One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide.

Answer:

Add 1 1/4 x 1 1/4

Step-by-step explanation:

Let's use the variable x to represent the list price of the car.

The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.

We can write this as an equation:

Total cost = List price + 0.07(List price) + 450

We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:

12,755 = x + 0.07x + 450

Simplifying the right side:

12,755 = 1.07x + 450

Subtracting 450 from both sides:

12,305 = 1.07x

Dividing both sides by 1.07:

x = 11,500

Therefore, the list price of the car your cousin bought was $11,500.

The list price of the car your cousin bought was $11,500.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's start by setting up an equation to represent the total cost of the car:

Total cost = List price + 7% of List price + $450

We know that the total cost is $12,755, so we can substitute that in:

$12,755 = List price + 0.07(List price) + $450

Simplifying this equation, we get:

$12,755 = 1.07(List price) + $450

Subtracting $450 from both sides, we get:

$12,305 = 1.07(List price)

Dividing both sides by 1.07, we get:

List price = $11,500

Therefore,

The list price of the car your cousin bought was $11,500.

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Answer:

x<-1/5

Step-by-step explanation:

Imma assume the _ is a - soo

3x-1<-2x

5x<-1

x<-1/5

The probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

Since the arrival of customers at a Starbucks shop can be modeled as a Poisson process with an average rate of 1/min, the probability of exactly k customers arriving in a one-minute interval is given by the Poisson probability mass function:

P(k arrivals) = (λ^k * e^(-λ)) / k!

where λ is the average rate of arrivals (in this case, 1/min), e is the mathematical constant e, and k! is the factorial of k.

To find the probability that at least one customer arrives during a one-minute interval, we can use the complement of the probability that zero customers arrive (i.e., the probability of at least one arrival is 1 minus the probability of zero arrivals).

Thus, the probability of at least one customer arriving during a one-minute interval is:

P(at least one arrival) = 1 - P(0 arrivals)

P(at least one arrival) = 1 - [([tex]1^{0}[/tex] * [tex]e^{-1}[/tex]) / 0!] = 1 - [tex]e^{-1}[/tex] = 0.632

Therefore, the probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

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The area of Habib's diagram when s = 1/2 is 7.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.

To find the area of Habib's diagram when s = 1/2, we just need to substitute s = 1/2 into the expression for the area:

Area = 6 + 4s²

Area = 6 + 4(1/2)²

Area = 6 + 4(1/4)

Area = 6 + 1

Area = 7

Therefore, the area of Habib's diagram when s = 1/2 is 7.

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Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

To calculate the mean absolute deviation (MAD), we first need to find the mean of each sample.

Sample 1:[tex]17/25 = 0.68[/tex]

Sample 2: [tex]12/25 = 0.48[/tex]

Sample 3: [tex]14/25 = 0.56[/tex]

Sample 4: [tex]9/25 = 0.36[/tex]

Next, we calculate the deviation of each observation from its respective sample mean:

Sample 1: |0.68 - x1|, |0.68 - x2|, ..., |0.68 - x25|

Sample 2: |0.48 - x1|, |0.48 - x2|, ..., |0.48 - x25|

Sample 3: |0.56 - x1|, |0.56 - x2|, ..., |0.56 - x25|

Sample 4: |0.36 - x1|, |0.36 - x2|, ..., |0.36 - x25|

where xi is the satisfaction rating (0 or 1) of the Ith customer in the sample.

The MAD is the average of these deviations:

MAD = (|0.68 - x1| + |0.68 - x2| + ... + |0.36 - x25|)/100

Since we don't know the actual ratings of the customers, we cannot calculate the MAD exactly. However, we can say that the MAD is likely to be higher for samples 2 and 4, which have lower satisfaction rates, compared to samples 1 and 3, which have higher satisfaction rates. Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

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It will take John approximately 17 months to pay off the balance.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:

Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:

Monthly interest rate = 19% / 12 = 0.01583

Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:

Monthly finance charge = $2000 x 0.01583 = $31.66

Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:

Payment applied to balance = $150 - $31.66 = $118.34

Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:

Number of months to pay off balance = $2000 / $118.34 = 16.9

(rounded up to the nearest whole number)

Therefore, it will take John approximately 17 months to pay off the balance.

