Write a quadratic function f whose zeros are -2 and 12.

f(x) = 0

In the above isosceles trapezoid,

Since R is the midpoint of HN, HR = RN. Similarly, since T is the midpoint of KJ, KT = TJ.

Let's use these properties to write expressions for HJ and NK in terms of x:

HJ = 5x + 9

NK = 3x - 2

Since NKJH is an isosceles trapezoid, we know that HJ = NK + 2RT. Substituting the expressions we found earlier, we get:

5x + 9 = (3x - 2) + 2(3x + 6)

Simplifying this equation gives:

5x + 9 = 9x + 10

Subtracting 5x from both sides gives:

4 = 4x

Dividing both sides by 4 gives:

x = 1

Now that we know x, we can find the values of HJ, NK, and RT:

HJ = 5x + 9 = 14 cm

NK = 3x - 2 = 1 cm

RT = 3x + 6 = 9 cm

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the nicknames of the four friends are:

Andre: Boss

Bilal: Buzz

Glenna: Cosmo

Juanita: Tiger

From clue 1, we realize that Juanita's moniker isn't Tiger or Buzz, and Tiger's epithet isn't Chief or Cosmo. Along these lines, Juanita's epithet should be Cosmo or Chief, and Tiger's moniker should be Buzz or Tiger.

From clue 2, we realize that Glenna's moniker isn't Chief or Buzz, and Tiger's epithet isn't Cosmo or Tiger (currently disposed of in the past step). In this way, Glenna's moniker should be Cosmo, and Tiger's epithet should be Buzz.

From clue 3, Cosmo's nickname has already been determined to be Glenna, and we are aware that Andre's nickname cannot be Boss, Buzz, or Tiger (all of which have been eliminated). Boss has to be Andre's nickname.

From clue 4, Cosmo's nickname has already been identified as Glenna, and we are aware that Juanita's nickname cannot be Buzz or Tiger (both of which have already been eliminated). Therefore, Juanita must go by the name Boss.

So, the nicknames of the four friends are:

Andre: Boss

Bilal: Buzz

Glenna: Cosmo

Juanita: Tiger

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a. The stairs can be broken into a cuboid, the dimensions of the cuboid are 2.4 x 0.6 x 0.4

b. The amount of concrete needed will be 3.456 cubic units.

The amount of concrete required is solved by solving for the voulme of a cuboid and multiplying by the number of cuboids used

The dimension of each of the cuboid is 2.4 x 0.6 x 0.4

To find the volume of the cuboid, we simply multiply the dimensions together. Therefore:

2.4 x 0.6 x 0.4 = 0.576 cubic units

Therefore, the volume of the each cuboid is 0.576 cubic units.

the number of cuboids used is 6, hence we have

= 6 x 0.576 cubic units.

= 3.456 cubic units.

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Answer: your in my class I’m not a snitch though

Step-by-step explanation:

The volume of the cone with height of 9 inches and a diameter of 12 inches is approximately 339.3 cubic inches.

To find the volume of a cone, we need to use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.

Since the diameter of the cone is given as 12 inches, we can find the radius as half of the diameter, which is 6 inches. The height of the cone is given as 9 inches.

Now, we can substitute the values of r and h in the formula to get the volume as follows

V = (1/3)πr^2h

= (1/3)×3.14×6^2×9

= 339.12 cubic inches (rounded to the nearest tenth)

Therefore, the volume of the given cone is approximately 339.1 cubic inches.

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The missing measure of the square pyramid and the net would be 11.18 units.

The amount of wood that Dee needs to make the doghouse is 98 square feet of wood.

The missing measure is the side of the pyramid and this can be found using the Pythagorean Theorem with 11 ft being the height of the triangle and 4/ 2 = 2 being one of the sides and the missing measure being the hypotenuse.

The side length is:

= √ (2 ² + 11²)

= √ ( 4 + 121)

= 11.18 units

To determine the amount of wood needed for Dee's doghouse, we need to calculate the surface area of the square pyramid using its net.

Calculate the area of all four triangular faces:

Total area of triangular faces = 4 x area of one triangular face = 4 x 20.5 = 82 square feet

Calculate the total surface area of the pyramid (net):

Total surface area = area of base + total area of triangular faces = 16 + 82 = 98 square feet

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Answer: 3/8 >2/6

Step-by-step explanation:

Answer:

a) m || n

b) p || q, and m must be perpendicular to both p and q.

c) p || q

d) p || q

e) m || n and p || q

A function has access to parameters that are passed to it and any variables created within the function (local and function scope).

The variable names that a function has access to depend on the scope of the variables. Scope refers to the visibility of a variable within a program.

There are four different scopes that a variable can have in relation to a function:
Global scope -

A variable that is declared outside of a function has global scope.

This means that it can be accessed by any function within the program.
Local scope -

A variable that is declared within a function has local scope.

