What is the quotient of (x3 – 3x2 + 5x – 3) ÷ (x – 1)?

Answer:

  see attached

Step-by-step explanation:

The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.

If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.

The arrangement of functions according to the given condition

[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]

[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]

[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]

[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]

[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]

[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]

[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]

[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]

A limit is the value that  a function approaches as the input approaches some value.

According to the given question

[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]

⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]

= 5           ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity  [tex]\frac{1}{x^{2} }[/tex] tends to 0)

[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] =  [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex]  =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]

As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4

[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.

[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]

⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex]  [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1

As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.

[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]

⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4

as x tends to infinity 1/x tends to 0

and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]

[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex]  = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]

[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]

[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0

As x tends to infinity 1/x tends to 0

[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]

[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex]  = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.

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Answer:

Point A

Step-by-step explanation:

We know that on a coordinate plane, negative numbers can be found by moving down or moving to the left. This point must be found by moving down and left. To establish whether it is point A or point Y, we can remember that x coordinates move left and right and y coordinates move up and down. So, we would need to move 3.5 units left for x and then 4.5 units down for y. This leads us to point A.

hope this helps!

Answer:

it is point A

Step-by-step explanation:

Answer:

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Step-by-step explanation:

Given;

Confidence interval CI = (a,b) = (0.036, 0.086)

Lower bound a = 0.036

Upper bound b = 0.086

To express in the form;

p-e< p < p+e

Where;

p = mean Proportion

and

e = margin of error

The mean p =( lower bound + higher bound)/2

p = (a+b)/2

Substituting the values;

p = (0.036+0.086)/2

Mean Proportion p = 0.061

The margin of error e = (b-a)/2

Substituting the given values;

e = (0.086-0.036)/2

e = 0.025

Re-writing in the stated form, with p = 0.061 and e = 0.025

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Answer:

[tex]n = \frac{k}{ {d}^{2} } [/tex]

[tex] {d}^{2} = \frac{k}{n} [/tex]

[tex]d = \sqrt{ \frac{k}{n} } [/tex]

Answer:

d = √(k/n)

Step-by-step explanation:

n = k/d²

n/1 = k/d²

Cross multiply.

k = nd²

Divide both sides by n.

k/n = nd²/n

k/n = d²

Take the square root on both sides.

√(k/n) = √(d²)

√(k/n) = d

Answer:

(a)[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]

(b)13.3 kg

Step-by-step explanation:

The volume of brine in the tank = 4000L

Initial Amount of salt, A(0)=18 kg

The rate of change in the amount of salt in the tank at any time t is represented by the equation:

[tex]\dfrac{dA}{dt}=$Rate In$-$Rate Out[/tex]

Rate In = (concentration of salt in inflow)(input rate of brine)

Since pure water enters the tank, concentration of salt in inflow =0

Rate In = 0

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]=\frac{A(t)}{4000}\times 40\\ =\frac{A(t)}{100}[/tex]

Therefore:

[tex]\dfrac{dA}{dt}=-\dfrac{A(t)}{100}\\\dfrac{dA}{dt}+\dfrac{A(t)}{100}=0[/tex]

This is a linear D.E. which we can then solve for A(t).

Integrating Factor: [tex]e^{\int \frac{1}{100}d}t =e^{ \frac{t}{100}[/tex]

Multiplying all through by the I.F.

