The figure shows an isosceles right triangle. What is the length of the hypotenuse? Show your work.

The Figure Shows An Isosceles Right Triangle. What Is The Length Of The Hypotenuse? Show Your Work.

Answers

Answer 1

The length of the hypotenuse is 4√2.

What is the Pythagoras theorem?

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, we have

Given: base = 4

perpendicular = 4

We have to find the length of the hypotenuse.

We apply here Pythagoras theorem and we get

b² + p² = h²

(4)² + (4)² = h²

16 + 16 =  h²

32 =  h²

h = 4√2

Hence, the length of the hypotenuse is 4√2.

To learn more about the Pythagoras theorem from the given link

https://brainly.com/question/31146786

#SPJ1


Related Questions

Name an acute angle and give its measure.
Angle: ______ Measure: _____

Name an obtuse angle and give its measure. (2 points)
Angle: _____ Measure: _____

Name one right angle. (1 point

Name one straight angle. (1 point)

Answers

11. Angle KEF = 40°, Angle KEJ = 50°

12. Angle HEF = 115°, Angle KED = 140°

13. Angle JEF = 90°, Angle KEF = 90°

14.   Angle DEF = 180°

Define the term geometry?

The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.

11.  Acute angles: Those angles are less than 90 degree angles.

     Angle KEF = 40°

     Angle KEJ = 50°

     Angle KEH = 75°

     Angle JEH = 25°

     Angle HED = 65°

12. Obtuse angles: Those angles are more than 90 degree angles.

     Angle HEF = 115°

     Angle KED = 140°

13. Right angle: Those angles are 90 degree angle.

     Angle JEF = 90°

     Angle KEF = 90°

14. Straight angle: Those angles make 180 degree angle.

     Angle DEF = 180°

To know more about geometry, visit:

https://brainly.com/question/247911

#SPJ1

14. As shown in the figure, the area of ​​square ABCD is known to be 1320 square centimeters, E is the midpoint of AB, F is a quarter point of BC close to point B, and the intersection points of CE, DB and DF are P and Q , find the area of ​​the quadrilateral BPQF.

Answers

The coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

What is the triangle?

A triangle is a closed, two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and can be formed by connecting three non-collinear points. Triangles can be classified based on their side lengths and angles.

To solve this problem, we can use the fact that the area of a triangle is equal to half the product of its base and height. Let's first find the length of the sides of the square.

Since the area of the square is 1320 square centimeters, we can find its side length by taking the square root of 1320:

√(1320) ≈ 36.32

So the side length of the square is approximately 36.32 cm.

Next, let's find the coordinates of points E and F. Since E is the midpoint of AB, its coordinates are:

E = ((0+36)/2, (36+0)/2) = (18, 18)

Similarly, since F is a quarter point of BC close to point B, its coordinates are:

F = (36, (3/4)36) = (36, 27)

Now let's find the equation of line CE. Since we know two points on the line (C and E), we can use the point-slope form of a linear equation to find its equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. We can find the slope of the line by taking the difference in y-coordinates and dividing by the difference in x-coordinates:

m = (0 - 36)/(36 - 18) = -2

Using the point-slope form with point C, we get:

y - 0 = -2(x - 36)

y = -2x + 72

Similarly, the equation of line DB can be found using points D and B:

m = (0 - 36)/(0 - 18) = 2

y - 0 = 2(x - 0)

y = 2x

Finally, we can find the coordinates of point P by solving the system of equations:

y = -2x + 72

y = 2x

Setting the two expressions for y equal to each other, we get:

-2x + 72 = 2x

4x = 72

x = 18

Substituting x = 18 into either equation, we get:

y = 2x = 36

So the coordinates of point P are (18, 36). To find the coordinates of point Q, we can use the fact that it lies on line DF. Since we know two points on the line (D and F), we can again use the point-slope form of a linear equation:

m = (27 - 0)/(36 - 0) = 3/4

y - 0 = (3/4)(x - 0)

y = (3/4)x

To find the intersection point of lines DF and CE, we need to solve the system of equations:

y = (3/4)x

y = -2x + 72

Setting the two expressions for y equal to each other, we get:

(3/4)x = -2x + 72

(11/4)x = 72

x = 64/11

Substituting x = 64/11 into either equation, we get:

y = (3/4)(64/11) ≈ 14.73

So the coordinates of point Q are (64/11, 14.73).