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If a sample of 100 Americans is taken that same week, then the probability that "sample-proportion" has between a 42% and a 47% approval rating is 0.7693 or 76.93%.

To calculate the probability that the sample-proportion falls between 42% and 47% for a sample of 100 Americans, we use the standard normal distribution.

The Sample size (n) is = 100,

The Sample proportion (p) = 46% or 0.46,

The "Standard-deviation" (σ) = √(p×(1-p)/n) = √(0.46×(1-0.46)/100) ≈ 0.0497,

We now calculate the "z-scores" corresponding to the lower and upper bounds of the desired range,

We know that, the value of "z" is (x - μ)/σ,

where x = desired proportion, μ = mean proportion, and σ = standard deviation,

So, The probability that the sample proportion has between a 42% and a 47% "approval-rating", is written as :

⇒ P(0.42 < x < 0.47) = P[(0.42 - 0.46)/0.0497 < z < (0.47 - 0.46)/0.0497],

⇒ P(0.42 < x < 0.47) = P[-0.807 < z < 2.015],

⇒ P(0.42 < x < 0.47) = 0.9783 - 0.209,

⇒ P(0.42 < x < 0.47) = 0.7693,

Therefore, the required probability is 0.7693 or 76.93%.

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1. Mean = 54

2. Standard Deviation = 6.3

3. Probability = 0.077

4. Probability = 0.845

5. Probability = 0.155

6. Probability = 0.323

Answer:

mean= 56.9

median= 55.5

mode= 64

The only true statement is 2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4.

option A.

BODMAS is an acronym that stands for "Brackets, Orders, Division, Multiplication, Addition and Subtraction".

The rule of BODMAS states that when you have a mathematical expression that involves multiple arithmetic operations, you need to perform them in a certain order. You should start by evaluating anything inside brackets or parentheses first. Then, you should work out any exponents or square roots. After that, you should perform any division or multiplication from left to right, and finally, you should perform any addition or subtraction from left to right.

If we apply the rule of BODMAS to all the given options, we would notice that only option 1 is true.

2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4

L.H.S ⇒ 2 x (6) - 6

= 12 - 6

= 6

R.H.S ⇒ 14 ÷ (3.5 x 2 ) + 4

= 14 ÷ (7) + 4

= 2 + 4

= 6

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The value of p would be could be approximately -0.391 or  0.321.

Let's start by using the quadratic formula to find the roots of the polynomial [tex]px^2 + 5x + 8p[/tex]

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

Plugging in the coefficients, we get:

[tex]x = (-5 ± √(5^2 - 4p(8p))) / 2p[/tex]

Simplifying, we get:

[tex]x = (-5 ± √(25 - 32p^2)) / 2p[/tex]

Now, we know that the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a. So:

Sum of roots = [tex](-5 + √(25 - 32p^2)) / 2p + (-5 - √(25 - 32p^2)) / 2p = -5/p[/tex]

Product of roots = [tex][(-5 + √(25 - 32p^2)) / 2p] * [(-5 - √(25 - 32p^2)) / 2p] = (25 - 32p^2) / 4p^2[/tex]

Since we're given that the sum of the roots is equal to the product of the roots, we can set these expressions equal to each other and solve for p:

[tex]-5/p = (25 - 32p^2) / 4p^2[/tex]

Multiplying both sides by 4p^2 gives:
[tex]-20p = 25 - 32p^2[/tex]

Adding [tex]32p^2[/tex] to both sides and rearranging, we get:
[tex]32p^2 + 20p - 25 = 0[/tex]

Now we can use the quadratic formula again to solve for p:

[tex]p = (-b ± √(b^2 - 4ac)) / 2a[/tex]

Plugging in the coefficients, we get:

[tex]p = (-20 ± √(20^2 - 4(32)(-25))) / 2(32)[/tex]

Simplifying, we get:

[tex]p = (-20 ± √1560) / 64[/tex]

p ≈ -0.391 or p ≈ 0.321

Therefore, the value of p could be approximately -0.391 or approximately 0.321.

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The equation that will tell us measure of additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground is given option 155 - 110 = a.

Highest kick went when Ranim started karate from the ground is

= 110 degrees

Highest kick limit given by instructor from the ground = 155 degrees

This equation represents the difference between the final desired angle of 155 degrees and the initial angle of 110 degrees.

