if a = b, then does ax = bx and ay = by?

The rate of change is -5.

The number of treat left in the bag after 20 dyas is 70.

A bag of cat treats has 170 individual treats inside. Your cat can eat 5 treats per day. Therefore, the rate of change can be calculated as follows:

The rate of change is the rate at which one quantity is changing with respect to another quantity.

Therefore, using equation

y = mx + b

where

Therefore,

y = 170 - 5x

where

Hence,

rate of change = -5

Let's find the treat left in the bag after 20 days

y = 170 - 5x

y = 170 - 5(20)

y = 170 - 100

y = 70

Therefore, 70 treat is left in the bag.

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The relative size of the samples from each school should be proportional to the square root of the enrollment at each school.

The relative size of the samples from each school should be proportional to the square root of the enrollment at each school. So, for Wabash College, we would want to sample approximately √(900) = 30 students, and for Purdue University, we would want to sample approximately √(36,000) = 180 students.

This would ensure that the standard deviation of the sample proportions from each school would be approximately the same.

So, the relative size of the samples from each school should be proportional to the square root of the enrollment at each school.

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The sum of cubes identity states that a^3 + b^3 = (a+b)(a^2 - ab + b^2). To find the factors of 8x^6 + 27y^3, we can apply this identity to the expression by identifying a and b:

What is the identity of the sum of cubes?

What Does the Algebraic Sum of Cubes Formula Mean? One of the key algebraic identities is the sum of cubes formula. Its symbol is written as a3 + b3 and is interpreted as a cube plus a cube. A3 + b3 = (a + b) (a2 - ab + b2) is how the sum of cubes formula (a3 + b3) is written.

8x^6 + 27y^3 = (2x^2)^3 + (3y)^3

We can then apply the identity to get:

(2x^2)^3 + (3y)^3 = (2x^2 + 3y)((2x^2)^2 - 2x^2*3y + (3y)^2)

This gives us the factors of 8x^6 + 27y^3 as (2x^2 + 3y)(4x^4 - 6x^2y^2 + 9y^2).

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To fill the blank of the given table above is represented below as follows:

1= 11.4 grams

2= 22.8 grams

6= 68.4 grams

10 = 114 grams

If 2 packages = 22.8 g

1 package = X grams

Make X the subject of formula;

x grams = 22.8/2 = 11.4grams

If 1 package = 11.4 grams

6 packages = y grams

Make y the subject of formula;

y = 6×11.4

y = 68.4 grams

If 1 package = 11.4 grams

z packages = 114 grams

make z the subject of formula;

z = 114/11.4

z = 10 packages.

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Answer:

1/2

Step-by-step explanation:

So the point of this question is to compare all of the answers and see which one fits best.  To do this, first change the denominator to match 5/8.  To convert 1/2 into eighths, multiply 2 by 4 so you get eight.  Since you did that, you have to do the same to the numerator.  Therefore:  

1/2 = 4/8

Is 4/8 less than 5/8?  Yes.  Is it greater than 1/9?  Yes, but how?  Do the same thing but instead convert 1/2 into ninths.  Multiple 2 by 4.5 to get 9 and 1 by 4.5 to get 4.5.  

1/2 =  4.5/9

4.5/9 is greater than 1/9, so you answer would be 1/2.  

Normally you would test every answer, but to save time I'll just stop there because the first option was correct.  I hope you understand.  :)

Answer:

1/2

Step-by-step explanation:

1/2 = 4/8 which is less than 5/8.

1/9 = 2/18

1/2 = 9/18 which is greater than 2/18 (same as 1/9)

The required payment for the SUV after the discount was applied is 136,000. Option C is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
All SUVs are marked down by 15%.
Cost of G wagon = 160, 000
Cost after discount = 160000 - 15% of 160,000
                             = 136000

Thus, the required payment for the SUV after the discount was applied is 136,000. Option C is correct.

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The amount after discount is $136000.

Given is that Mercedes is running a special in which all SUVs are marked down for 15%. Mr. Estes purchased a G wagon for 160,000.

The amount after the discount was applied is -

D = 15% of 160000

D = (15/100) x 16000

D = 15 x 160

D = 2400

A = 160000 - 2400 =

A = 136000

Therefore, the amount after discount is $136000.