[tex]\dfrac{dA}{dt}e^{ \frac{t}{100}}+\dfrac{A(t)}{100}e^{ \frac{t}{100}}=0e^{ \frac{t}{100}}\\(Ae^{ \frac{t}{100}})'=0[/tex]

Taking integral of both sides

[tex]Ae^{ \frac{t}{100}}=C\\A(t)=Ce^{ -\frac{t}{100}}[/tex]

Recall our initial condition

A(0)=18 kg

[tex]18=Ce^{ -\frac{0}{100}}\\C=18[/tex]

Therefore, the amount of salt in the tank after t minutes is:

[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]

(b)When t=30 mins

[tex]A(30)=18e^{ -\frac{30}{100}}\\=18e^{ -0.3}\\=13.3 $kg(correct to 1 decimal place)[/tex]

The amount of salt in the tank after 30 minutes is 13.3kg

In this exercise we have to use the integral to calculate the salt concentration:

(a)[tex]A(t)=18e^{-\frac{t}{100} }[/tex]

(b)[tex]13.3 kg[/tex]

Knowing that the volume of brine in the tank = 4000L, the initial Amount of salt, A(0)=18 kg. The rate of change in the amount of salt in the tank at any time t is represented by the equation:

[tex]\frac{dA}{dt} = Rate \ in - Rate \ out[/tex]

Rate In = (concentration of salt in inflow)(input rate of brine). Since pure water enters the tank, concentration of salt in inflow =0.

Rate In = 0

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]\frac{A(t)}{4000}*(40)[/tex]

[tex]= \frac{A(t)}{100}[/tex]

Therefore:

[tex]\frac{dA}{dt} = \frac{A(t)}{100}\\\frac{dA}{dt} + \frac{A(t)}{100} = 0[/tex]

This is a linear D.E. which we can then solve for A(t). Integrating Factor:  [tex]e^{\int\limits {\frac{t}{100} } \, dt\\e^{t/100}[/tex] . Multiplying all through by the Integrating Factor:  

[tex]\frac{dA}{dt} = e^{t/100}+\frac{A(t)}{100}e^{t/100}\\(Ae^{1/100})'=0[/tex]

Taking integral of both sides:

[tex]Ae^{t/100}=C\\A(t)=Ce^{-t/100}[/tex]

Recall our initial condition:

[tex]A(0)=18 kg\\18=Ce^{0}\\C=18[/tex]

Therefore, the amount of salt in the tank after t minutes is:

[tex]A(t)=18e^{-t/100}[/tex]

(b)When t=30 mins

[tex]A(30)=18e^{-30/100}\\=18e^{-0.3}\\=13.3[/tex]

The amount of salt in the tank after 30 minutes is 13.3kg.

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Answer:

123.75 g  

Step-by-step explanation:

You have three unknowns: protein (p), carbohydrate (c), and fat (f)

You need three equations for the three unknowns.  They are

(1)    p +   c +   f =    725

(2) 4p + 4c + 9f = 3500

(3) 4p         + 9f = 0.45(3500) = 1575

Subtract (3) from (2)

   4c = 1925

(4)  c =   481.25

Substitute (4) into (1)

    p + 481.25 + f = 725

(5) p +                f = 243.75

Multiply (5) by 4

(6) 4p + 4f = 975

Subtract (6) from (3)

  5f = 600

(7) f =   120

Substitute (7) into (3)

4p + 1080 = 1575

4p             =   495

 p             =    123.75

The diet will include 123.75 g of protein.

Check:

[tex]\begin{array}{rcl}\\123.75 + 481.25 + 120 &=&725\\ 725 & = & 725\\&&\\4(123.75) + 4(481.25) + 9(120) &=& 3500\\495 + 1925 + 1080& =& 3500\\3500 &=& 3500\\&&\\4(123.75) + 9(120) &=& 1575\\495 + 1080&=& 1575\\1575&=& 1575\\\end{array}[/tex]

It checks.

Answer:

The answer is option B.

Step-by-step explanation:

f(x) = √x

g(x) = x - 7

To find f o g(x) replace every x in f (x) by

g(x)

That's

[tex]f \: o \: g \: (x) = \sqrt{x - 7} [/tex]

Hope this helps you

Answer: f(f(f(x)))=8x-7

Step-by-step explanation:

Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).

2(4x-3)-1                          [distribute]

8x-6-1                              [combine like terms]

8x-7

It's the same vallue. If they were different, i could argue that 2.000 is greater than 2.00. Impossible, because 2 is equal to 2.

