7. AFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph AFIG and AP'I'G' after a rotation of 90° clockwise about the origin.​

Option A) Cannot tell with the given information as the question doesn't provide any information about the relationship between having a dog and having a cat.

Without additional information, we cannot determine if these events are independent, dependent, disjoint, or have any other relationship. Independent events are events in which the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.

In other words, the probability of one event happening does not depend on whether or not the other event happens.

Formally, events A and B are independent if and only if:

P(A ∩ B) = P(A) * P(B)

Where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A ∩ B) is the probability of both events A and B occurring simultaneously.

If the above equation holds true, then we can say that events A and B are independent. If not, then events A and B are dependent.

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Variable expenses are expenses that fluctuate from month to month, and are typically not a fixed amount. Examples of variable expenses include groceries, fuel, clothing, and entertainment. These expenses can be influenced by various factors such as personal choices, seasonality, and external events.

In Luis's expenses, the following expenses are variable expenses:

On the other hand, the following expenses are fixed expenses:

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Answer:

groccieries is the answer for plato 2023

Answer:

80

Step-by-step explanation:

v=bxh

v=10x8

v=80

The solution to the inequality is x ≥ -1.

We solve the inequality 1/3(2x-1)≤1-2/5(2-3x).

Let's go step by step:
Begin by distributing the fractions to the terms inside the parentheses:
  (1/3 * 2x) - (1/3 * 1) ≤ 1 - (2/5 * 2) + (2/5 * 3x)
  (2x/3) - (1/3) ≤ 1 - (4/5) + (6x/5)
Combine like terms on each side of the inequality:
  (2x - 1)/3 ≤ (1 - 4/5) + 6x/5
  (2x - 1)/3 ≤ (1/5) + 6x/5.

To eliminate the fractions, find a common denominator, which in this case is 15.

Multiply each term by 15:
  15 * (2x - 1)/3 ≤ 15 * (1/5) + 15 * 6x/5
  5(2x - 1) ≤ 3 + 18x
Distribute and simplify:
  10x - 5 ≤ 3 + 18x
Move the variables to one side and constants to the other side:
  10x - 18x ≤ 3 + 5
  -8x ≤ 8
Divide both sides by -8 (remember to flip the inequality sign since we are dividing by a negative number):
  x ≥ -1.

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Answer:

Baltimore Train: 1,020 mi/12 hr = 85 mph

Pennsylvania Train: 75 mph

So the correct answer is A.

The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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Answer: ln|y/8| + C
Explanation:

First, we need to recognize that the derivative of arctan(x) is 1/(1+x^2). Therefore, the derivative of arctan(y/8) is 8/(64+y^2).

Now, using the substitution u = y/8, we can rewrite the integral as:

∫(1/u)(64+64u^2)(8/(64+64u^2))du

Simplifying, we get:

∫(1/u)du = ln|u| = ln|y/8|

Therefore, the final answer is:

ln|y/8| + C

where C is the constant of integration.

The button's area is approximately 50.27 square centimeters.

To find the area of the button, we need to know the diameter of the button. We can find this by using the formula for circumference of a circle:

C = πd

where C is the circumference and d is the diameter.

Substituting the given value for C:

25.12 cm = πd

Solving for d:

d = 25.12 cm / π

d ≈ 8 cm

Now that we know the diameter, we can use the formula for area of a circle:

A = πr^2

where r is the radius (half the diameter).

Substituting the value for d:

r = d/2 = 4 cm

Substituting this value into the formula:

A = π(4 cm)^2

A ≈ 50.27 cm^2

Therefore, the button's area is approximately 50.27 square centimeters.

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The equation that represents the asymptote of the function, y = tan x is: C. x = π/4.

Option A, x = -π, and Option D, x = (3π)/2, do not represent asymptotes of the graph of the function y = tan x.

