Triangle ABC was dilated using a center of dilation at (8, 0) to create image triangle A'B'C'. What scale factor was used to perform this dilation?





2


3


2/3


3/2

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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The point (2, 5) is a solution to the system of equations:

y = -x/2 + 6

y = 3x - 1

To determine which system of equations the point (2, 5) is a solution to, we can substitute the values of x and y into each equation and check if they satisfy the equations.

Let's substitute (2, 5) into each system of equations:

1. y = x - 8:

Substituting x = 2 and y = 5:

5 = 2 - 8

This equation is not satisfied.

2x + y = 7:

Substituting x = 2 and y = 5:

2(2) + 5 = 7

4 + 5 = 7

This equation is not satisfied.

2. y = x + 2:

Substituting x = 2 and y = 5:

5 = 2 + 2

5 = 4

This equation is not satisfied.

y = x + 5:

Substituting x = 2 and y = 5:

5 = 2 + 5

5 = 7

This equation is not satisfied.

3. y = -x/2 + 6:

Substituting x = 2 and y = 5:

5 = -(2)/2 + 6

5 = -1 + 6

5 = 5

This equation is satisfied.

y = 3x - 1:

Substituting x = 2 and y = 5:

5 = 3(2) - 1

5 = 6 - 1

5 = 5

This equation is satisfied.

4. y = 2x/3 + 6:

Substituting x = 2 and y = 5:

5 = 2(2)/3 + 6

5 = 4/3 + 6

This equation is not satisfied.

3y + 6x - 18 = 0:

Substituting x = 2 and y = 5:

3(5) + 6(2) - 18 = 0

15 + 12 - 18 = 0

27 - 18 = 0

9 = 0

This equation is not satisfied.

From the above calculations, we can see that the point (2, 5) is a solution to the system of equations:

y = -x/2 + 6

y = 3x - 1

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Therefore, the constant of variation for this seesaw is 70/x, where x is the weight of the other child in pounds.

To find the constant of variation for the seesaw, we need to use the formula for direct variation which is y = kx, where y is the weight on one side of the seesaw, x is the weight on the other side of the seesaw, and k is the constant of variation.

We can use the weight of the daughter, which is 70 pounds, and the weight of the other child, which we do not know, as our x and y values.

Let the weight of the other child be x pounds. Then we can set up the equation as follows:

70 = kx

To solve for k, we need to isolate it on one side of the equation.

We can do this by dividing both sides by

x:70/x = k

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The number of boxes that the librarian would need, given the capacity, would be 5 boxes.

In the given scenario, the librarian is tasked with the responsibility of packing 28 books into boxes. To determine the number of boxes required, we consider that each box has the capacity to hold 6 books.

Dividing the total number of books by the capacity of each box allows us to ascertain the number of complete boxes needed.

The number of boxes needed is therefore :

= 28 / 6

= 4. 66

= 5 boxes

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Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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The probability that it is raining if the flight has been delayed is approximately 0.111 or 11.1% when rounded to the nearest thousandth.

To solve this problem, we can use Bayes states:

P(A|B) = (P(B|A) × P(A)) / P(B)

Let's define the events:

A = It is raining

B = The flight has been delayed

Given information:

P(A) = 0.07 (probability that it will rain)

P(B) = 0.18 (probability that the flight will be delayed)

P(~A ∩ ~B) = 0.8 (probability that it will not rain and the flight will leave on time)

We want to find P(A|B), the probability that it is raining if the flight has been delayed.

To calculate P(B|A), the probability that the flight is delayed given that it is raining, we can use the formula for conditional probability:

P(B|A) = P(A ∩ B) / P(A)

From the given information, we can see that P(A ∩ B) is not directly given. However, we can use the complement rule to rewrite P(A ∩ B) as:

P(A ∩ B) = 1 - P(~A ∩ ~B)

Substituting the values, we get:

P(A ∩ B) = 1 - 0.8

= 0.2

Now, we can calculate P(B|A):

P(B|A) = (P(A ∩ B)) / P(A)

= 0.2 / 0.07

≈ 2.857

Finally, we can use Bayes to calculate P(A|B):

P(A|B) = (P(B|A) × P(A)) / P(B)

= (2.857 × 0.07) / 0.18

≈ 1.112

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Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

The number of elements in the Q complement set, n(Q') is 7

From the question, we are to determine the number of elements that are in the given set.

To find n(Q'),

First, we will determine the elements in Q'

NOTE: Q' means Q complement, that is, the elements that are present in the universal set but not in Q

The universal set is

ξ = {numbers between 3 and 19}

That is,

ξ = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

From the given information,

Q = {3, 5, 6, 7, 9, 10, 12, 13, 17, 18}

Therefore,

Q' = {4, 8, 11, 14, 15, 16, 19}

The value of n(Q') is the number of elements in the q' set

That is,

n(Q') = 7

Hence, n(Q') = 7

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h = 0.5d + 35, shows the total amount of hours h, Julia exercised last year if she exercised d days the rest of the year.