Which Ranim's kick went when she started karate.

The result of this subtraction will give us the measure of the additional angle, a.

That Ranim needs to add to her kick to reach the new desired angle.

Therefore, equation representing the measure of the additional angle a, of Ranim karate kick is equal to 155 - 110 = a.

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The above question is incomplete, the complete question is:

When Ranim started karate, her highest kick went 110 degrees from the ground. Her instructor asked her to practice until her highest kick goes 155 degrees from the ground. Which equation will tell us the measure of the additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground?

155−110=a

155+110=a

180−110=a

155+90=a

The complete table is:

x (weeks since 5 years ago)         y (in $)

260                                                 150.01

259                                                 150.06

256                                                 149.42

234                                                 142.03

208                                                 152.79

104                                                   97.65

0                                                       70.43

The coordinates are given by (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).

The X axis suggests the weeks since 5 years ago and Y axis suggests the closing price at each time.

Number of weeks in a year is 52 weeks.  

Most recent time suggests, x = 52*5 = 260

when x = 260, then y = 150.01

7 days ago that is 1 weeks ago, x = 260 -1 = 259

The value of y then = $ 150.06

1 months ago that is 4 weeks ago, x = 260 - 4 = 256

The closing price then is, y = 149.42

6 months ago, x = 260 - 52/2 = 260 - 26 = 234

The closing price then is, y = 142.03

1 year ago that is 52 years ago, x = 260 - 52 = 208

The closing price was then, y = 152.79

3 years ago, x = 260 - 52*3 = 260 - 156 = 104

The closing price was then, y = 97.65

5 years ago, x = 260 - 52*5 = 260 - 260 = 0

The closing price was then, y = 70.43.

Then the coordinates are (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).

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Answer:

$384

Step-by-step explanation:

$3,200 x 0.12 = $384

It should be noted that to prove that arc AB is equal to arc CD, we can use the fact that vertical angles are equal. Specifically, the angles formed by radii OA and OB are vertical angles with angles formed by radii OC and OD.

Let's call the angle formed by radii OA and OB angle x, and the angle formed by radii OC and OD angle y. Since ZAOB is a central angle of circle O, we know that arc AB is equal to twice angle x. Similarly, since COD is a central angle of circle O, we know that arc CD is equal to twice angle y.

Now, since angles x and y are vertical angles, they are equal. Therefore, arc AB is equal to twice angle x, which is equal to twice angle y, which in turn is equal to arc CD.

Therefore, we have proven that arc AB is equal to arc CD.

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Assuming line ABCD is a diameter. The proof is not valid in general for any chord.

To prove AB = CD, we show triangles ABO and DCO are congruent.

1. OB=OC     radius of inner circle

2. OA=OD     radius of outer circle

3. angle ABO = angle DCO

4. SSA = SSA indicates congruent triangles

Therefore AB = CD

Angles ABC and DCB are straight angles.

Angles OBC and OCB are congruent triangle OBC is isosceles with OB=OC

Therefore angle ABO = ABC - OBC = DCB - OCB = DCO

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Jose needs 61.23 square inches of paper to cover the stack of coins.

The total thickness of the stack of 100 coins is 100 x 0.18 = 18 inches. The diameter of each coin is 1 inch, so the radius of each coin is 0.5 inches.

To find the amount of paper needed to cover the stack of coins, we need to calculate the total surface area of the stack.

The area of each circle is given by:

πr^2 where r is the radius of the coin.

The area of the top and bottom circles is:

2 x π x (0.5)^2 = 0.5π

The circumference of the circle is given by:

2πr

So, the circumference of each coin is:

2π(0.5) = π

The height of the stack is 18 inches, so the area of the curved surface is:

π x 18 = 18π

Therefore, the total surface area of the stack is:

1.5π + 18π = 19.5π

To cover the stack of coins with paper, Jose will need 19.5π square inches of paper.

19.5π ≈ 19.5 x 3.14 ≈ 61.23 square inches.

Therefore, Jose will need approximately 61.23 square inches of paper to cover the stack of coins.

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The final absolute value inequality that represents the solution set x ≤ -9 or x ≥ -5 is |x + 7| ≥ 2.