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Answer:

see below

Step-by-step explanation:

z+66+z+69+43z=180

so 45z=180-66-69 = 45

so z=1

so angle U= 43 its opposite side length ST is the smallest

same logic for the other 2.

66+1=67

69+1=70

so ST<US <TU

Combining the given information, ∫51′() = f(5) - f(1) = -7 - (-2) = -5. , the integral of ∫51′() is equal to -5.

In order to evaluate the integral ∫51′(), we need to use the Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus states that the integral of a function's derivative is equal to the function value evaluated from one point to another. For example, if f'(x) is the derivative of a function f(x), then the integral of f'(x) from x = a to x = b is equal to f(b) - f(a).

Using the given information, we can solve the integral ∫51′() as follows. We know that the derivative of our function is 1, so the integral of 1 from x = 1 to x = 5 is equal to f(5) - f(1). Therefore, combining the given information, ∫51′() = f(5) - f(1) = -7 - (-2) = -5. Therefore, the integral of ∫51′() is equal to -5.

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Answer:

D. 64x4964, x, 49

Step-by-step explanation:

The expression [4x4(2x3)]2 means to square the result of the expression inside the brackets.

4x4 = 16x4

2x3 = 6x3

So, [4x4(2x3)] = [16x4(6x3)] = 96x7.

Squaring this result, we get

[4x4(2x3)]2 = 96x7 * 96x7 = (96 * 96)x(7 * 7) = 9216x49 = 9216x^49.

Therefore, the expression [4x4(2x3)]2 is equivalent to 64x49, x, 49.

Answer:

Step-by-step explanation:

Divide both sides by 9. Xavier had $8.

if Lucy has 9 times as much as Xavier 8 times 9 =72

The transitive term accurately completes the proof

What is the vertical angle theorem?

According to the vertical angle theorem, the vertical angles that are created when two lines intersect are congruent. The opposing angles of two intersecting lines must be congruent, or identical in value.

Here, we have

Given: segment UV is parallel to segment WZ. According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem.

we are given a line of thought trying to prove different entities proven to be congruent by different arguments or proof.

Eventually, the two are associated using a property called transitivity. This property is used to associate A and C when A is equal to B and B is equal to C.

Hence, the transitive term accurately completes the proof.

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The value given is from a continuous data set because there are infinitely many possible values.

In statistics, a discrete data set is a set of data that can only take certain values, typically whole numbers, that can be counted. A continuous data set is a set of data that can take any value within a certain range, and the values can't be counted as they are infinite in number.

In the given scenario, the weight of a car can take any value within a certain range, and there are infinitely many possible values between any two values. For example, between 1628.3 kg and 1628.4 kg, the car's weight could be an infinite number of values. Hence, the weight of the car is a continuous variable, and the given value of 1628.3 kg is part of a continuous data set.

Hence, the correct answer is d.

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The linear formulas with integer coefficients for width and height are (x - 1)(x+3)(x+4).

A algebraic, a set, or the multiplying coefficient of a specific term in an equation have all been examples of variables in mathematics. Usually numeric, but any phrase is acceptable. If the coefficients are variables, they can also be referred to as "parameters" by themselves. A coefficient is a number multiplied by a variable. Examples of coefficients include: In the expression 14c 14c 14c, the coefficient is 14. Word g has a coefficient of 1, which doubles the element by this figure. example The coefficient is 6 because "z" is a constant and the term is defined as is 6z. The square of x's coefficient is one.

given

by long division method

x³ - 9x² + 23x - 15 / (x - 1)

= x2 + 4x + 3

( x2 + 4x + 3 ) (x - 1)

= (x - 1)(x+3) (x+4)

The linear formulas with integer coefficients for width and height are (x - 1)(x+3)(x+4).

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Answer:

-2, -1, 0, 6

Step-by-step explanation:

The range is the outputs or the y values.  I just put them in order from least to greatest

(1, -2)

(9, -1)

(2, 0)

(-6, 6)

The height of the rectangular prism is 5 feet.

A box is in the shape of a right rectangular prism. The area of one of the bases is shown.

Let's find the height of the box.