Given,

Last year, Julia had already exercised 35 hours prior to May 1.

After that she exercised on some days during the rest of the year.

So,

Number of hours Julia has already exercised before may 1 = 35 hours.

For rest of the years Julia exercised on some days = 0.5 hours .

Hence,

The equation that satisfies the given condition of Julia for rest of the years will be,

h = 0.5d + 35

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The cost of the pass is approximately $26, the cost of the souvenir is approximately $19.50, and the cost of the burger is approximately $3.25.

Let's break down the problem step by step:

Let's assume the cost of the pass is x dollars.

The cost of the souvenir:

The souvenir cost is 3/4 of the pass, which is (3/4) × x = (3x/4) dollars.

The cost of the burger:

The burger cost is 1/6 of the souvenir, which is (1/6) × (3x/4) = (x/8) dollars.

Total cost of the items:

The total cost of the items is the sum of the pass, souvenir, and burger costs:

x + (3x/4) + (x/8) = (8x + 6x + x)/8

= (15x/8) dollars.

Remaining amount:

Kent had $1.50 left over, so the remaining amount is $1.50 = 1.5 dollars.

Set up the equation:

The remaining amount should be the initial amount minus the total cost:

$50.25 - (15x/8) = 1.5.

Solve the equation:

$50.25 - (15x/8) = 1.5

15x/8 = $50.25 - $1.5

15x/8 = $48.75.

Multiplying both sides by 8 to eliminate the fraction:

15x = 8 × $48.75

15x = $390.

Dividing both sides by 15 to solve for 'x':

x = $390 / 15

x ≈ $26.

Calculate the cost of each item:

Pass: x ≈ $26.

Souvenir:

(3x/4) ≈ (3 × $26/4)

≈ $19.50.

Burger:

(x/8) ≈ ($26/8)

≈ $3.25.

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*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

The best example of a numerical statistical question among the given options is How many minutes of music do students listen to on average? The correct option is B.

The objective of this topic is to gather numerical data (musical minutes) and find an average value that represents a measure of central tendency. It focuses on the actions of a certain demographic—students—and how they listen to music.

By requesting the average, the questioner shows curiosity in learning about the typical or average behaviour of students with relation to their musical listening preferences.

It is a good illustration of a numerical statistical inquiry since it is written in a way that makes it possible to gather quantitative data.

Thus, the correct option is B.

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The best example of a numerical statistical question is How many minutes of music do students listen to on average, the correct option is B.

We are given that;

Four options

Now,

A numerical statistical question is a question that can be answered with a numerical value that varies from one individual or group to another. A numerical statistical question also implies that there is more than one possible answer and that the answer can be analyzed using statistical methods.

Therefore, by statistics the answer will be How many minutes of music do students listen to on average.

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The binomial theorem states that: [tex](x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k[/tex]. So, the binomial expansion of (2x - 3y)⁵ is: [tex]32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5[/tex].

Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]

Term k = 0: [tex] {5 \choose 0} (2x)^5 (-3y)^0[/tex] = 32x⁵

Term k = 1: [tex]{5 \choose 1} (2x)^4 (-3y)^1[/tex] = -240x⁴y

Term k = 2: [tex]{5 \choose 2} (2x)^3 (-3y)^2[/tex] = 720x³y²

Term k = 3: [tex]{5 \choose 3} (2x)^2 (-3y)^3[/tex] = -1080x²y³

Term k = 4: [tex]{5 \choose 4} (2x)^1 (-3y)^4[/tex] = 810xy⁴

Term k = 5: [tex]{5 \choose 5} (2x)^0 (-3y)^5[/tex] = -243y⁵

Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:[tex](2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5[/tex]

Therefore, the binomial expansion of (2x - 3y)⁵ is: [tex]32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5[/tex].

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1. The unknown in the 'x- mean' column are 2 and -8

2. The unknown in the '(x-mean)²' square column is

25 and 106

A frequency table is simply a “t-chart” or two-column table which outlines the various possible outcomes and the associated frequencies observed in a sample.

A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

1. X - mean = 13 - 11 =2

X - mean = 3 -11 = -8

2. (X - mean)² = 5²

= 25

The total value of (x-mean)²

= 9+ 4+25+4+4+64

= 13 +25 + 8 +64

= 106

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The Probability that none of the compressors in a sample of 7 are defective is (9/16)^7.

1. To find the probability that all compressors in a sample of 7 are defective, we need to calculate the probability of selecting a defective compressor for each pick and multiply them together.

In this case, there are 7 defective compressors in a shipment of 16. So, for the first pick, the probability of selecting a defective compressor is 7/16. Since there are no replacements (each pick is independent), for the second pick, the probability remains the same: 7/16. We continue this process for all 7 picks.