Answer:

x=25

Step-by-step explanation:

2(x+25)=100

2x+50=100

2x=50

x=25

[tex]-9x+3y = 0\\\\-9x = -3y\\\\3x = y\\\\\\12x+4y =24\\\\3x+y = 6\\\\y+y=6\\\\2y =6\\\\y =3 \\\\3x=y\\\\x = 1\\\\(x,y) = (1,3)[/tex]

Answer:

-41

Step-by-step explanation:

(7 + 1) - (11 + 39) =

= 8 - 50

= -41

Answer:

Step-by-step explanation:

Do the work inside parentheses first.  We get:

(8) - (50)(4), or

8 - 200 = -192

Answer:

13 Compute using the 2 right angles, we know that m<FIG=90* and

Answer:

The equation of the tangent line of the given curve

  [tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]

The tangent of the given curve at the point

 [tex](\frac{dy}{dx})_{(7,9)} = \frac{33}{4}[/tex]

Step-by-step explanation:

Explanation :-

Step(i):-

Given equation of the parabola

            x²+2xy−y²+x=101  ...(i)

apply derivative Formulas

   a)   [tex]\frac{dx^{n} }{dx} = n x ^{n-1}[/tex]

   b)  [tex]\frac{d U V }{dx} = U \frac{dV}{dx} + V \frac{dU}{dx}[/tex]

Step(ii):-

Differentiating equation (i) with respective to 'x' , we get

 [tex]2 x + 2 ( x \frac{dy}{dx} + y) - 2 y \frac{dy}{dx} +1 = 0[/tex]

 [tex]2 x + 2 x \frac{dy}{dx} +2 y - 2 y \frac{dy}{dx} +1 = 0[/tex]

on simplification , we get

[tex]( 2 x - 2 y) \frac{dy}{dx} = - (2x +2y +1)[/tex]

        [tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]

The tangent of the given curve at the point ( 7,9)

    [tex](\frac{dy}{dx})_{(7,9)} = \frac{- ((2(7) +2(9) +1))}{( 2 (7) - 2 (9)}[/tex]

    [tex](\frac{dy}{dx})_{(7,9)} = \frac{- (33)}{( -4} = \frac{33}{4}[/tex]

Final answer :-

The equation of the tangent line of the given curve

  [tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]

The tangent of the given curve at the point

 [tex](\frac{dy}{dx})_{(7,9)} = \frac{33}{4}[/tex]

Hey there! :)

Answer:

(x - 9)(x - 3)

Step-by-step explanation:

We are given the polynomial:

x² - 12x + 27

Factor the equation by finding two numbers that sum up to -12 and multiply into 27. The numbers -9 and -3 satisfy these conditions:

Therefore, the equation in factored form would be:

(x - 9)(x - 3)

(x - 9)(x-3)

multiply the first and last numbers of the equation to get 27

find two numbers that multiply to 27 and add to  - 12 [the middle number]

- 9 and -3 multiply to 27 and add to  - 12

because there is no coefficient on the x2, thats your answer. (x - 9)(x-3)

hope that makes some sense :)

Answer:

21794.495 units/month

Step-by-step explanation:

Some data are missing which i can assume as per requirement of the Question.

Let us consider that profit generated by a product is given by

p(x) =4√x

Also, consider that the profit keeps changing at a rate of $1000 per month.

Now, Using the chain rule we can write

dp/dx=(dp/dt)÷(dx/dt).

So, we  can calculate

dp/dx=2x^(-1/2)=2/√x.

As per  question we have to find out  dx/dt

Since, dx/dt= (dp/dt)/(dp/dx),

so plugging  x=1900  we get 1000√1900/2=21794.495 units/month increase in sales.

Step-by-step explanation:

Given that Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. We are to calculate the probability that Rita will need to pick atleast 5 beads before she picks a grey bead from her collection.