Using the volume of a rectangular prism,

volume of a rectangular prism = Bh

where

V = B × h

where V is the volume of the right rectangular prism, B is the area of the base, and h is the height.​

Hence,

h = V / B

h = 60 / 12

Therefore,

h = 5 ft

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The expression's result is -2 [tex]\sqrt[3]{89}[/tex] when it is stated that a = 64 and b = -5. Scientific operation, expression, and numeral

Multiplying, split, adding, and withdrawing are all possible in mathematics. As an example, consider the following expression: Scientific operation, expression, and numeral The elements that make up a mathematical expression include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) One can contrast two expressions or sentences. The terms "expression" or "algebraic expression" refer to any mathematical statement that has variables, numbers, and also an arithmetic procedure between them. For instance, the statement 4m + 5 consists of the terms 4m and 5, as well as the variable m from the given expression, all of which are divided by the arithmetic sign +.

given

a = 64

b = -5

= -2[tex]\sqrt[3]{a+b^{2} }[/tex]

= -2  [tex]\sqrt[3]{89}[/tex]

The expression's result is -2 [tex]\sqrt[3]{89}[/tex] when it is stated that a = 64 and b = -5.

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The correct question is :- What is the value of this expression when a = 64 and b = -5 ?

-2[tex]\sqrt[3]{a+b^{2} }[/tex]

Answer:

The next four multiples of 5/10 are:

1.              ➡️                       1/2

2.             ➡️                       3/4

3.             ➡️                        1

4.             ➡️                      1 1/4

The number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.

The number of ways to choose 3 hearts from the 13 available hearts is given by the binomial coefficient C(13,3). The number of ways to choose 2 diamonds from the 13 available diamonds is given by C(13,2). The total number of ways to choose 3 hearts and 2 diamonds from the deck of 52 cards is the product of these two binomial coefficients: C(13,3) * C(13,2).

i.e.

There are 13 hearts and 13 diamonds in a deck of 52 cards.

To choose 3 hearts, we have C(13,3) = 13!/(3!(13-3)!) = 286 ways.

To choose 2 diamonds, we have C(13,2) = 13!/(2!(13-2)!) = 78 ways.

Therefore, the number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.

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When two or more roads or lines cross each other, they come together. You may also remark that two roads or lines cross.

They are referred to be intersecting lines when two or more lines in a plane cross each other.The common point shared by all intersecting lines is known as the point of intersection, and it can be found on all of them. Point O in this case represents the intersection of lines P and Q.

A line is something that is made up of indivisible points that stretch in many directions, to put it simply. Let's use the two points A and B as an example. Now, a line connecting points A and B can be drawn.

Line AB is the name of this line, which stretches in both directions. Arrows are used to represent lines to show that they have no ends and go on forever.

solve log(x)=-x+6

log(x)=-x+6 it can be written as

⇒log(x)+x+6=0

⇒log(1/x+6)=0

It will  be in the form of lod(1/a+b)

so we can write log(x)+log(1+6/x)

Therefore, if modulus of 6/x <0 then it can be written as

                        ∞ =log(x)-∑xn/n

            n-1

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The time complexity average of this problem is O(n³). It involves three nested loops, each loop iterating n times. Therefore, the time complexity is O(n³).

The time complexity of this problem is O(n³). This problem involves three nested loops, each loop iterating n times. This means that the problem requires at least O(n³) time to complete. In the outer loop, which is the first loop, the value of i is initialized to 1 and then the loop iterates n times, meaning that the outer loop requires O(n) time. In the second loop, which is the nested loop, the value of j is initialized to 1 and then the loop iterates n times, meaning that the second loop requires O(n) time. In the third loop, which is the innermost loop, the value of k is initialized to 1 and then the loop iterates n times, meaning that the third loop requires O(n) time. Since the three loops are nested, the total time complexity of this problem is the product of the time complexities of the three loops, which is O(n³). Therefore, the time complexity of this problem is O(n³).

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The length of the rectangular pool is x + 7.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Area of a rectangular shape = Length × Width

Given that,

Area = x² + 15x + 56

Width = x + 8

Substituting,

x² + 15x + 56 = Length (x + 8)

Length = (x² + 15x + 56) / (x + 8)

Factorize x² + 15x + 56.

x² + 15x + 56 = (x + 7) (x + 8)

So length = x + 7

Hence the length of the pool can be represented as x + 7.

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The value of x is 4 which means that the first digit in the sequence is 4, the second digit is 5, the third digit is 6, and so on.