Hence, Now that we have the coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

To learn more about area  click:

https://brainly.com/question/27683633

#SPJ1

Select the correct answer.
What transformations are applied to the graph of the function f(x) = 10 to produce the graph of the function g (a) = 3(10) 2?
O A. a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units
OB.
a vertical dilation by a factor of 3 and a vertical shift down 2 units
O C.
a vertical dilation by a factor of
and a vertical shift down 2 units
OD.
a vertical dilation by a factor of
and a horizontal shift to the right 2 units

Answers

The transformations that are applied to the graph of the function [tex]f(x) = 10^x[/tex] to produce the graph of the function [tex]g(x) = 3(10)^x - 2[/tex] is: C. a vertical dilation by a factor of 3 and a vertical shift down 2 units.

What is a transformation?

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.

What is a dilation?

In Mathematics and Geometry, a dilation refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Based on the parent function (exponential), we can logically deduce that the exponential function g(x) can be produced by vertically stretching the parent function by a scale factor of 3, followed by a vertical shift down 2 units;

[tex]f(x) = 10^x[/tex]

[tex]g(x) = 3(10)^x - 2[/tex]

Read more on transformation here: https://brainly.com/question/21503974

#SPJ1

Select any of these that are LINEAR. (Select MORE THAN ONE answer !)

Responses

A
A

B
B

C
C

D
D

Answers

The linear equations from the options given are expressed as: y = 5 and y = -2/5x + 4.

How to Determine an Equation that is Linear or Non-linear?

An equation is linear can be expressed in the following forms:

y = mx + b

x = b

y = b

In the above, y is the dependent variable and x is the independent variable, m = slope, and b = y-intercept.

Note that in a linear equation the exponent of the variable is always 1. On the other hand, a nonlinear equation has an exponent that is not equal to 1 and can be expressed as:

y = x²

Therefore, the equations that are linear are:

y = 5 and y = -2/5x + 4.

Learn more about the linear equation on:

https://brainly.com/question/28871326

#SPJ1

A new hair cream was just given to a random sample of
500 people that are either bald, or currently losing their hair. The results showed that
175 of people either started growing back hair or stopped losing their hair, and the results had a margin of error of 0.065
.
If the new hair cream will be administered to 7810
people, how many are expected to see improvement?
Between [DROPDOWN1] and [DROPDOWN2] are predicted to see an improvement in their baldness.

Answers

Between 2226 and 3241 people are predicted to see an improvement in their baldness.

How to obtain the amounts?

The expected amount of people expected to see improvement is obtained applying the proportions in the context of the problem.

The sample proportion is given as follows:

175/500 = 0.35.

Considering the margin of error, the bounds are given as follows:

0.35 - 0.065 = 0.285.0.35 + 0.065 = 0.415.

Hence the amounts out of 7810 people are obtained as follows:

0.285 x 7810 = 2226 people.0.415 x 7810 = 3241 people

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Which scenario has the ratio 1/2?

Answers

Triangles to total shapes because triangles= 5 total, and total shapes = 10. 5/10 simplifies to 1/2

find the discriminant x^2-5x+22=7x+2

Answers

[tex]x^2-5x+22=7x+2\implies x^2-12x+20=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-12}x\stackrel{\stackrel{c}{\downarrow }}{+20}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-12)^2-4(1)(20)\implies 144-80\implies 64[/tex]

39. Firefighters must reach a fire anywhere
in the city within 7 minutes. They are
currently reaching fires in 3.5 minutes
less than the maximum time allotted.
Which equation shows how much time
it takes them to reach a fire?
A. t + 3.5=7
B. t - 3.57
C. t - 7 = 3.5
D. t + 7 = 3.5

Answers

Es la B esa es la respuesta

How likely is it that
at least > or them are vowe tiles?
) Which simulation could be used to fairly represent the situation?

