From the top of abuilding, Cecilia finds that the angle of depression of a table on the ground is 30 degrees. If the table is 40 m from the base of the building, find the height of the building
​

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

108

Step-by-step explanation:

200 divided by 60 equals 3 then 36 times 3 equals 108

Answer:

120 heads

Step-by-step explanation:

The Experimental probability for heads is 36/60. now we have to find the experimental probability for 200 flips. so 36/60 = ?/200. We have to find a number that 60 multiplies by to get 200. That number is 200/60 = 20/6 = 3 1/3. So multiply 36 by 3 1/3: 36 * 3 = 108. 36 * 1/3 = 12. 108 + 12 = 120. So it is 120 heads

Recall that the triangles have the following property:

If the sides of a triangle are a,b, and c, then:

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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Answer:

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

Step-by-step explanation:

Use rise over run to find the slope, which will get you 1/2 as the slope

The y-intercept is at (0, -5) so put -5 in the equation

Answer: y= 1/2x + -5

Step-by-step explanation: slope is 1/2 because the line is going up one and over 2 (rise over run),  the y intercept is -5 because that is where the line hits on the y axis

Answer:

\(a. \:\:3x^3 + 4x\:\:R1\)

Step by step explanation:

Hope it helps you in your learning process.

Have a great day ahead.

The quotient and remainder for the last row of the synthetic division 3, 0, 4, 0, 1 are 3x³ + 4x, and 1 respectively.

The option representing this is, a. 3x³ + 4x R1.

Synthetic division is a short method of dividing a polynomial p(x) by another polynomial (x - c), to get the quotient and remainder.

The last row represents the quotient and remainder, the last digit being the remainder, and the others being the quotient multiplied by leading powers of x, starting from x⁰, starting from the second last term of the last row.

In the question, we are given the last row of a synthetic division as 3, 0, 4, 0, 1, and we are asked to find the quotient of the division.

The last number, 1 represents the remainder and can be written as R1.

Now we move from the back to the front and multiply every number with the leading power of x, starting from x⁰.

Therefore, the quotient and remainder for the last row of the synthetic division 3, 0, 4, 0, 1 are 3x³ + 4x, and 1 respectively.

The option representing this is, a. 3x³ + 4x R1.

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(a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

The Continuous Compounding formula for the principal P , rate of interest r , and time t is

A = P×\(e^{rt}\)

In the question ,

it is given that

Part(a)  

the amount deposited (P) = $5200

rate percent (r) = 3.7% = 3.7/100 = 0.037

time = 9 years

Amount = 5200×\(e^{0.037\times9}\)

= 7254.76

the future value after 9 years is $7254.76   .

Part(b)

the effective rate is calculated using the formula

effective rate = \(e^{r}\) - 1

effective rate = \(e^{0.037}\) - 1

= 1.03769 - 1

= 0.03769

= 3.769%

Part(c)

the time to reach $10000 is calculated using the formula

10000 = 5200\(e^{0.037\times t}\)

\(e^{0.037\times t}\) = 10000/5200

\(e^{0.037\times t}\) = 100/52

taking ㏑both the sides , we get

0.037×t×㏑(e) = ㏑(100/52)

0.037t = 0.65392

t = 0.65392/0.037

t = 1.76735

t ≈ 1.77 years

Therefore , (a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

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The percentage of increase in sales from last month to this month is 9%.

Given,

Sales for last month = £180 000.

Sales for this month = £196 200.

To calculate the percentage increase, we must first find the difference in sales between the two months:-

Difference between the two months = £180,000 -  £196,200 = £16,200

Percentage of this difference = (16,200 ÷ 180,000) * 100 = 9

Thus, the percentage of increase is 9% from the last month to this month.

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Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

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Check the picture below.

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

name me brainleist and say thank you, and rate 5 stars.

Answer:80 square meters

Step-by-step explanation:

Answer:

x is 60⁰ because 180 - 40 is 120 divide it by 2 because the bottem angles are equal and u get 60

Answer:

6x^2+4xy

Step-by-step explanation:

You distribute the 2x by multiplying it with each term
2x(3x)+ 2x(2y)

6x^2+4xy

hopes this helps please mark brainliest

The probability that 89% or more in the sample will have earned a high school diploma is p ~ N = ( 0.87 , 0.001131 )

The normal distribution can be used to model the sample proportions.

The Central Limit Theorem and the importance of the normal distribution model in statistics (CLT). According to this theory, regardless of the type of distribution, the variables are sampled from, averages calculated from independent, identically distributed random variables have approximately normal distributions (provided it has finite variance).