If the absolute value expression is greater than or equal to a number (e.g. |x| >= 5).

We can write it as two separate inequalities: x >= 5 or x <= -5.
The absolute value expression is less than or equal to a number (e.g. |x| <= 3)

We can write it as the single inequality: -3 <= x <= 3.
Using these rules:

We can write an absolute value inequality that has the solution set x <= -9 or x >= -5200 as follows:
| x + 2604 | >= 5193
To see why this works,

Let's first look at the case where x is less than or equal to -9. In this case, we have:
x + 2604 <= -9
x <= -2613
Plugging this into our inequality:
| -2613 | >= 5193
Which is true, since |-2613| = 2613 >= 5193.
Now let's look at the case where x is greater than or equal to -5200. In this case, we have:
x + 2604 >= -5200
x >= -7804
Plugging this into our inequality, we get:
| -7804 | >= 5193
Which is also true, since |-7804| = 7804 >= 5193.
Therefore, the inequality | x + 2604 | >= 5193 has the solution set x <= -9 or x >= -5200, as desired. I hope this helps! Let me know if you have any other questions.
Midpoint = (-9 + (-5)) / 2 = -7
The absolute value inequality will have the form |x - (-7)|.
|x + 7| ≥ 2, since the distance between -9 and -7 is 2.
|x + 7| ≤ -2, since the distance between -5 and -7 is -2.
However,

An absolute value cannot be negative, so the second inequality doesn't make sense. Therefore, we'll only use the first inequality.
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The cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.

The formula for the surface area of a cone is:

A = πr² + πrs

Where: A = surface area r = radius of the base s = slant height of the cone

Base area = 22/7 × 5 mm × 5 mm

Base area = 78.6 mm²

Lateral area = 22/7 × 5 mm × 21 mm

Lateral area = 330 mm³

Surface area = 78.6 mm + 339 mm²

Surface area = 408.6 mm²

Therefore, the cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.

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The solution to the system of inequalities is given by the image presented at the end of the answer.

One point on the solution set is given as follows:

(-9,3).

A system of inequalities is a set of two or more inequalities involving one or more variables. In a system of inequalities, the solution is a set of values for the variables that satisfy all of the given inequalities simultaneously.

The solution is the shaded region on the graph given by the image presented at the end of the answer.

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If the value of the 2022 Jeep Wrangler Rubicon depreciates at a rate of 9.7% per year, then its value after t years can be modeled by:

V(t) = 67,035(1 - 0.097)^t

Simplifying the right side:

V(t) = 67,035(0.903)^t

Therefore, the function that models the car's value, V, t years since 2022 is V(t) = 67,035(0.903)^t.

Answer: They both intersect once.

Step-by-step explanation: Solving for x, we get:

3x = 0

x = 0

Now we can substitute x = 0 into either equation to find the y-coordinate:

y = 2(0) + 4 = 4

So the two lines intersect at the point (0,4).

Therefore, the graphs of the equations y = 2x + 4 and y = −x + 4 intersect once.

Answer:

It intersects once.

Step-by-step explanation:

To plot y = 2x + 4, you start at the y-intercept which is 4. Then you go up 2 times, and to the right once.

To plot y = -x + 4, you start at the y-intercept which is also at 4. Then you go down once and to the right one time.

The graph will intersect at (0, 4).

The second time when harry feel like consuming 17 kg of sheep after he wakes up is equal to 39.7 hours ( round to nearest tenth of an hour).

Function is equal to

H (t) = 12 sin (2/24t) +15

Where  H(t) models the weight of sheep in kg that Harry like to swallow in 't' hours after wakes up.

't' in radians.

Harry wants to consumes 17kg

⇒ H(t) = 17 for t.

Substituting the given expression for H(t), we get,

⇒ 12 sin(2/24 t) + 15 = 17

⇒ 12 sin(2/24 t) = 2

⇒ sin(2/24 t) = 1/6

⇒ 2/24 t = sin^(-1)(1/6)

We know that sin^(-1)(1/6) = 0.167

Substitute the value we get,

⇒ t = 12 × 0.167

⇒ t = 2.004 radians

This gives us the first time after Harry wakes up that he feels like consuming 17 kg of sheep.