Prob for drawing atleast 5 beads before she picks a grey bead from her collection

= 1-Prob for drawing atleast one grey beed in the first 5 draws.

(Because these two are complementary events)

no of grey beeds drawn in first 5 trials is

Bi=(5,1/6)

Prob for drawing atleast one grey beed in the first 5 draws.

=1-Prob of no grey

Hence required prob=P(X=0 in first 5 draws)

= 0.4018

6th beeds onwards can be grey also.

Nearest answer is c)0.45

Answer:

o.45

Step-by-step explanation:

i just did the test

Answer:

Step-by-step explanation:

Given Forty-two divided by seven plus the quantity three divided by six, the equivalent numerical expression will be;

[tex]\frac{42}{7} + \frac{3}{6}[/tex]

To evaluate the numerical expression, we will find the LCM of the denominator

[tex]\frac{42}{7} + \frac{3}{6} = \frac{6(42)+7(3)}{42}\\ = \frac{252+21}{42}\\= \frac{273}{42}\\= 6.5[/tex]

The value of the expression 6.5

Answer:

Write and simplify this numerical expression.

  Forty-two divided by seven plus the quantity three divided by six

1.  Write the numerical expression.  

✔ 42 ÷ 7 + (3 ÷ 6)

2.  Evaluate within parentheses.  

✔ 42 ÷ 7 + 0.5

3.  There are no exponents to evaluate.

4.  Multiply and divide from left to right.  

✔ 6 + 0.5

5.  Add and subtract from left to right.  

✔ 6.5

Step-by-step explanation:

hope this helps! :)

Step-by-step explanation:

In the problem 5 is raised to an odd exponent(9).  Thus, there is no way to halve it apart from doing 5^4.5, which equals 1397.54249, which is not a whole number.

Hope it helps <3

Answer:

1) There exists a real number x such that for all real numbers y, xy ≤ y.

Step-by-step explanation:

Given the statement:

"There exists a real number x such that for all real numbers y, xy > y"

The negation of the statement is:

"There exists a real number x such that for all real numbers y, xy ≤ y"

The correct option is 1

Answer:

c = 5.5

Step-by-step explanation:

We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:

-4/-8 = 1/2

Now, we can plug in the slope and a point into the equation y = mx + b to find b:

5 = 1/2(5) + b

5 = 2.5 + b

2.5 = b

Then, we can plug in 6 in the point (6,c) to find c:

y = (1/2)(6) + 2.5

y = 3 + 2.5

y = 5.5

c = 5.5

Answer:

c = 5.5

Step-by-step explanation:

Find the slope with two points

m = (y2-y1)/(x2-x1)

m = (1-5)/(-3-5)

   = -4/-8

   = 1/2

If all the points are on the same line, then they have the same slope

m = (y2-y1)/(x2-x1)

Using the first and third points

1/2 = (c-5)/(6-5)

1/2 =  (c-5)/1

1/2 = c-5

Add 5 to each side

5+1/2 = c

5.5 =c

Answer:

a) p=0.154

b) P(X≤2)=0.019

c) He can argue that the proportion of minority jurors is not representative of the proportion of that minority in the population.

Step-by-step explanation:

a) The proportion can be calculated dividing the number of jurors that are from the minority race by the total number of jurors:

[tex]p=X/N=2/13=0.154[/tex]

b) We can model this with a binomial random variable, with sample size n=13 and probability of success p=0.47.

The probability of k minority jurors in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{13}{k}\cdot0.47^k\cdot0.53^{13-k}[/tex]

We have to calculate the probability that 2 or less minority jurors. This can be calculated as:

[tex]P(x\leq2)=P(x=0)+P(x=1)+P(x=2)\\\\\\P(x=0)=\dbinom{13}{0}\cdot0.47^{0}\cdot0.53^{13}=1\cdot1\cdot0.0003=0.000\\\\\\P(x=1)=\dbinom{13}{1}\cdot0.47^{1}\cdot0.53^{12}=13\cdot0.47\cdot0=0.003\\\\\\P(x=2)=\dbinom{13}{2}\cdot0.47^{2}\cdot0.53^{11}=78\cdot0.221\cdot0.001=0.016\\\\\\\\P(x\leq2)=0.000+0.003+0.016\\\\P(x\leq2)=0.019[/tex]

The probability that 2 or less minority jurors is 0.019.