Option B, x = 0, represents a vertical asymptote of the graph of y = tan x because tan x is undefined at x = π/2 + kπ, where k is an integer. Therefore, tan x is undefined at x = π/2, 3π/2, 5π/2, etc. and there is a vertical asymptote at x = 0.

Option C, x = π/4, represents a linear asymptote of the graph of y = tan x. As x approaches π/4 from either side, the tangent function approaches a straight line with slope 1 and x-intercept 0. Therefore, the equation of the asymptote is y = x - π/4.

Thus, the answer is C. x = π/4.

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Answer: $193.42

Step-by-step explanation:

Based on the given designs, the cost to make the triangular and circular street signs would be $68.60 and $124.42 respectively, making the total cost of making both signs $193.02.

To calculate the cost of making the two street signs, we need to first find the area of each sign. The area of a triangle is given by the formula 1/2 x base x height. So, for the triangular street sign, the area would be 1/2 x 3 x 2.6 = 3.9 square feet.

The area of a circle is given by the formula π x radius². So, for the circular street sign, the area would be π x (1.5)² = 7.065 square feet.

Now that we have the areas of both signs, we can calculate the total cost of the material needed. The cost per square foot of material is $17.64, so we need to multiply this by the total area of the signs.

For the triangular sign, the cost would be 3.9 x $17.64 = $68.60.

For the circular sign, the cost would be 7.065 x $17.64 = $124.42.

Therefore, the total cost to make both signs would be $68.60 + $124.42 = $193.02.

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The average rate of change for the number of shares from 2 minutes to 4 minutes is 25 shares per minute.

To find the average rate of change for the number of shares from 2 minutes to 4 minutes, we need to know the initial number of shares at 2 minutes and the final number of shares at 4 minutes. Once we have those values, we can use the formula:

average rate of change = (final value - initial value) / (time elapsed)

Let's say the initial number of shares at 2 minutes was 100 and the final number of shares at 4 minutes was 150. The time elapsed between 2 minutes and 4 minutes is 2 minutes. Plugging these values into the formula, we get:

average rate of change = (150 - 100) / 2
average rate of change = 50 / 2
average rate of change = 25

Therefore, the average rate of change is 25 shares per minute.

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The type of statistical study in which the population is influenced by researchers is known as an experimental study.

In an experimental study, researchers manipulate one or more variables to observe the effect on another variable. The population in an experimental study is usually a sample that is randomly selected to represent the larger population.

The researchers intentionally intervene in the study, which can impact the behavior or responses of the participants. This can be seen as a form of bias since the researchers are influencing the population. However, in some cases, this is necessary to determine causality or to test a hypothesis.

To minimize bias, experimental studies often use control groups. The control group is used to provide a baseline for comparison with the group that is exposed to the manipulated variable. This helps to determine if any observed effects are due to the intervention or if they are due to other factors.

In summary, an experimental study is the type of statistical study in which the population is influenced by researchers. While this can introduce bias, the use of control groups and other measures can help to minimize the impact of this bias on the results.

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r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.

a. To test whether there is a significant reduction in mental alertness after consuming tryptophan versus before, we can use a paired samples t-test. The null hypothesis is that there is no difference in mental alertness scores before and after the meal, and the alternative hypothesis is that the scores are lower after the meal:

H0: μd = 0 (no difference)

Ha: μd < 0 (lower scores after the meal)

Here, μd is the mean difference score in mental alertness before and after the meal. We will use a one-tailed test with α = .05, since we are only interested in the possibility of lower scores after the meal.

The t-statistic for a paired samples t-test is calculated as:

t = (Md - μd) / (sd / sqrt(n))

Where Md is the mean difference score, μd is the hypothesized mean difference (in this case, 0), sd is the standard deviation of the difference scores, and n is the sample size.