Answers

There is a probability of 0.117 for at least 2 of the tiles to be vowel tiles.

Given that,

Probability that the tiles getting is a vowel tile is 30%.

P(V) = 30% = 0.3

That is there will be only 3 tiles out of 10 tiles which are vowels.

Out of 8, there will be 8 × 0.3 = 2.4 tiles which are vowels.

There would be either 2 or 3 vowels.

Probability that at least 2 of them is vowel tiles is,

Probability = (0.3)² + (0.3)³

                 = 0.117

Here,

The simulation which can be used to fairly represent the situation is,

Use a computer to randomly generate 8 numbers from 1 to 10. Each time 1, 2 or 3 appears, it represents a vowel tile.

Hence, the required probability is 0.117.

Learn more about Probability here :

brainly.com/question/30034780

#SPJ1

Adjacent angles .help me solve

Answers

BGC or AGF

Adjacent means next to or adjoining something else and both of the mentioned angles are next to angle AGB.

Determine the number of triangles ABC possible with given parts

Answers

The number of triangles formed by triangle ABC is 1

How to determine the number of angles

In order to calculate the possible number of triangles ABC that can be made with the specified parts, it is essential to employ conditions for triangle congruence, which includes the Triangle Inequality Theorem.

If sides a, b, and angle A can create a valid triangle, then they must follow these requirements:

a + b > c

a + c > b

b + c > a

By replacing given values with assigned variables, we get:

38 + 77 > c,

38 + c > 77,

77 + c > 38.

After solving these inequalities, we determine that c should be

39 < c < 115.

However, if the Triangle Inequality Theorem is not observed, an unfeasible configuration results. Therefore, it would be impossible to generate a triangle using the following: AB = 38, AC = 77, and angle BAC = 74 degrees.

Learn more about formation of triangle at

https://brainly.com/question/29460507

#SPJ1

The country of Scotstats requires the people in their country to have license tags on their
car such that the first 3 characters are English letters but no letter may repeat. The last 3
characters must each be a number 0 - 9 and again no numbers can be repeated. How
many license tags are possible?

Answers

The licenses have space for 6 characters.

We need to note that there are 26 alphabets and 10 numbers to pick from.

So, for the first character, any of the 26 alphabets can take this spot.

For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)

For the third character, 24 alphabets are available for that.

For the fourth character, any of the 10 numbers can take up that spot.

For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)

For the sixth character, 8 numbers can take that spot.

So, mathematically, the number of license tags possible will be

[tex]\bold{26 \times 25 \times 24 \times 10 \times 9 \times 8 = \underline{11,232,000} \ possible \ license \ tags}[/tex]

Answer:

11,232,000

Step-by-step explanation:

26 choices for the first letter.

25 choices left for the second letter (can't repeat letters)

24 choices left for the third letter

26 x 25 x 24 = 15,600 = possible first 3 characters.

10 choices for the first number

9 choices left for the second number (can't repeat numbers)

8 choices left for the third number

10 x 9 x 8 = 720 = possible last 3 characters.

chatgpt

Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man who is 66.7 inches tall. (to 4 decimal places)

Answers

Answer:

!

Step-by-step explanation:

The table below shows the costs for
different numbers of folders.
Folder Costs:

•Number of Folders
1 = $0.17
3 = $0.51
5 = $0.85
7 = $1.19

Based on this information, what is the constant of proportionality?

A0.15
B 0.17
C 0.51
D 0.85

Answers

The answer for that question is B because it’s the only one that sense for you to choose for that question

a local bakery was trying to determine what kind of desserts their customers would like to see offered in the bakery they conducted several random surveys over a period of two weeks to gather data on customers preferred desserts the results of the surveys are shown in the table?​

Answers

Therefore, the closest option to the calculated percentage is option (d) 44%.

What is percent?