P(all defective) = (7/16) * (7/16) * (7/16) * (7/16) * (7/16) * (7/16) * (7/16) = (7/16)^7

Therefore, the probability that all compressors in a sample of 7 are defective is (7/16)^7.

2. To find the probability that none of the compressors in a sample of 7 are defective, we need to calculate the probability of selecting a non-defective compressor for each pick and multiply them together.

In this case, there are 9 non-defective compressors in a shipment of 16. So, for the first pick, the probability of selecting a non-defective compressor is 9/16. Since there are no replacements, for the second pick, the probability remains the same: 9/16. We continue this process for all 7 picks.

P(none defective) = (9/16) * (9/16) * (9/16) * (9/16) * (9/16) * (9/16) * (9/16) = (9/16)^7

Therefore, the probability that none of the compressors in a sample of 7 are defective is (9/16)^7.

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According to the information, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely.

In probability, an event is considered likely if its probability is high, and it is considered unlikely if its probability is low. An event is considered neither likely nor unlikely if its probability is close to 0.5 or 50%. In this case we have to consider the probability of each option to establish a conclusion. Here is the analysis:

According to the above, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely because its probability is exactly 0.5 or 50%.

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The pattern is formed by adding 4 tiles to the previous cross.

In the first cross, there is 1 tile on each arm. In the second cross, there are 5 tiles on each arm, which is 4 more than the first cross. In the third cross, there are 9 tiles on each arm, which is 4 more than the second cross. And so on.

The following formula can be used to calculate the number of tiles in the nth cross:

tiles = 4 × (n - 1) + 1

where n = number of the cross.

For example, to calculate the number of tiles in the 4th cross, use the following formula:

tiles = 4 × (4 - 1) + 1 = 17

Therefore, there are 17 tiles in the 4th cross.

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The simplified form of 13¹/3 + 2¹/3 - 10/2 is a fraction 64/6 that can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2 the final answer is 32/3.

Given

13¹/3+2¹/3-10/2​

Required simplified it =?

First, we have simplified both constants separately

13¹/3 = (3 * 13 + 1) / 3 = 40/3

2¹/3 = (3 * 2 + 1) / 3 = 7/3

now the expression become = 40/3 + 7/3 - 10/2

now taking LCM of 3 and 2 which is 6.

                                                = 80/6 + 14/6 - 30/6

 now we have to simplify this fraction by dividing by 2 = 64/6

Therefore, the simplified form of 13¹/3 + 2¹/3 - 10/2 is 32/3.

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80 percent of 150 is ​120 .

Given,

Double line diagram

Now ,

Each mark on upper line increases by 30.

Each mark on upper line increases by 20%

Thus the fourth mark is the one which gives the value of percentage as 80.

So,

80% of 150 = 120

Thus both the mark coincides and fourth mark and gives the answer as 80% .

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Answer: 52.8

Step-by-step explanation:

Surface area=

2*the top of the tent or 2*15 or 30

The base, or another 15

And (3*2.6)/2=3.9 and multiply by 2

So:

30+15+3.9+3.9

Or 45+8

Or 52.8

Answer: he will be 14

Step-by-step explanation:

Anna is 14 and her brother is 10. Two years ago she was 12. 3/4 of 12 is 9. 9+5 more years is 14. :)))

The y-intercept of the line of best fit, which is the point (0, 3) in this case, indicates the initial value of the dependent variable (y) when there are no guests or pizzas (x = 0).

In the context of the scatter plot and the equation for the line of best fit, the y-intercept represents the value of the dependent variable (y) when the independent variable (x) is zero. The y-axis in the scatter plot represents the dependent variable, which could be the number of guests or pizzas. The x-axis represents the independent variable, which could be the number of orders or time.

The y-intercept of the line of best fit, which is the point (0, 3) in this case, indicates the initial value of the dependent variable (y) when there are no guests or pizzas (x = 0). In terms of the number of guests and pizzas, the y-intercept of 3 suggests that even without any guests or orders, there is a base value of 3 for the dependent variable. This could represent a fixed cost or a minimum number of pizzas that need to be prepared or served regardless of the number of guests.

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1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, the amount paid for the month of June is approximately $252.75, and the amount paid for the entire year is approximately $6,144.

To calculate the amount paid for the month and the year, we need to consider the number of days covered by the insurance policy. Let's break it down step by step:

Step 1: Determine the number of days covered in June.

Since the policy doesn't go into effect until June 16th, there are 15 days remaining in June that will be covered by the insurance policy.

Step 2: Calculate the daily rate.

To find the daily rate, we divide the total cost of the insurance policy by the number of days in a year:

Daily rate = 6,144 / 365

Step 3: Calculate the amount paid for June.