We are given that Md = 14, and the standard deviation of the difference scores (sd) is:

sd = sqrt(SSd / (n - 1)) = sqrt(1152 / 8) = 12

Substituting these values, we get:

t = (14 - 0) / (12 / sqrt(9)) = 3.5

Using a one-tailed t-distribution table with 8 degrees of freedom and α = .05, the critical value is -1.86. Since our calculated t-value (3.5) is greater than the critical value, we reject the null hypothesis and conclude that there is a significant reduction in mental alertness after consuming tryptophan versus before.

b. To compute r2 to measure the size of the effect, we can use the formula:

r2 = t2 / (t2 + df)

Where t is the calculated t-value for the test, and df is the degrees of freedom, which is n-1 in this case.

Substituting the values , we get:

r2 = (3.5)2 / ((3.5)2 + 8) = 0.523

Therefore, r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.

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Answer:

First, we need to calculate the control limits for the X-chart. Since the sample size is 4, the standard deviation of the sample mean is:

σ/√n = 2/√4 = 1

The 3σ control limits for the X-chart are:

Upper Control Limit (UCL) = 8 + 3(1) = 11

Lower Control Limit (LCL) = 8 - 3(1) = 5

Next, we need to find the probability that a point falls outside the control limits when the process mean shifts to 9. This can be calculated using the Gaussian distribution:

P(X < 5 or X > 11) = P(Z < (5-9)/2) + P(Z > (11-9)/2) = 0.00135 + 0.00135 = 0.0027

where Z is the standard normal distribution.

Therefore, the average run length (ARL) is:

ARL = 1/p = 1/0.0027 = 370.37

So on average, it will take 370.37 samples before the process mean shift is detected on an X-chart.

The maximum concentration of the antibiotic between hours 1 and 7 is 1.03 mg/ug, which occurs at t = 1/39 hours.

To find the maximum concentration of the antibiotic between hours 1 and 7, we need to find the maximum value of the function C(t) on the interval [1, 7]. We can do this by taking the derivative of C(t), setting it equal to zero, and solving for t.

C(t) = 4te^{-39t}

C'(t) = 4e^{-39t} - 156te^{-39t}

Setting C'(t) equal to zero, we get:

4e^{-39t} - 156te^{-39t} = 0

4e^{-39t}(1 - 39t) = 0

1 - 39t = 0

t = 1/39

We can now evaluate C(t) at t = 1/39 and the endpoints of the interval [1, 7] to determine the maximum concentration:

C(1) = 4e^{-39} ≈ 0.00011 mg/ug

C(7) = 28e^{-273} ≈ 0.000000003 mg/ug

C(1/39) = 1.0256 mg/ug

Therefore, the maximum concentration of the antibiotic between hours 1 and 7 is 1.03 mg/ug, which occurs at t = 1/39 hours.

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Let the fraction be x/y.

We know that x + y = 12, and that (x) / (y + 3) = 12.

Multiplying both sides of the second equation by (y + 3), we get:

x = 12(y + 3)

Substituting this into the first equation, we get:

12(y + 3) + y = 12

Expanding and simplifying, we get:

13y + 36 = 12

Subtracting 36 from both sides, we get:

13y = -24

Dividing both sides by 13, we get:

y = -24/13

Substituting this value of y into the equation x + y = 12, we get:

x - 24/13 = 12

Multiplying both sides by 13, we get:

13x - 24 = 156

Adding 24 to both sides, we get:

13x = 180

Dividing both sides by 13, we get:

x = 180/13

Therefore, the fraction is 180/13 divided by -24/13, which simplifies to -15/2.

The ferris wheel will take a total time of 10 seconds for the platform to reach the 11 o'clock position and the diver's height off the ground when he is at the 11 o'clock position is 50 feet.

To determine the time it takes for the platform to reach the 11 o'clock position and the diver's height off the ground, we will use the given information about the ferris wheel.

1. The ferris wheel has a radius of 50 ft and turns counterclockwise at a constant speed with a period of 40 seconds.
2. The center of the wheel is 65 ft off the ground.
3. The platform is at the 3 o'clock position when it starts moving (t=0).