Given,

N ( sample size ) = 100

probability of earning a high school diploma (p)  = 0.87

probability of not earning a high school diploma ( q ) = 0.13

hence ;

∈( P ) = p = 0.87

Var ( p ) = \(\frac{pq}{n}\)  = \(\frac{0.86*0.13}{100}\)  = 0.001131

therefore ; p ~ N = ( 0.87 , 0.001131 )

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Answer:

XY ≈ 14.87 units

Step-by-step explanation:

Calculate the distance using the distance formula

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

with (x₁, y₁ ) = X(- 6, 3) and (x₂, y₂ ) = Y(8, - 2)

d = \(\sqrt{(8+6)^2+(-2-3)^2}\)

   = \(\sqrt{14^2+(-5)^2}\)

   = \(\sqrt{196+25}\)

   = \(\sqrt{221}\)

   ≈ 14.87 ( to 2 dec. places )

Since am a number greater than 0and a factor of 2 multiple of 5 then am 10 ie ans =10

10÷2=5

5*2=10

Answer:

a) 34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b) 78.81% of​ 10-year-old boys is tall enough to ride this​ coaster

c) 44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 54, \sigma = 5\)

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

This is 1 subtracted by the pvalue of Z when X = 56.

So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{56 - 54}{5}\)

\(Z = 0.4\)

\(Z = 0.4\) has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

This is 1 subtracted by the pvalue of Z when X = 50.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{50 - 54}{5}\)

\(Z = -0.8\)

\(Z = -0.8\) has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% of​ 10-year-old boys is tall enough to ride this​ coaster.

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

From a), when X = 56, Z has a pvalue of 0.6554

From b), when X = 50, Z has a pvalue of 0.2119

0.6554 - 0.2119 = 0.4435

44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

Answer:

\frac{27}{17}+\frac{28}{17}i

Step-by-step explanation:

By the chain rule,

\(\dfrac{dy}{dx} = \dfrac{dy}{dt} \cdot \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}\)

So first differentiate both x and y with respect to t.

• dx/dt :

\(x = \dfrac{\sin^3(t)}{\sqrt{\cos(2t)}} = \sin^3(t) \left(\cos(2t)\right)^{-\frac12}\)

By the product rule,

\(\dfrac{dx}{dt} = \dfrac{d(\sin^3(t))}{dt} \left(\cos(2t)\right)^{-\frac12} + \sin^3(t) \dfrac{d\left(\cos(2t)\right)^{-\frac12}}{dt}\)

By the power and chain rules,

\(\dfrac{dx}{dt} = \dfrac{d(\sin(t))}{dt} 3\sin^2(t) \left(\cos(2t)\right)^{-\frac12} -\dfrac12 \sin^3(t) \left(\cos(2t)\right)^{-\frac32} \dfrac{d(\cos(2t))}{dt}\)

\(\dfrac{dx}{dt} = 3\sin^2(t) \cos(t) \left(\cos(2t)\right)^{-\frac12} -\dfrac12 \sin^3(t) \left(\cos(2t)\right)^{-\frac32} (-2 \sin(2t))\)

We can clean this up a bit and write

\(\dfrac{dx}{dt} = \dfrac{3\sin^2(t) \cos(t)}{\sqrt{\cos(2t)}} + \dfrac{\sin^3(t) \sin(2t)}{\sqrt{\cos^3(2t)}}\)

\(\dfrac{dx}{dt} = \dfrac{\sin^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \cos(t) \cos(2t) + \sin(t) \sin(2t)\right)\)

• dy/dt : (I'll skip some steps here, the derivative is nearly the same)

\(y = \cos^3(t) \left(\cos(2t)\right)^{-\frac12}\)

\(\dfrac{dy}{dt} = 3\cos^2(t) (-\sin(t)) \left(\cos(2t)\right)^{-\frac12} + \cos^3(t) \left(-\dfrac12\right) \left(\cos(2t)\right)^{-\frac32} (-2 \sin(2t))\)

\(\dfrac{dy}{dt} = -\dfrac{3\cos^2(t) \sin(t)}{\sqrt{\cos(2t)}} + \dfrac{\cos^3(t) \sin(2t)}{\sqrt{\cos^3(2t)}}\)

\(\dfrac{dy}{dt} = -\dfrac{\cos^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \sin(t) \cos(2t) - \cos(t) \sin(2t)\right)\)

Finally, we get dy/dx by dividing the two derivatives above:

\(\dfrac{dy}{dx} = \dfrac{-\frac{\cos^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \sin(t) \cos(2t) - \cos(t) \sin(2t)\right)}{\frac{\sin^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \cos(t) \cos(2t) + \sin(t) \sin(2t)\right)}\)

\(\dfrac{dy}{dx} = -\cot^2(t) \dfrac{3\sin(t)\cos(2t) - \cos(t)\sin(2t)}{3\cos(t)\cos(2t) + \sin(t)\sin(2t)}\)

and by applying some trig identities,

\(\dfrac{dy}{dx} = -\cot^2(t) \dfrac{\sin(3t) - 2\sin(t)}{\cos(3t) + 2\cos(t)}\)

\(\boxed{\dfrac{dy}{dx} = -\dfrac{\cos(3t)}{\sin(t) (2\cos(2t) + 1)}}\)

Answer:

\($\frac{dy}{dx}=-\cot (3 t)$\)

Very important note!

