Find the rate of change between the following points:
(1,-6)
(-6,2)

The situation can be clearly represented by the equation y = 6x.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws.

As per the given data:

Relation between different cabbage eaten and minutes is given.

To find the proportional relation:

Let's consider y as pieces of cabbage eaten.

and x as the time in minutes

If the relation is y = ax

From the table

18 = a × 3 ; a = 6

30 = a × 5 ; a = 6

42 = a × 7 ; a = 6

∴ y = 6x

Hence, the situation can be clearly represented by the equation y = 6x

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The surface area of the cylinder with a radius of 1 ³/₄ and height of 3 ¹/₄ units will be 35.72 square units.

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πrh square units

The radius is 1 ³/₄ units and the height is 3 ¹/₄ units.

First, convert the mixed fraction number into a fraction number. Then we have

1 ³/₄ = 7/4 units

3 ¹/₄ = 13/4 units

The surface area of the cylinder is calculated as,

SA = 2 x 3.14 x (7/4) x (13/4)

SA = 35.72 square units

The surface area of the cylinder with a radius of 1 ³/₄ and height of 3 ¹/₄ units will be 35.72 square units.

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The complete question is given below.

Exact surface area. The radius is 1 3/4 and the height is 3 1/4 of the cylinder.

Answer:

To simplify this expression, we need to first evaluate the terms inside the square root:

(-1)² = 1

(-2 - (-1))² = (-2 + 1)² = (-1)² = 1

Now we can substitute these values and simplify the expression:

√(6 - (-1)² + (-2 - (-1))²)

= √(6 - 1 + 1)

= √6

Therefore, the simplified form of the expression is √6.

Answer:

To evaluate the expression √(6-(-1)² + (-2-(-1)²), we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

1. First, we need to evaluate the expressions inside the parentheses:

-1² = (-1) × (-1) = 1

-2-(-1)² = -2-1 = -3

2. Next, we substitute these values into the expression:

√(6-(-1)² + (-2-(-1)²)

= √(6-1 + (-2-1))

= √(5 - 3)

= √2

Therefore, the value of the expression √(6-(-1)² + (-2-(-1)²) is √2.

Step-by-step explanation:

wag na e delete ang bob0 nang mag dedelete nito

The simple interest due on a 67-day loan of $2600 at a rate of 5% is $23.86.

To calculate this, we can use the following formula: I = Prt, where I is the interest due, P is the principal (or initial loan amount), r is the interest rate, and t is the time in years. We can calculate the time in years by taking the number of days (67) divided by the number of days in a year (365). Therefore, t = 0.1831. We can now plug this into our formula to get I = 2600 * 0.05 * 0.1831, which simplifies to I = 21.50. Therefore, the simple interest due is $21.50.

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Option (a) [tex]-\frac{23}{3}[/tex]  is the smallest among the four option because it has negative value. We can easily find it by seeing negative value but we do by taking LCM of denominator .

The smallest multiple that two or more numbers share is known as the least common multiple. Least Common Multiple short form is LCM.

We can find LCM of these number by taking least common multiple.

LCM of 3, 3, 17, 13 is 663 .

(a) [tex]-\frac{22}{3} *663 = -22*221[/tex]

[tex]= -4862[/tex]

(b) [tex]\frac{4}{3} * 663 = 4 * 221[/tex]

[tex]= 884[/tex]

(c) [tex]\frac{6}{17} *663 = 6 * 17[/tex]

[tex]= 102[/tex]

(d) [tex]\frac{2}{13}*663 = 2*51[/tex]

[tex]=102[/tex]

So, the Smallest no [tex]-\frac{22}{3}[/tex].

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The horizontal distance between the airplane and runway is, 2607.6 meters or 2.6 kilometers

To solve the problem, we can use the tangent function, which relates the opposite side of a right triangle to its adjacent side:

tanα = opposite/adjacent

where theta is the angle of depression, opposite is the height of the airplane above the ground, and adjacent is the horizontal distance between the airplane and the beginning of the runway.

