2, R) and that AI IA A for all AE SL(2, R). =(c) Show that every element of SL(2, R) has an inverse. That is, given A e SL(2, R), there is a matrix A-1 SL(2, R) such that AA-1 A-A = I.(d) Show that SL(2, R) is nonabelian by giving an example of matrices A and B in SL (2, R) such that AB BA (note this also demonstrates that the general linear group GL(2, R) is nonabelian). Alfred Wegner proposed the theory of plate tectonics. Explain the theory and what evidence has been found to support his theory. 32.For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.32. (2, 4) and (4, 10) Which of the following modifications of a tumor suppressor gene (TSG) could result in uncontrolled cell proliferation (multiple answers)?A.Somatic mutation that inactivates both copies of TSGB.Methylation of promoter on both copies of TSGC.Loss of heterozygosity of TSGD.Deletion of one copy of TSGE.Somatic mutation that increases expression of TSG In a poll of 489 adults, 132 of then said they have a tattoo. Find critical value and margin of error, and then construct a 95% confidence interval for the proportion of all adults that have a tattoo.