The ferris wheel has a period of 40 seconds, which means it takes 40 seconds for it to make a full rotation. The distance between the 3 o'clock position and the 11 o'clock position is 90 degrees out of 360, which is one-fourth of the total distance around the circle.

Therefore, it will take 1/4 of the total time for the platform to reach the 11 o'clock position, which is 40/4 = 10 seconds.

To find the diver's height off the ground at the 11 o'clock position, we can use the sine function. Let's call the angle formed by the radius from the center of the ferris wheel to the diver and the radius from the center of the ferris wheel to the 3 o'clock position θ.

Since the platform starts at the 3 o'clock position and rotates counterclockwise, θ will increase as time passes. At the 11 o'clock position, θ will be 90 degrees.

We know that the radius of the ferris wheel is 50 feet and the center of the ferris wheel is 65 feet off the ground. Let's call the height of the diver off the ground h. Then we have:

sin θ = h / (50 ft)

h = (50 ft) * sin θ

At the 11 o'clock position, θ = 90 degrees, so we have:

h = (50 ft) * sin 90°

h = 50 ft

Therefore, the diver's height off the ground when he is at the 11 o'clock position is 50 feet.

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To find the derivative of h(x) = 8x, we use the power rule, which states that the derivative of x^n is nx^(n-1). Applying this rule to h(x), we get h'(x) = 8.

To find the value of h'(4), we simply plug in x = 4 into our derivative expression: h'(4) = 8.

Therefore, the derivative of h(x) = 8x at x = 4 is h'(4) = 8.
To find the derivative of the function h(x) = 8x at x = 4, you can use the power rule for differentiation. The power rule states that if h(x) = x^n, then h'(x) = n * x^(n-1).

For h(x) = 8x, n = 1, so:

h'(x) = 1 * 8x^(1-1) = 8

Now, to find h'(4), just plug in x = 4:

h'(4) = 8

So, h'(4) = 8.

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Answer:

y = 5x + 5

Step-by-step explanation:

If x is the number of boxes sold and y is the cost

The first box costs $10

Each additional box costs $5.

If the total number of boxes sold is x, then after selling the first box for $10, there will be x - 1 boxes left to be sold

The cost of x -1 boxes at $5 per box = 5(x - 1) = 5x - 5

Therefore for a total of x boxes sold the total cost, y in dollars is
y = 10 (for the first box)  +  5x - 5 (for the remaining x - 1 boxes)

= 10 + 5x - 5

= 5 + 5x

which in standard form is written as
y = 5x + 5

We can verify our equation using specific numbers for x
For x = 1
y = 5 + 5(1) = 10   ; since only one box has been sold, the cost is fixed at $10

For x = 2 y = 5 + 5(2) = 5 + 10 = $15
This works out to since first box is sold at $10 and the second box at $5

Leave it to you to work out for other numbers

The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the  t-value (-1.732) is less than the critical value (-2.429).

Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.

Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.

Level of significance = 1%

We can use a one-sample t-test to test the hypothesis.

t = (X - μ) / (s / √n)

where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the values, we get

t = (998,946 - 1,000,000) / (23,876 / √65)

t = -1.732

Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.

Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.

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The solution of the graphs of the equations is; )(6, 3 2/3)

A system of equation consists of two or more equations that share the same variables.

The solution of a system of equations obtained graphically can be obtained from the point of intersection of the lines of the graph of the equations

Taking the axis as the lowermost and  leftmost white lines, we get;

The points on the function f are (0, 1), and (9, 5)

The slope is; (5 - 1)/(9 - 0) = 4/9

The y-intercept is; (0, 1)

The equation is; y = (4/9)·x + 1

The equation of the line g is; x = 6

Therefore, the point of intersection is; y = (4/9)×6 + 1 = 8/3 + 1 = 11/3 = 3 2/3

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The value of x is 26.5, found using the property of intersecting chords in a circle and the Pythagorean theorem.