We can rearrange this formula to solve for adjacent:

adjacent = opposite/tanα

Plugging in the values, we get:

adjacent = 500/tan(11°)

adjacent ≈ 2607.6

Therefore, the horizontal distance between the airplane and the beginning of the runway is approximately 2607.6 meters or 2.6 kilometers when rounded to the nearest tenth of a kilometer.

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Opposite interior bof a quadrilateral are supplementary if and only if the quadrilateral is cyclic.

A quadrilateral is called cyclic if its vertices lie on a circle. This means that there is a circumcircle that passes through all four vertices of the quadrilateral. If opposite interior angles of a quadrilateral are supplementary, then the sum of these angles is 180 degrees. This means that the opposite angles of a cyclic quadrilateral are supplementary.

To prove this, let us consider a quadrilateral ABCD that is cyclic. Let O be the center of the circumcircle that passes through all four vertices of the quadrilateral.

Since the quadrilateral is cyclic, angle AOB and angle COD are both subtended by the same arc, and therefore they are equal. Similarly, angle BOC and angle DOA are both subtended by the same arc, and therefore they are equal.

Now, let us consider the sum of the opposite interior angles of the quadrilateral.

Angle A + angle C = angle AOB + angle BOC + angle COD + angle DOA = 2(angle AOB) + 2(angle BOC) = 2(180) = 360

Since the sum of the opposite interior angles of the quadrilateral is 360 degrees, this means that the opposite interior angles of the quadrilateral are supplementary.

Therefore, opposite interior angles of a quadrilateral are supplementary if and only if the quadrilateral is cyclic.

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Interval notation is (−∞, −4) U (−4, ∞)

The given inequality is ∣x + 4∣ > − 9. Step-by-step explanation: Absolute value inequalities: Inequalities that contain absolute values are known as absolute value inequalities. The absolute value inequality ∣x + 4∣ > − 9 is given.Inequality means that x can take any value except the value that makes the inequality false. If x satisfies the inequality, we write x ∈ (A, B) or x ∈ [A, B), where A and B are any two values that satisfy the inequality.The inequality ∣x + 4∣ > − 9 implies that the absolute value of x + 4 is greater than −9. The absolute value of x + 4 is always greater than or equal to zero.Therefore, the inequality can be written as∣x + 4∣ > 0This inequality implies that x is not equal to −4.The interval of x satisfying the given inequality is x ∈ (−∞, −4) U (−4, ∞), where U represents the union of two intervals. Therefore, the answer in interval notation is (−∞, −4) U (−4, ∞).Thus, the solution to the inequality |x + 4| > -9 in interval notation is (−∞, −4) U (−4, ∞).

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a) The value of k is 0.04.

b) The value of E[X] is 3.3333 and the value of var[X] is 1.3889.

c) The standard deviation of G is 5.8916.

d) The standard deviation of H is 7.0711.

(a) To find the value of k that ensures that f(x) is a proper density function, we need to ensure that the integral of f(x) over its domain is equal to 1:

∫05 (0.1 + kx) dx = 1

0.5 + 12.5k = 1

12.5k = 0.5

k = 0.04

Therefore, the value of k is 0.04.


(b) To find E[X], we need to evaluate the integral of x*f(x) over its domain:

E[X] = ∫05 x(0.1 + 0.04x) dx

E[X] = 0.5 + 0.02(125/3) = 3.3333

To find var[X], we need to evaluate the integral of (x - E[X])2*f(x) over its domain:

var[X] = ∫05 (x - 3.3333)2(0.1 + 0.04x) dx = 1.3889


(c) If G = 5X - 6, then E[G] = 5E[X] - 6 = 11.6667 and var[G] = 52var[X] = 34.7225. The standard deviation of G is the square root of var[G], which is 5.8916.