Percent, denoted by the symbol "%", is a way of representing a fraction or proportion out of 100. It is used to express a part of a whole in terms of hundredths. For example, 50% is the same as 50 out of 100, which simplifies to 1/2 or 0.5 as a decimal. Percentages are commonly used in many areas such as finance, statistics, and everyday life to express changes, rates, or comparisons.

Here,

To calculate the percentage of customers who prefer cookies, we need to add up the number of customers who prefer cookies from each survey and divide it by the total number of customers who took the survey.

Number of customers who prefer cookies: 25 + 9 + 28 + 11 = 73

Total number of customers who took the survey: 17 + 11 + 20 + 13 + 25 + 8 + 9 + 30 + 26 + 11 = 170

Percentage of customers who prefer cookies: (73/170) x 100% ≈ 44%

To know more about percent,

https://brainly.com/question/29172752

#SPJ1

Question 8 (Essay Worth 10 points)
(07.04 MC)
Given the functions f(x)=x²+x²-3x+4 and g(x)=2"-4, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common?
(Consider domain, range, x-intercepts, and y-intercepts.)

Answers

The prominent similar feature between f(x) and g(x) is the present y-intercept.

How to explain the information

Since the discriminant is negative, there are no possible solutions to the given equation, which implies that f(x) has no x-intercepts.

It should be noted that to identify the y-intercept, we set x = 0 and evaluate f(x):

f(0) = 2(0)² - 3(0) + 4

f(0) = 4,

The y-intercept of f(x) can be determined as (0, 4).

Moreover, the function g(x) = 2x-4 is a power function having a negative exponent, which makes it a reciprocal function. It's domain comprises all real numbers but 0, while its range includes all real numbers excluding 0.

In order to obtain the x-intercept of g(x), we set g(x) equal to zero and solve for x:

0 = 2x-4

2x = 4

x = 2

Consequently, the x-intercept of g(x) is (2, 0), together with the y-intercept (0, -4).

The prominent similar feature between f(x) and g(x) is the present y-intercept. On the other hand, f(x) does not contain any x-intercepts, whereas g(x) has a single x-intercept. Also, f(x) is categorized as a second-degree polynomial function, whereas g(x) is classified as a reciprocal function.

Learn more about domain on

https://brainly.com/question/26098895

#SPJ1

If cos a = 0.5, then sin a could equal:

Answers

Answer:

Step-by-step explanation:

If cos a = 0.5, then sin a could equal √(1 - cos^2 a) = √(1 - 0.5^2) = √0.75 ≈ 0.866.

Gary, the technology coordinator of a high school, is planning to purchase one memory stick for each of the teachers. There are 86 teachers at the school.

Answers

Answer: 86 memory sticks should be purchased

Step-by-step explanation: If he needs to be a stick for each teacher, and there are 86 teachers, then he needs to be 86 sticks.

Find the standard form of the equation of the hyperbola with the given characteristics.
Vertices:
(1, −2), (5, −2);
passes through the point
(−3, 6)

Answers

The standard form of the hyperbola is:

(x-3)²/4 - (y+2)²/(64/35) = 1

How to solve

Given vertices (1, -2) and (5, -2), the center is (3, -2) and the semi-major axis, a = 2.

The hyperbola is horizontal.

Using point (-3, 6), we find the semi-minor axis, b² = 64/35.

The standard form of the hyperbola is:

(x-3)²/4 - (y+2)²/(64/35) = 1

Read more about hyperbola here:

https://brainly.com/question/26250569

#SPJ1

What are the correct answers for this.

Answers

Answer:

True, False, True, False, False (answered top to bottom)

Step-by-step explanation:

The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertisi dollars. The summary output for the regression model is given below.

Answers

R2, since the model only has one independent variable.