To find the value of x, we can use the property that states that if two chords intersect in a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

In this case, we can draw radii from O to points P and S, and label their lengths as 19. Then, we can label the segments of chords FG and RS as follows:

                     Let a = FG and b = GP

                      Let c = RS and d = SP

Since OP is a radius of the circle, we know that a + b = 19. Similarly, since OS is a radius of the circle, we know that c + d = 19.

Using the property mentioned above, we can write:

                      a * b = c * d

Substituting the given values, we get:

                   25 * (19 - b) = 28 * (19 - d)

Expanding and simplifying, we get:

                      475 - 25b = 532 - 28d

Substituting a + b = 19 and c + d = 19, we get:

                 b = 19 - a and d = 19 - c

Substituting these values, we get:

                 25a - 25(19 - a) = 28c - 28(19 - c)

Simplifying, we get:

                    53a - 475 = 28c - 532

Rearranging, we get:

                       53a - 28c = -57

We also know that a + c = 25 + 28 = 53.

We can solve these two equations simultaneously to find the values of a and c:

                        a = 13.8

                        c = 39.2

Therefore, the length of the segment RS is 39.2, and the length of the segment RP19S is 58.2.

Using the Pythagorean theorem, we can find the length of the segment OP:

                  (OP)²= (RP19S)² - (19)²

                  (OP)² = (58.2)² - (19)²

                  (OP)² = 3136.24

                        OP = 56

Finally, we can find x using the fact that the chords FG and RS are parallel:

                           x = (1/2) * (FG + RS)

                           x = (1/2) * (25 + 28)

                           x = 26.5 (rounded to the nearest tenth)

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The smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.

To find the measure of both angles in a right triangle with the given conditions, we will use the information provided:

Let x be the measure of the smallest angle. The problem states that the measure of one of the small angles is 30 less than 7 times the smallest angle, which can be written as:

Other non-right angle = 7x - 30

Since this is a right triangle, the sum of the two small angles must be 90 degrees (because the other angle is 90 degrees, and the sum of angles in a triangle is 180 degrees). So, we can set up the following equation:

x + (7x - 30) = 90

Now, solve for x:

8x - 30 = 90
8x = 120
x = 15

So, the smallest angle is 15 degrees. Now, we can find the measure of the other non-right angle:

Other non-right angle = 7x - 30 = 7(15) - 30 = 105 - 30 = 75 degrees

In summary, the smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.

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The value of x as an improper fraction in its simplest form is 14/5.

To solve the inequality 5x - 4 < 10, we need to isolate x on one side of the inequality. First, we add 4 to both sides:

5x - 4 + 4 < 10 + 4

5x < 14

Then, we divide both sides by 5:

5x/5 < 14/5

x < 2.8

Therefore, the solution to the inequality is x < 2.8. However, the question asks for the answer as an improper fraction in its simplest form. To convert 2.8 to an improper fraction, we multiply both the numerator and denominator by 10 to get rid of the decimal:

2.8 * 10 / 1 * 10 = 28 / 10

To simplify the fraction, we divide both the numerator and denominator by their greatest common factor, which is 2:

28 / 10 = 14 / 5

Therefore, the answer is 14/5.

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When Kimberly rolls two six-sided number cubes numbered 1 through 6, it creates 36 possible outcomes which is represent in the tree diagram below

A tree diagram is a visual representation of outcomes. It consists of branches that represent the possible outcomes of each step.

When it comes to Kimberly rolling two six-sided number cubes, we can start by rolling the first cube, and then rolling the second cube.

For each roll of the first cube, there are six possible outcomes (1 to 6). For each outcome of the first cube, there are six possible outcomes for the second cube.

This results in a total of 6 x 6 = 36 possible outcomes.

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A score of at least 183 is required to stay out of the bottom 1.5%. To find the minimum score required to receive the award, we need to determine the z-score corresponding to the top 3% of students.