Answer:

  5/9

Step-by-step explanation:

  total present = males + females = 60 + 48 = 108

The desired ratio is ...

  males/total present = 60/108 = 5/9

The ratio of the males to the total number of people present is 5/9

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Giiven,

No. of males present at rally = 60

No. of females present at rally = 48

Total no. of people present = males + females = 60 + 48 = 108

The ratio of the males to the total number of people present = No. of males /Total present

∴ No. of males/Total present = 60/108 = 5/9

Thus, the ratio of the males to the total number of people present is 5/9

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The complete question is;

A surgeon performed two types of surgeries to treat large kidney stones and small kidney stones. Treatment A on large stones was successful 73% of the time, but on small stones it was successful 93% of the time. Treatment B was successful on large stones 69% of the time, but on small stones it was successful 87% of the time. The overall report stated treatment B was more successful. What may make this claim possible?

Group of answer choices;

Sampling error

Cause-and-effect relationship

Convenience error

Confounding

Simpson's Paradox

Answer:

Correct Option is Simpson's Paradox

Step-by-step explanation:

Looking at all the options, The correct option is Simpson's Paradox because the concept of the other options don't depict the paradox displayed in the question.

Now, Simpson's paradox, is simply a phenomenon in probability and statistics, whereby a trend appears in several different groups of data but will disappear or reverse when these groups are combined. This result is often encountered in many areas of statistics and is very problematic especially when frequency data is given causal interpretations. The paradox can be resolved when causal relations are appropriately addressed in the statistical modeling.

Now, in this question, it concluded that treatment B was more successful than treatment A without considering the conditions under which both treatments were carried out neither did it consider the severity of cases of patients involved in the treatment.

Answer:

Therefore the x - coordinate of the minimum is x = -8

Step-by-step explanation:

[tex]y = 2x^2 + 32x + 56 = 2(x^2 + 16x ) + 56 = 2(x^2 + 16x +64 - 64) + 56 \\= 2(x^2 + 16x +64) - 128 + 56 = 2(x+8)^2 - 72[/tex]

Therefore the x - coordinate of the minimum is x = -8

Answer:

452.4

Step-by-step equation:

surface area of a sphere formula= 4πr²

plug 6 in for r

4π(6)² =452.389 rounded  to 452.4

Answer:

A 1,296

B 1,369

36 answer

Answer:

93 ft

Step-by-step explanation:

the area of a triangle is :

A = (b*h)/2 where b is the base and h the height(here t)

4092 = (88*t)/2

2*4092 = 88*t

t= (4092*2)/88 = 93 ft

Step-by-step explanation:

Place one point at 3,-6 and the other at 5,-7

It doesn't matter where you place the second point, as long as the slope is -1/2. This means that the line goes one half down for every unit it goes to the right, so it goes down one unit when it goes two units to the right.

Answer:

Option D is correct.

XY = 10 cm

Step-by-step explanation:

Complete Question

Which of the following statements must be true, given that ABC = XYZ and AB = 10 cm?

The diagram for the question is missing.

Solution

The diagram for the question isn't attached.

But from the condition, ABC = XYZ, it is evident that the two triangles are similar according to the SSS congruent theorem.

If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar. And from the condition given, we can predict, without seeing the diagram for the question, that

(AB/XY) = (BC/YZ) = (CA/ZX)

We can also predict that the triangles are exactly the same and the proportionality bbetween is 1.

AB = XY

BC = YZ

CA = ZX

Hence, AB = XY = 10 cm.

Hope this Helps!!!