How to solve

Find R2:

R^{2} = [tex]\frac{SSR}{SST}[/tex]

R^{2} = [tex]\frac{18.26347892}{26.24578040}[/tex]

R^{2} = 0.6958634

[tex]R^{2} = 0.6959}}[/tex]

Part 2 of 3:

Find Ra2:

[tex]R^{2}_{a}= 1-\frac{(1-R^{2}) \\times (n-1)}{n-k-1}[/tex]

where

n = 9

since dftotal = n -1 = 8

thus n = 8+1=9

and k = number of independent variables = 1

Thus

[tex]R^{2}_{a}= 1-\frac{(1-0.6958634 ) \\times (9-1)}{9-1-1}[/tex]

[tex]R^{2}_{a}= 1-\frac{0.3041366 \\times 8}{7}[/tex]

[tex]R^{2}_{a}= 1-0.3475846[/tex]

[tex]R^{2}_{a}= 0.6524154[/tex]

[tex]R^{2}_{a}= 0.6524}}[/tex]

Part 3 of 3:

R2, since the model only has one independent variable.

Read more about regression model here:

https://brainly.com/question/28580475

#SPJ1

Finding the mean of data

Answers

To find the mean of a set of data, you need to add up all the values in the data set and then divide the sum by the total number of values in the data set.

For example, let's say you have the following data set: 2, 4, 6, 8, 10.

To find the mean of this data set, you would add up all the values:

2 + 4 + 6 + 8 + 10 = 30

Then, you would divide the sum by the total number of values in the data set:

30 / 5 = 6

Therefore, the mean of this data set is 6.

Supplementary angles. I will be giving out points

Answers

Answer: Angle aeb

Step-by-step explanation: To be supplementary, the angle(s) must add up to 180. Angle AEB and angle DEA add to 180. Another way to find this is to find the angle that the angle is adjacent to in a straight line.

3. Ronald Kivetsky bought a new car and received these price quotes
from his insurance company.
a. What is the annual premium?
b. What is the semiannual premium?
c. How much less would Ronald's semiannual payments be if he
dropped the optional collision insurance?

Answers

Answer:

A.the annual premium can be found by multiplying the monthly premium by 12:

Annual premium = Monthly premium x 12

Annual premium = $65 x 12 = $780

b. The semiannual premium can be found by dividing the annual premium by 2:

Semiannual premium = Annual premium / 2

Semiannual premium = $780 / 2 = $390

c. To calculate how much less Ronald's semiannual payments would be if he dropped the optional collision insurance, we need to subtract the cost of the optional insurance from the semiannual premium:

Semiannual payment with optional insurance = Semiannual premium - $120

Semiannual payment with optional insurance = $390 - $120 = $270

Semiannual payment without optional insurance = Semiannual premium - $120

Semiannual payment without optional insurance = $390 - $120 = $270

Therefore, Ronald's semiannual payments would be $270 if he dropped the optional collision insurance.

PLEASE HELP QUICKLY(25 points)!!

Match the description with the correct answer.

(questions)
———————
y-intercept -

slope-

domain-

range-

is this graph increasing, decreasing or both-

x-intercept-
———————
(answer choices)

(4,0), (0,4), (-2,0), (0,-2), +2, -4,
input values, increasing, decreasing,
both increasing and decreasing, output values
———————
please help quickly its worth 10.34 points on my test

Answers

Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

please answer question on picture

Answers

The probability that Mason does not arrive at work by 9 a.m. is given as follows:

p = 17/50.

How to calculate a probability?

A probability is calculated dividing the desired number of outcomes by the total number of outcomes.

The outcomes relating to the bus not arriving on time are divided as follows:

1 - 3/4 = 1/4 of 4/5. -> bus arrives on time.1 - 3/10 = 7/10 of 1 - 4/5 = 1/5. -> bus does not arrive on time.

Hence the probability is given as follows:

p = 1/4 x 4/5 + 7/10 x 1/5

p = 1/5 + 7/50

p = 10/50 + 7/50

p = 17/50.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

At the beginning of an environmental study, a forest covered an area of 1500 km^2. Since then, this area has decreased by 7.75% each year.
Let t be the number of years since the start of the study. Let y be the area that the forest covers in km^2.
Write an exponential function showing the relationship between y and t.

Answers

If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × [tex](0.9225)^{t}[/tex].

An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.

In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).

We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.

The formula for an exponential function is y = a × [tex]b^{t}[/tex], where "a" = initial value and "b" = growth or decay factor.