(d) If H = 5 - 6X, then E[H] = 5 - 6E[X] = -14.9998 and var[H] = 62var[X] = 49.9994. The standard deviation of H is the square root of var[H], which is 7.0711.

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Answer: 24

Step-by-step explanation:

Answer:

60% of 44 is 26.4

Step-by-step explanation:

In response to supplied query, we may state that The connection shown in the table is represented by a linear equation in the slope-intercept form.

In mathematics, the intersection point is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that may be rewritten to seem to be slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.

We must know the slope and the y-intercept of the line in order to find the slope-intercept form of a linear equation.

The first and last points in the table should be chosen:

slope = [tex](5 - (-5)) / (3 - (-2)) = 10/5 = 2[/tex]

Now that we have the slope, we can write the equation of the line using the point-slope form of a linear equation:

y - y1 = m(x - x1) (x - x1)

Each position along the line may be chosen as (x1, y1). Let's pick point number one (3, -5):

[tex]y - (-5) = 2(x - 3) (x - 3)\\y + 5 = 2x - 6\\y = 2x - 11[/tex]

The connection shown in the table is represented by a linear equation in the slope-intercept form.

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The correct answer to this question is a. 13/3.

To find the value of E(x^2), we need to multiply each value of x by its corresponding probability and then sum the results. This can be written as E(x^2) = (1^2)(1/6) + (2^2)(2/3) + (3^2)(1/6).

Simplifying the equation gives us:

E(x^2) = (1/6) + (8/3) + (9/6) = (1/6) + (16/6) + (9/6) = (26/6) = 13/3

Therefore, the value of E(x^2) is 13/3.

In conclusion, the correct answer to this question is a. 13/3.

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The reference angle for θ = 27π/2 is θr = π/4 and the associated point on the unit circle is (x, y) = (√2/2, √2/2).

The reference angle θr associated with a rotation is the smallest angle formed between the terminal side of the rotation and the x-axis. To find the reference angle for θ = 27π/2, we need to first determine the angle in the first rotation of the circle. Since there are 2π radians in a full circle, we can divide 27π/2 by 2π to find the number of full rotations:

27π/2 ÷ 2π = 27/4 = 6 3/4

This means that there are 6 full rotations and a partial rotation of 3/4. The reference angle for this partial rotation is θr = π/4.

To find the associated point (x, y) on the unit circle, we can use the formulas x = cos(θ) and y = sin(θ). For θ = 27π/2, we can use the reference angle θr = π/4:

x = cos(π/4) = √2/2
y = sin(π/4) = √2/2

Therefore, the associated point is (x, y) = (√2/2, √2/2).

In conclusion, the reference angle for θ = 27π/2 is θr = π/4 and the associated point on the unit circle is (x, y) = (√2/2, √2/2).

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We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

Which nation experienced the hottest summer?

We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.

Country A: (21.4°C) (18+20+22+23+24)/5

(24+26+28+29+27)/5 = 26.8°C for Country B.

The summer was therefore hotter in Country B, with an average temperature of 26.8°C.

b) Over the summer, which nation saw more erratic weather?

We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.

24°C - 18°C equals 6°C in Country A.

29°C - 24°C equals 5°C in country B.

As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

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The statistical measures or five-number summary for the given data set are as follows:

In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

In order to determine the five-number summary, we would arrange the data set in an ascending order:

4,6,6,8,11,12,13,17

Next, we would use an online graphing calculator to create the box plot as shown in the image attached below.

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Answer:

Step-by-step explanation:

Well first we know that there are 25 squares. If we use some quick arithmetic, we can find how much each square represents out of 100%:

100/25 = 4

100% divided by 25 squares represents 4% for each square in the diagram. If we want to cover 48%, we can use some algebra:

4s = 48

s = 12

We need to shade in 12 squares to cover 48% of the diagram.

Hopefully this explanation was thorough enough!