Both answer are correct, the thing is: the expression can be more simplified  as

\(\sin(t)(2\cos(2t)+1) = \sin(3t)\)

that will lead the the answer I just gave.

Step-by-step explanation:

The question is looking for \(\dfrac{dy}{dx}\)

We have

\(x = \dfrac{\sin^3 (t)}{\sqrt{\cos(2t)}} \quad \text{ and } \quad y = \dfrac{\cos^3 (t)}{\sqrt{\cos(2t)}}\)

One approach would be calculating \(\dot{x}\) and \(\dot{y}\) considering

\(\dfrac{dy}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}\)

We would have

\($\frac{dx}{dt}=\frac{3 \sin ^2(t) \cos(t)}{\sqrt{\cos (2 t)}} + \frac{\sin (2 t) \sin ^3(t)}{\cos ^{3/2}(2 t)} $\)

\($= \frac{\sin^{2} t}{\cos ^{3/2}(2 t)}(3\cos (t) \cos(2t)+2\sin^{2} (t) \cos(t))$\)

\($=\boxed{ \frac{\sin ^2(t) (2 \cos (t)+\cos (3 t))}{\cos ^{3/2}(2 t)}}$\)

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

\($\frac{dy}{dt}=\frac{\sin (2 t) \cos ^3(t)}{\cos ^{\frac{3}{2}}(2 t)}-\frac{3 \sin (t) \cos ^2(t)}{\sqrt{\cos (2 t)}}$\)

\($= \frac{\cos^{2} t}{(\cos ^{3/2}(2 t)} (-3\sin (t) \cos (2t)+2\cos^{2} (t) \sin (t))$\)

\($=\boxed{ \frac{\sin (t)-\sin (5 t)}{4 \cos ^{3/2}(2 t)}}$\)

Finally,

\($\frac{dy}{dx}= \frac{\sin (t)-\sin (5 t)}{4 \cos ^{3/2}(2 t)} \cdot \frac{\cos ^{3/2}(2t) }{ \sin ^2(t) (2 \cos (t)+\cos (3 t))}$\)

\($=\frac{\cos(t)(2\cos^{2} t-3(2\cos^{2} t-1))} {\sin(t)(2\sin^{2} t+3(1-2\sin^{2} t))} $\)

\($=-\frac{4\cos^{3} (t)-3\cos (t)}{3\sin (t)-4\sin^{3} (t)} $\)

\($=-\frac{\cos (3t)}{\sin (3t)}$\)

\(=\boxed{-\cot (3t)}\)

Kareem has $22, Raina has $28, Eric has $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raina, Kareem, and Eric have a total of $138 in their wallets.

let Kareem has x dollar.

Then Raina has (x+6) dollar

and, Eric has 4x dollar

So, x+ 4x + x + 6 = 138

6x + 6 = 138

6x = 132

x= 22

Thus, Kareem has $22.

Raina has = 22 +6 = $28

and, Eric has =4x = $88

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Answer:

its $95 dollars

Step-by-step explanation:

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

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

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

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

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

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

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

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

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

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

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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Answer:

P(10 packet) = 0.000976

Therefore, there is a 0.000976 probability of packet loss if the number of packets in residence is limited to 10.

Step-by-step explanation:

We are given an M/M/1 queuing system

The mean arrival rate is

λ = 500 packets/second

The mean service rate is

μ = 1000 packets/second

The number of packets in residence is

n = 10

The probability of packet loss is given by

P(n packet) = ρⁿ

When n is the number of packets and ρ is the gateway utilization

The gateway utilization is given by

ρ = λ/μ

Where λ is the mean arrival rate and μ is the mean service rate.

ρ = 500/1000

ρ =0.50

So, the probability is

P(10 packet) = (0.50)¹⁰

P(10 packet) = 0.000976

Therefore, there is a 0.000976 probability of packet loss if the number of packets in residence is limited to 10.

The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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Answer:

False

Step-by-step explanation:

This is all I can think of.

Multiply two matrices and obtain the identity matrix, it can be assumed the matrices are inverses of one another. so, this statement is true.

Inverse of matrix is a matrix derived from another matrix such that if you multiply the two you get a unit matrix. Square matrices with a an inverse are called non singular matrices while those without an inverse are called singular matrices (determinant is zero). Inverses and determinant are only calculated for square matrices.

Two matrices are said to be inverse of each other.

If A B = B A = I, where I is the identity matrix.

So, the matrices are inverses of one another if the product of two square matrices is the identity matrix.

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