In this case, the initial area of the forest is = 1500 km², and

The forest is decreasing by 7.75% each year.

So, the "decay-factor" is = 1 - 0.0775 = 0.9225,

The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:

⇒ y = 1500 × [tex](0.9225)^{t}[/tex],

Therefore, the required "exponential-function" is y = 1500 × [tex](0.9225)^{t}[/tex].

Learn more about Exponential Function here

https://brainly.com/question/26930525

#SPJ1

Can anyone help with the geometry notes

Answers

Based on the Tangent Chord Theorem:

m∠1 = ¹/₂ ABm∠1 = ¹/₂ ACBm∠DEG = 154°m∠DBC = 84°m XY = 56°

What is the tangent chord theorem?

The Tangent Chord Theorem states that if a chord and a tangent intersect at the point of tangency, then the measure of each angle formed is equal to half the measure of its intercepted arc.

Considering the given angles;

m∠1 = ¹/₂ AB

m∠1 = ¹/₂ ACB

m∠DEG = ¹/₂ * 308°

m∠DEG = 154°

m∠DBC =  ¹/₂ * (360 - 192)

m∠DBC = 84°

m XY = 360 - (151 * 2)

m XY = 56°

Learn more about Tangent Chord Theorem at: https://brainly.com/question/13950364

#SPJ1

In a triathlon, Farhan swims a distance of 1.5 km at an average speed of 2.5 km/h,
hours.
cycles 40 km in 12 hours and runs at an average speed of 9 km/h for 1
Find his
average speed for the entire competition.

Answers

Answer:

We can use the formula:

average speed = total distance / total time

To find the total distance, we add the distances for each event:

total distance = 1.5 km (swimming) + 40 km (cycling) + 1 km (running) = 42.5 km

To find the total time, we add the times for each event:

time for swimming = distance / speed = 1.5 km / 2.5 km/h = 0.6 hours

time for cycling = 40 km / 12 km/h = 3.33 hours

time for running = 1 km / 9 km/h = 0.11 hours

total time = 0.6 hours + 3.33 hours + 0.11 hours = 4.04 hours

Now we can calculate the average speed:

average speed = total distance / total time = 42.5 km / 4.04 hours ≈ 10.52 km/h

Therefore, Farhan's average speed for the entire competition is approximately 10.52 km/h.

I will give brainliest and ratings if you get this correct ​

Answers

Answer:

below

Step-by-step explanation:

To show that (AB)^-1 = B^-1A^-1, we need to show that:

(AB)(B^-1A^-1) = (B^-1A^-1)(AB) = I

where I is the identity matrix.

Using the associative property of matrix multiplication, we can simplify the left-hand side of the equation as:

(AB)(B^-1A^-1) = A(BB^-1)A^-1 = AIA^-1 = AA^-1 = I

Similarly, using the associative property of matrix multiplication, we can simplify the right-hand side of the equation as:

(B^-1A^-1)(AB) = B^-1(A^-1A)B = B^-1IAB = BB^-1 = I

Therefore, we have shown that (AB)^-1 = B^-1A^-1.

To show this identity, we need to demonstrate that:

(AB)^-1 = B^-1 A^-1

To do this, we start by multiplying both sides of the equation by (AB):

(AB)^-1 (AB) = B^-1 A^-1 (AB)

On the left side, we know that (AB)^-1 is the inverse of AB. So we can simplify to:

I = B^-1 A^-1 (AB)

Where I is the identity matrix. We can now simplify the right side by rearranging the terms:

B^-1 A^-1 (AB) = B^-1 (A^-1 A) B

Since A^-1 A = I, we can simplify further to:

B^-1 (A^-1 A) B = B^-1 IB = B^-1 B = I

Therefore, we have shown that:

(AB)^-1 = B^-1 A^-1

Q.E.D.