This problem is asking for the value of x in a sequence of 14 digits where the sum of any three consecutive digits is equal to 15. To solve for x, we can use the information provided and basic algebra.

Let's assign a variable to each of the 14 digits in the sequence. For example, let x be the first digit, (x + 1) be the second digit, (x + 2) be the third digit, and so on. Then, the sum of any three consecutive digits must equal 15:

x + (x + 1) + (x + 2) = 15

Expanding and solving for x, we get:

3x + 3 = 15

3x = 12

x = 4

So, the value of x is 4. This means that the first digit in the sequence is 4, the second digit is 5, the third digit is 6, and so on. By continuing this pattern, we can fill in the entire sequence of 14 digits such that the sum of any three consecutive digits is equal to 15.

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57  times more material was used to build the Hoover dam than the American falls .

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Volume of Hover dam = 4 x [tex]10^6[/tex]

Volume of American Falls dam = 7 x [tex]10^4[/tex]

So, the number of times more material used

= Volume of Hover dam / Volume of American Falls dam

= 4 x [tex]10^6[/tex] / 7 x [tex]10^4[/tex]

= 400 x  [tex]10^4[/tex] / 7 x [tex]10^4[/tex]

= 57.14

Hence, 57.14 times more material used.

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1. Considering the equation [tex]z^{16}[/tex] = −1−i.The value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π as z=r[tex]e^{i\theta}[/tex] where r = [tex]\underline{2^{1/32}}[/tex] and θ = 13π/64.

2. Considering the equation [tex]z^{13}=(-1+\sqrt{3i})[/tex]. The value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π as z=r[tex]e^{i\theta}[/tex] where r = [tex]\underline{2^{1/13}}[/tex] and θ = 8π/39.

1. The equation is z^{16} = -1 - i.

We have express our answer in the form of

[tex]\; z = re^{i\theta }[/tex]

When we enter it into the first equation, we obtain,

[tex]r^{16}e^{16i\theta }=-1-i\; \; \; \; \; \; \; \; \; \; \; \;[/tex]--(2)

Using the modulus of both sides, we obtain,

[tex]\left |r^{16} \right |\: \: \left | e^{16i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( -1 \right )^{2}}[/tex]

Simplifying

[tex]\; \; \; \; \; r^{16}=\sqrt{2}[/tex]

Taking root of 16 on both side, we get

[tex]r=2^{1/32}[/tex]

Plugging this value of 'r' back in equation (2), we get,

[tex]\sqrt{2}\; \; e^{16i\theta }=-1-i[/tex]

Divide by √2 on both side, we get

[tex]e^{16i\theta }=-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i[/tex]

We can write [tex]e^{16i\theta }[/tex] as

[tex]\; \; \; \;cos16\theta +isin16\theta =-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i[/tex]

On comparing, we get

[tex]\; \; \; \;cos16\theta=-\frac{1}{\sqrt{2}}\;, \; \; \; \; \; \; \; sin16\theta =-\frac{1}{\sqrt{2}}[/tex]

Angle must therefore be in the third quadrant.

[tex]16\theta=\pi +\frac{\pi }{4}=\frac{5\pi }{4}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;16\theta=\frac{5\pi }{4}+2\pi =\frac{13\pi }{4}[/tex]

[tex]\theta=\frac{5\pi }{64}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{13\pi }{64}[/tex]

So, second smallest positive argument = 13π/64.

2) The equation is [tex]z^{13} = -1 +\sqrt{3i}[/tex].

We have express our answer in the form of

[tex]\; z = re^{i\theta }[/tex]

When we enter it into the first equation, we obtain,

[tex]r^{13}e^{13i\theta }=-1+\sqrt{3}i\; \; \; \; \; \; \; \; \; \; \; \;[/tex]

Using the modulus of both sides, we obtain,

[tex]\left |r^{13} \right |\: \: \left | e^{13i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( \sqrt{3} \right )^{2}}[/tex]

Simplifying

[tex]r^{13}=2[/tex]

Taking root of 13 on both side, we get

[tex]r=2^{1/13}[/tex]

Reintroducing this 'r' value into the equation from [tex]r^{13}e^{13i\theta }=-1+\sqrt{3}[/tex], we get,

[tex]2e^{13i\theta }=-1+\sqrt{3}i[/tex]

Divide 2 on both side, we get

[tex]e^{13i\theta }=-\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

We can write [tex]e^{13i\theta }[/tex] as

[tex]\; \; \; \;cos13\theta +isin13\theta =-\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

[tex]\; \; \; \;cos13\theta=-\frac{1}{2}\;, \; \; \; \; \; \; \; sin13\theta =\frac{\sqrt{3}}{2}[/tex]

Angle must therefore be in the second quadrant.