The amount paid for June can be found by multiplying the daily rate by the number of days covered:

Amount paid for June = Daily rate * Number of days covered in June

Step 4: Calculate the amount paid for the year.

To calculate the amount paid for the year, we simply multiply the daily rate by 365 (the total number of days in a year):

Amount paid for the year = Daily rate * 365

Now let's perform the calculations:

Step 2: Daily rate

Daily rate = 6,144 / 365 ≈ 16.85 (rounded to two decimal places)

Step 3: Amount paid for June

Amount paid for June = 16.85 * 15 ≈ 252.75 (rounded to two decimal places)

Step 4: Amount paid for the year

Amount paid for the year = 16.85 * 365 ≈ 6,144 (rounded to two decimal places)

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Answer:

The sum of their ages is 29, which we can express as the equation:

P + (P - 11) = 29

Simplifying the equation:

2P - 11 = 29

Adding 11 to both sides:

2P = 40

Dividing both sides by 2:

P = 20

Therefore, Pete's age, represented by "P," is 20 years old.

The sum f(x) + g(x) is (x³ + 16x² + 6x - 99) / (x²-9)(x² + 3x) and the type of discontinuity for f(x) at x = ±3 is a removable discontinuity, and for g(x) at x = 0, it is an infinite discontinuity or vertical asymptote.

To find f(x) + g(x), we need to add the two functions together:

f(x) + g(x) = (x+2)/(x²-9) + 11/(x²+3x)

To add these fractions, we need a common denominator.

The common denominator in this case is (x² - 9)(x² + 3x), which is the product of the denominators.

Rewriting the fractions with the common denominator, we have:

f(x) + g(x) = [(x+2)(x² + 3x)]/[(x²-9)(x² + 3x)] + [11(x²-9)]/[(x²-9)(x² + 3x)]

Combining the fractions, we have:

f(x) + g(x) = [(x+2)(x² + 3x) + 11(x²-9)]/[(x²-9)(x² + 3x)]

Simplifying the numerator:

[(x+2)(x² + 3x) + 11(x²-9)] = (x³ + 5x² + 6x + 11x² - 99)

= (x³ + 16x² + 6x - 99)

Therefore, the sum f(x) + g(x) is (x³ + 16x² + 6x - 99) / (x²-9)(x² + 3x).

The excluded values for the function f(x) are x = ±3, and for the function g(x), the excluded value is x = 0.

The type of discontinuity for f(x) at x = ±3 is a removable discontinuity, and for g(x) at x = 0, it is an infinite discontinuity or vertical asymptote.

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The length of arc WK is given as follows:

WK = 141.856 m.

We consider a triangle with side lengths and angles related as follows:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

Due to the diameter of 212 m, the radius is of 106 m, hence:

WG = GK = 106.

We have an isosceles triangle, and the sum of the internal angles of a triangle is of 180º, hence the bottom angles are given as follows:

2x + 84 = 180

2x = 96

x = 48º.

Hence the relation to obtain the length of arc WK is given as follows:

sin(84º)/WK = sin(48º)/106

WK = 106 x sine of 84 degrees/sine of 48 degrees

WK = 141.856 m.

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Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

The amount payable on a solicitor’s bill is 258.5.

We are given that;

Solicitors bill = 220 + 17.5% VAT​

Now,

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

To find the amount payable on a solicitor’s bill, we need to add the VAT (value-added tax) to the original amount. VAT is a percentage of the original amount that is charged as a tax. In this case, the VAT rate is 17.5%.

To calculate the VAT amount, we multiply the original amount by the VAT rate and divide by 100. This gives us:

VAT = 220 x 17.5 / 100 VAT = 38.5

To find the total amount payable, we add the VAT amount to the original amount. This gives us:

Total = 220 + 38.5 Total = 258.5

Therefore, by algebra the answer will be 258.5.

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1. The length of side AC is 21.5 units.

2. The magnitude of ∠R is 36.9°

3. The length of side ML is 7.5 units.

3. The length of side JK is 8.5 units.

In order to determine the length of side AC, we would apply sine trigonometric ratio because the given side lengths represent the opposite side and hypotenuse of a right-angled triangle;

sin(θ) = Opp/Hyp

Where:

By substituting the given side lengths, we have:

sin(34) = 12/x

x = 12/sin(34)

x = 21.5 units.

Question 2.

For the magnitude of ∠R, we have:

TanR = opposite side/adjacent side

TanR = 6/8

∠R = tan⁻¹(0.75)

∠R = 36.9°.

Question 3.

For side length ML, we have the following:

Tan28 = 4/ML

ML = 4/tan28

ML = 7.5 units.

Question 4.

For side length JK, we have the following:

cos(θ) = Adjacent side/Hypotenuse

cos(58) = JK/16

JK = 16cos(58)

JK = 8.5 units.

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