Other Questions
Based on a poll, among adults who regret getting tattoos, 13% say that they were too young when they got their tattoos.Assume that ten adults who regret getting tattoos are randomly selected, and find the indicated probability. Completeparts (a) through (d) below. The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 2980 yes votes, what was the totalnumber of votes?total votes Urgent - will give brainliest for simple answer Select the correct answer.Which description best fits the role of computer network architects?O A.A.OB.They design, implement, and test databases.They maintain and troubleshoot network systems.O C. They design, test, install, implement, and maintain network systems.O D.They design, configure, install, and maintain communication systemsResetNe 1. as repairs on warranty items take place, the accrual account is ____. 2. auditors need to compare the percentage of claims accrued to current year ____. 3. with respect to auditing product warranty accruals, auditors should be alerted to changes in the client's ____sold. 4. when all of a company's products are sold with warranties, the balance in the accrual account should move ____ the balance in sales. 5. tax guidelines do not allow the ____ of the accrual for warranty claims. URGENT!! ILL GIVEBRAINLIEST! AND 100 POINTS Which descriptions of this function are true? Select 4 that apply.A. the function is increasingB. the slop of the function is -4/3 and the y-intercept is 9.C. the slope of the function is -3/4 and the y-intercept is 7.D. y= -3/4x + 7 represents this function. E. the function is linear and continuous.F. y = 7x -3/4 represents this function.G. the function is decreasing.H. the function is linear and discrete.I. y = -4/3x +9 represents this function imagine that you are clara enjoying every bit of the mountains, express your joy to your grandmother, in your daily letter (HEIDI BY JOHANNA SPYRI BASED QUESTION) In biomedical approaches to therapy, the mineral salt lithium may be used to treat _______ disorders. why do you think the locations of globular clusters and open clusters are different? choose all that apply. 1. The idea of spiritual leadership is considered an approach because it does not have empirical research to validate it.A . TrueB . False Banks and other financial institutions can best manage interest rate risk by _____.A. maximizing the duration of assets and minimizing the duration of liabilitiesB. minimizing the duration of assets and maximizing the duration of liabilitiesC.matching the durations of their assets and liabilitiesD. matching the maturities of their assets and liabilities 1) The promotional tactics employed by Red Bull are evidence of . a. a push strategy. b. socially responsible marketing. c .a pull strategy. d. sales promotion. Assume a merchandising company provides the following information from its master budget for the month of May: Sales Cost of goods sold Selling and administrative expenses Accounts receivable, May 1st Accounts receivable, May 31st $119,000 $ 95,000 $ 29,000 $ 18,000 $ 24,500 If all of the company's sales are on account, what is the amount of cash collections from customers included in the cash budget for May? Multiple Choice $101,000 $107,500 $119,000 $112,500 During protein synthesis, hereditary information (in the form of the sequence of DNA bases) is taken from the nucleus to the cytoplasm by a/an_______ strand The velocity profile of this fluid can be described by: Eq.1. u(y) = (pg/) [hy - (y^2)/2] sin(e) If the coordinate axis is aligned with the inclined plane, in the equation above: p: fluid density, u: viscosity, g: the acceleration of gravity, h: is the thickness of the fluid film, and%: is the angle of inclination of the plane A. Sketch a diagram of the system (inclined and fluid) and reference coordinates B. Derive an expression for the shear stress (t) inside the fluid, as a function of the coordinate y and the other parameters of the system. Which step is necessary in verifying that InB + 2 = -2t is a solution to dB/dt= -2B? A. e^InB + 2 = -2tB. dB = e^-2t-2 C. 1/B dB/dt = -2 D. (In B+2) dB = 1-2t dt 1.Which of the following does not affect how fast a sound travels?the density and pressure of the medium in which it travelsthe stiffness of the medium in which it travelsMacBook Airthe direction that the sound waves travelthe temperature of the medium in which it travel Rank from largest to smallest atomic radius. To rank items as equivalent, overlap them. View Available Hint(s) Reset Help O s Se Te Largest Smallest what is the forecast for july if you assume forecast for june is 1000 and alpha is 0.5? What would the expected temperature change be (in C) if a 0.5 gram sample of water released 0.0501 kJ of heat energy? The specific heat of liquid water is 4.184 J/g-C.