[tex]13\theta=\pi -\frac{\pi }{3}=\frac{2\pi }{3}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;13\theta=\frac{2\pi }{3}+2\pi =\frac{8\pi }{3}[/tex]

[tex]\theta=\frac{2\pi }{39}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{8\pi }{39}[/tex]

So, second smallest positive argument = 8π/39.

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Based on the given information, the theorem the paragraph proof offers proof for is: A. Alternate Interior Angles Theorem

The Alternate Interior Angles Theorem states that when two parallel lines are intersected by a transversal (a line that intersects two or more other lines), the pairs of alternate interior angles formed are congruent.

In other words, if you have two parallel lines and a transversal intersecting them, and you draw a line segment connecting two nonadjacent interior angles on opposite sides of the transversal, then those two angles will be congruent. This is because they are alternate (they are on opposite sides of the transversal and between the parallel lines) and interior (they are inside the parallel lines).

Therefore, the theorem the paragraph proof offers is: Alternate Interior Angles Theorem.

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Answer: (A) Alternate Interior Angles Theorem

Step-by-step explanation: cyberia

This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.

We have a pond which is completely filled with the water.

Area of the side face ( trapezium shaped)

= 1/2 x (1.4 + 0.6) x 2

= 2 m²

Volume = area x height (here width)

V = 2x1 = 2 m³

The level goes down by 20cm in the first 30 mins

Volume of water that will be taken down =

=0.2 x 1 x 2

=0.4 m³ ( upper water will form cuboid face)

Now,

⇒0.4 m³ water is taken out in 30 minutes

⇒1 m³ water is taken out in 30/0.4 minutes

⇒2 m³ water is taken out in 30/0.4 x 2 minutes

⇒30x2/0.4

⇒150 minutes.

So the pond will be completely empty in 150 min that is 2hrs30mins.

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When calculating the percent of pitches thrown at least 92 mph, we subtract from 100% to find the percentage of pitches that fall within a certain threshold (in this case, 92 mph).

When calculating the percentage of pitches thrown at a certain speed, say 92 mph, we use 100% as a reference point. 100% means all of the pitches. By subtracting the percentage of pitches thrown below 92 mph from 100%, we find the percentage of pitches that were thrown at 92 mph or above. This helps us understand what proportion of pitches were thrown at this speed or higher, compared to the total number of pitches thrown. By doing this, we can see how many pitches fall within a certain threshold, in this case 92 mph or above.

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The price for wrapping small gifts is $2 and the price for wrapping large gifts is $7

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

Yesterday they wrapped 12 small gifts and 45 large gifts earning a total of $339

say small gifts = g and large gifts is = G

12g + 45G = $339

Today they wrapped 35 small gifts and 42 large gifts, and earned $364

35g + 42G = $364

The simultaneous equation

12g + 45G = $339

35g + 42G = $364

solving the simultaneous equation gives

g = $2 and G = $7

Hence the price for wrapping small gifts is $2 and that of big gifts is $7

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The formula that shows how to find C, circumference, when d, diameter is given is C = πd.

Circumference is the line that bounds a circle or other two-dimensional (2D) figure.

Diameter is any straight line between two points on the circumference of a circle that passes through the centre/center of the circle.

The diameter can be used to find the radius of a circle using the following formula;

D = 2r

Circumference of a circle = 2πr

Substituting D in the equation for circumference......

Circumference of a circle = 2πd/2

Circumference of a circle = πd

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The length of the line segment ML is 15 cm.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

From the given information,

m∠LJ = m∠LM = 90°.

So, m∠LJ + m∠LM = 180°.

Line segment ML is parallel to JK.

Therefore, NP is the midline of the trapezoid.

ML + JK = 2NP.

JK = 2NP - ML.

9 = 24 - ML.

ML = 15 cm.

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