For the second time,

Add one full period to the first time, since the function H(t) has a period of 12π/2 = 6π.

The second time is,

t = 2.004 + 6π

  = 2.004 + 6×3.14

 = 20.844 radians

To round to the nearest tenth of an hour,

Since there are 12 hours in a full revolution.

Convert radians to hours by dividing by 2π and then multiplying by 12.

t = 20.844/(2π) ×  12

 = 3.31 × 12 hours

 = 39.69

  = 39.7 (rounded to the nearest tenth)

Attached graph.

Therefore, the second time after Harry wakes up that he feels like consuming 17 kg of sheep is approximately 39.7 hours after he wakes up.

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Answer:

[tex]\frac{11}{8}[/tex]

Step-by-step explanation:

[tex]\frac{11}{2}[/tex] ÷ 4 = [tex]\frac{11}{2}[/tex]  x [tex]\frac{1}{4}[/tex] = [tex]\frac{11}{8}[/tex]

So, the answer is [tex]\frac{11}{8}[/tex]

The Number of atoms ≈ 5.119 x 10^24 atoms

The Mass ≈ 248.0 g

Mass ≈ 248.0 g

To find the number of atoms, we use Avogadro's number, which is 6.022 x 10^23 atoms/mole.

Number of atoms = (8.500 moles) * (6.022 x 10^23 atoms/mole)

Number of atoms ≈ 5.119 x 10^24 atoms

To find the mass, we need the molar mass of oxygen, which is 16.00 g/mole.

Mass = (15.50 moles) * (16.00 g/mole)

Mass ≈ 248.0 g

Determine the number of moles of helium in 1.953 x 10^8 g of helium.

To find the number of moles, we need the molar mass of helium, which is 4.00 g/mole.

Number of moles = (1.953 x 10^8 g) / (4.00 g/mole)

Number of moles ≈ 4.883 x 10^7 moles

Calculate the number of atoms in 147.82 g of sulfur.

To find the number of atoms, we first need to find the number of moles of sulfur, and then use Avogadro's number. The molar mass of sulfur is 32.07 g/mole.

Number of moles = (147.82 g) / (32.07 g/mole)

Number of moles ≈ 4.609 moles

Number of atoms = (4.609 moles) * (6.022 x 10^23 atoms/mole)

Number of atoms ≈ 2.772 x 10^24 atoms

Determine the molar mass of Co.

The molar mass of cobalt (Co) is 58.93 g/mole.

Determine the formula mass of Ca3(PO4)2.

To find the formula mass, we need to add up the molar masses of all the elements in the compound.

Ca3(PO4)2 contains 3 calcium (Ca) atoms, 2 phosphorus (P) atoms, and 8 oxygen (O) atoms.

Molar mass of Ca = 40.08 g/mole

Molar mass of P = 30.97 g/mole

Molar mass of O = 16.00 g/mole

Formula mass = (3 * 40.08) + (2 * 30.97) + (8 * 16.00)

Formula mass = 120.24 + 61.94 + 128.00

Formula mass ≈ 310.18 g/mole

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The alternative hypothesis can be written as H₁: pA < pB.

The alternative hypothesis would be that there is a difference in the proportion of Republicans (Group A) and Democrats (Group B) who favor the government investing billions of dollars to improve the country's train system. Expressly, it would state that the proportion of Republicans who favor this investment is less than the proportion of Democrats who favor it:

H₁: pA < pB

where pA denotes the proportion of Republicans who favor the investment and pB denotes the proportion of Democrats who favor the investment.

In the alternative hypothesis, we actually create the relationship between the variables which are being tested in that situation. According to these, we come across the comparison among the variables and how much they differ from each other. The alternative hypothesis is the statement the researcher tries to prove by conducting a statistical analysis.

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Answer: I’m pretty sure it’s B

Step-by-step explanation:

The measure of ∠JMK =52° and ∠KML = 38°.

Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove:  is a right angle.

Proof:

Statements  Reasons

1. m∠JMK = 52°                  Given

2. m∠KML = 38°                  Given

3. m∠JMK + m∠KML = m∠JML

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. 52° + 38° =m∠JML            Substitution property of equality

5. 90° = m∠JML                    Simplification

6. ∠JML is a right angle.      Definition of right angle

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