Since the distribution is normal, we can use the standard normal distribution table to find the z-score. From the table, we find that the z-score corresponding to the top 3% is approximately 1.88.

Therefore, we can use the formula z = (x - μ) / σ, where μ = 400 and σ = 100, to find the minimum score required: 1.88 = (x - 400) / 100

Solving for x, we get: x = 1.88(100) + 400 = 488. Therefore, a score of at least 488 is required to receive the award.

To find the minimum score required to stay out of the bottom 1.5%, we need to determine the z-score corresponding to the bottom 1.5%.

From the standard normal distribution table, we find that the z-score corresponding to the bottom 1.5% is approximately -2.17. Therefore, we can use the same formula as before to find the minimum score required: -2.17 = (x - 400) / 100.

Solving for x, we get: x = -2.17(100) + 400 = 183. Therefore, a score of at least 183 is required to stay out of the bottom 1.5%.

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Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

To answer your question about how many cups of water Abby should add to make 1 gallon of punch, let's first convert all the given measurements to cups. One gallon is equivalent to 16 cups.

1. Orange juice: Abby uses 2 quarts of orange juice. Since there are 4 cups in a quart, she uses 2 x 4 = 8 cups of orange juice.

2. Lemon juice: Abby uses 1 cup of lemon juice.

3. Pineapple juice: Abby uses 2 1/2 pints of pineapple juice. There are 2 cups in a pint, so she uses (2 1/2) x 2 = 5 cups of pineapple juice.

Now, let's add up the cups of orange juice, lemon juice, and pineapple juice: 8 + 1 + 5 = 14 cups. Since Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

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An answer option that could represent the quadratic equation, and why is: B.  x² + 2x - 35 = 0, the factors are (x + 7) and (x - 5) and (x + 7)(x - 5) = x² + 2x - 35.

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;

y = (x + 7)(x - 5)

y = x² + 2x - 35

x² + 2x - 35 = 0

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

You want the segment lengths DA and DE of the hypotenuse in the triangle shown in the figure.

The radius to a point of tangency always makes a right angle with the tangent. This is a right triangle with legs 8 and 15, so you know from your knowledge of Pythagorean triples that the hypotenuse is 17.

  DA = 17

  DE = 17 -8 = 9

__

Additional comment

In case you haven't memorized a few of the useful Pythagorean triples, {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, you can always figure the missing side length of a right triangle using the Pythagorean theorem.

It tells you the sum of the squares of the legs is the square of the hypotenuse:

  AC² +CD² = DA²

  8² +15² = DA²

  64 +225 = 289 = DA²

  DA = √289 = 17

Of course, AE is the radius of the circe, 8, so ...

  AE + DE = DA

  8 +DE = 17

  DE = 17 -8 = 9

Alternatively, you can solve this using the relation between tangents and secants. If the line DA is extended across the circle to intersect it again at X, then ...

  DC² = DE·DX

  15² = DE·DX = DE(DE +16) . . . . . . . EX is the diameter, twice the radius of 8

  DE² +16DE -225 = 0

  (DE +25)(DE -9) = 0 . . . . factor

  DE = 9  . . . . the positive solution

  DA = 9 +8 = 17

We like the Pythagorean theorem solution better, as the factors of the quadratic may not be obvious.

The height of the lean-to on its vertical side is 8 feet.

To find the height of the lean-to on its vertical side, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the vertical side is the hypotenuse, and the length and width are the other two sides.

So, we have:

[tex]height^2 = hypotenuse^2 - width^2[/tex]

We know the length of the roof (the hypotenuse) is 17 feet, and the width is 15 feet. So we can plug these values into the equation and solve for the height:

[tex]height^2 = 17^2 - 15^2\\height^2 = 289 - 225\\height^2 = 64\\height = 8[/tex]

Therefore, the height of the lean-to on its vertical side is 8 feet.

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