[tex]Area = \dfrac{6(7)}{2} = \dfrac{42}{2} = 21 \ cm^{2}[/tex]

Answer: x = 47.2°

Step-by-step explanation:

     We can use a trigonometry function to solve this question since it's a right triangle.

     Equation:

tanx = [tex]\frac{27}{25}[/tex]

     The tangent inverse of both sides of the equation:

[tex]\displaystyle tan^{-1} (\text{tan}x)=(\frac{27}{25} )tan^{-1}[/tex]

x = 47.2°

Answer:

3,200 Square centimeters

Step-by-step explanation:

In order to solve for the perimeter of a square with side lengths of 60, we can use this expression:

(We multiply by 4 because a square has four equal side lengths, and the perimeter is all of the side lengths added up)

Therefore, the perimeter of the square is 240cm.

Now that we know this, we can now take that perimeter, and subtract 160 from it.

(We subtract 160 from it because the length of the rectangle is 80cm, and because a rectangle has two sides that represent the length, we multiply the 80 by 2.)

Now, we can divide the 80 by 2 to get the length of the other 2 sides.

Therefore, the rectangles dimensions are 80cm by 40cm.

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve for the area of a rectangle, we use the expression:

Inserting the numbers into the equation:

Therefore, the area of the rectangle is 3,200 square centimeters.

The median is 138.

What is the median?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Here, we have

Given: data set:

135, 149, 156, 112, 134, 141, 154, 116, 134, 156.

To get the box plot we begin by arranging the data in ascending order:

135, 149, 156, 112, 134, 141, 154, 116, 134, 156

rearranging the data set we get:

112,116, 134, 134, 135, 141, 149, 154, 156, 156

then:

Lower value = 112

Q1 = 134

Median = (135+141)/2 = 138

Q3 = 154

Largest value =156

Hence, the median is 138.

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1. The equation for the cost of adult tickets is:

$8.97 x number of adult tickets

The equation for the cost of child tickets is:

$6.79 x number of child tickets

The equation for the cost of renting out the theater is:

$190

2. Yes, you can get at least 5 adult tickets and 4 kids tickets.

3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.

4.  It would be a better deal to rent out the theater if you had more than 24 people.

You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.

The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.

Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.

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Answer:

I think the original price of the pants is $20.63

Step-by-step explanation:

25% of 16.50 is 4.125

4.125 + 16.50 = 20.625

20.625 - 4.125 = 16.50 (the price after the discount is subtracted from it)

round 20.625 to the nearest cent and you get 20.63.

Hope this helps!

Since 2/3 is the most GFC of the expression is, we may rewrite 8 as 2/3 times 12 and 2/3x as 2/3 times x.

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both. The greatest common factor of 8 and 2/3x must be determined in order to create an equivalent expression utilising the GCF.

1, 2, 4, and 8 make up the number 8. 2/3x has the following factors: 1/3, 2/3, and x.

We thus have: 8/3 - 2/3x

= (2/3 * 4) / (2/3) - (2/3 * x)

= (2/3)(4 - x) (4 - x)

As a result, using the GCF, the formula for 8/3 - 2/3x is (2/3) (4 - x).

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Answer: It will take the rope 5 seconds to reach the ground if it continues travelling at a speed of 10 m/s

Step-by-step explanation:If the rope is going 10 m/s down a 50 m cliff,

50/10=5 It will take it 5 seconds becuase it is going at a speed of 10 meters a second

The domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0

The domain and range of a function are the set of possible inputs and outputs, respectively.

1. For the function \( f(x)=3 x^{2}+2 \), the domain is all real numbers because there are no restrictions on the input. The range is also all real numbers because the output can be any value.

2. For the function \( f(x)=\frac{1}{1-x} \), the domain is all real numbers except x=1, because when x=1, the denominator becomes 0 and the function is undefined. The range is also all real numbers except y=0, because the output can never equal 0.

3. For the function \( f(x)=\sqrt{x+2} \), the domain is all real numbers greater than or equal to -2, because the square root of a negative number is not a real number. The range is all real numbers greater than or equal to 0, because the square root of a number is always positive or 0.

In conclusion, the domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0

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Given that it includes a quadratic term ([tex]b^{2}[/tex]), this formula reduces to 4b(b) = 0, which is a complex quantity.

A function with the formula a=0, b=1, and c=2 is known as a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).

The quadratic formula may be used to determine a parabola's axis of symmetry, the amount of real zeros in the quadratic equation, and the noughts of any parabola. It also produces the zeros of the any parabola.

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If the mean of five scores is 27, then the number 33 must be added to the previous five scores to make the mean of six scores as 28.

It is given that mean of five scores is 27. If the unknown number x is added to the five scores, the new mean becomes 28. To calculate the value of x, the following equations are considered.

Let us say that the five scores are A, B, C, D and E.

∴ Mean of five scores = (A+B+C+D+E)/ 5 = 27

⇒ (A+B+C+D+E) = 27 × 5 = 135

Now, if sixth score x is added, then mean score becomes 28.

⇒ (A+B+C+D+E+x)/ 6 = 28

⇒ (A+B+C+D+E+x) = 28×6 = 168

Putting the value of (A+B+C+D+E) in above equation, we get:

135 + x = 168

x = 168 - 135 = 33

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Answer:

3^2 = 9

So 9 is the number.

The polynomial as a product of linear factor [tex]9(x) = x4 - 2x3 + 5x2 8x + 4 g(x)[/tex] are g(x) = (x-2)(x-1)(x+1)(x+4) , all the zeros of function are 2,1,-1,-4.

In order to write the polynomial as a product of linear factors, we must first find its zeros. The zeros of a polynomial are the values of x that make the polynomial equal to zero. The way to find the zeros is to set the polynomial equal to zero, and solve for x.

For this particular polynomial, the equation would be: x^4 - 2x^3 + 5x^2 + 8x + 4 = 0.

We can solve this equation by factoring. When factoring, we look for common factors among the terms and group them together. After factoring, the equation becomes: (x - 2)(x - 1)(x + 1)(x + 4) = 0.

The zeros of the equation are x = 2, 1, -1, -4. This means that the polynomial can be written as the product of linear factors, which is (x-2)(x-1)(x+1)(x+4). The zeros of this function are x = 2, 1, -1, -4.

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The polynomial as the product of linear factors. 9(x) = x4 - 2x3 + 5x2 8x + 4 g(x) is a product of (x - 2)(x - 1)(x + 1)(x + 4) . All the zeros of function are x = 2,1,-1,-4.

In order to write the polynomial as a product of linear factors, we must first find its zeros. The zeros of a polynomial are the values of x that make the polynomial equal to zero. The way to find the zeros is to set the polynomial equal to zero, and solve for x.

For this particular polynomial, the equation would be: x^4 - 2x^3 + 5x^2 + 8x + 4 = 0.

We can solve this equation by factoring. When factoring, we look for common factors among the terms and group them together. After factoring, the equation becomes: (x - 2)(x - 1)(x + 1)(x + 4) = 0.

The zeros of the equation are x = 2, 1, -1, -4. This means that the polynomial can be written as the product of linear factors, which is (x-2)(x-1)(x+1)(x+4).

The zeros of this function are x = 2, 1, -1, -4.

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Check the picture below.

so the base of the pyramid is a triangle whose base is 12 and altitude is "x", and the pyramid has a height/altitude of 15, so

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(12)(x)\\[1em] h=15\\ V=240 \end{cases}\implies 240=\cfrac{1}{3}\left[\cfrac{1}{2}(12)(x) \right](15) \\\\\\ 240=30x\implies \cfrac{240}{30}=x\implies 8=x[/tex]