This means that it can only be accessed within the function in which it was declared.
Parameter scope -

A variable that is passed as a parameter to a function has parameter scope.

This means that it can only be accessed within the function in which it was passed.
Function scope -

A variable that is created within a function has function scope.

This means that it can only be accessed within the function in which it was created.

It does not have access to variables declared outside of the function (global scope) unless they are explicitly passed as parameters.

It is important to note that naming conflicts can occur if variable names are not chosen carefully, especially when dealing with global and local scope.

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The correct statement regarding the annual interest rate for the given equations is (A) For A = P(1.025), the principal amount of money is increasing at a 2.5% interest rate.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=).

In the equation A = P(1 + r)t, the annual interest rate is represented by the variable "r". It is not correct to directly interpret the value of (1 + r) as the interest rate, as it represents the factor by which the principal amount is multiplied over time to yield the total amount.

Let's analyze each given equation to see which statement correctly relates information regarding the annual interest rate:

(A) For A = P(1.025), the equation does not have a term for time (t), so it cannot represent the growth of a principal amount over time. It simply represents the total amount (A) as 102.5% of the principal amount (P), which means that the interest rate is 2.5% per year.

(B) For A = P(1.0052), similar to the previous equation, this equation does not have a term for time (t), so it cannot represent the growth of a principal amount over time. It simply represents the total amount (A) as 100.52% of the principal amount (P), which means that the interest rate is 0.52% per year.

(C) For A = P(0.86)t, the value of (0.86) represents the factor by which the principal amount is multiplied over time to yield the total amount. Since (0.86) is less than 1, it means that the principal amount is decreasing over time, not increasing. The interest rate in this case is -14% per year (negative because the principal amount is decreasing).

(D) For A = P(0.68)t, similar to the previous equation, the value of (0.68) represents the factor by which the principal amount is multiplied over time to yield the total amount. Since (0.68) is less than 1, it means that the principal amount is decreasing over time, not increasing. The interest rate in this case is -32% per year (negative because the principal amount is decreasing).

Therefore, the correct statement regarding the annual interest rate for the given equations is:

(A) For A = P(1.025), the principal amount of money is increasing at a 2.5% interest rate.

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Answer:

5x - 15

Step-by-step explanation:

5(x - 3) ← multiply each term in the parenthesis by the 5 outside

= 5x - 15

The values of x that makes line segment m parallel to n (m ║ n) are as follows;

13. x = 107°.

14. x = 133°.

15. x = 20°.

16. x = 23°

The outer strings of the oud are parallel because they are all cut or intersected by a transversal.

In Mathematics and Geometry, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem, we have the following:

x + 73 = 180° (sum of all interior angles)

x = 180 - 73

x = 107°.

x + 14 = 147 (vertical angles theorem).

x = 147 - 14

x = 133°.

3x + 2x + 20 = 180° (sum of all interior angles)

5x = 180 - 20

x = 60/3

x = 20°.

7x - 11 = 4x + 58 (corresponding angles theorem)

7x - 4x = 58 + 11

3x = 69

x = 23°

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The surface area of solid B is 9000 cm².

What is ratio?

A ratio is a comparison of two quantities or values, often expressed as a fraction. Ratios can be used to express the relationship between two or more quantities.

Since solids A and B are similar, their corresponding linear dimensions are proportional. Let the scale factor be k, such that the dimensions of solid A are k times larger than the corresponding dimensions of solid B.

The ratio of their volumes is given as 27:1000. Therefore:

(volume of A) / (volume of B) = 27/1000

Let the volume of solid B be V. Then the volume of solid A is (27/1000)V.

Since the surface area of a solid is proportional to the square of its linear dimensions, we have:

[tex]$\frac{surface\ area\ of\ A}{surface\ area\ of\ B} = \frac{k_{A}^{2}}{k_{B}^{2}}$[/tex]

where kA and kB are the linear dimensions of solids A and B respectively.

Since the solids are similar, we can write:

[tex]$k_{A} / k_{B} = \frac{(volume\ of\ A)^{\frac{1}{3}}}{(volume\ of\ B)^{\frac{1}{3}}}$[/tex]

kA / kB = (volume of A)^(1/3) / (volume of B)^(1/3)

Substituting the given volume ratio and solving for kA / kB, we get:

[tex]$k_A/k_B = \left(\frac{27}{1000}\right)^{1/3} = 0.3$[/tex][tex]$k_A/k_B = \left(\frac{27}{1000}\right)^{1/3} = 0.3$[/tex]

Therefore, kA = 0.3 kB.

Now we can substitute the given surface area of solid A and solve for the surface area of solid B:

(surface area of A) / (surface area of B) = (kA)² / (kB)²

810 / (surface area of B) = 0.3²

(surface area of B) = 810 / 0.09

(surface area of B) = 9000 cm²

Therefore, the surface area of solid B is 9000 cm².

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Answer:

H = 45 ½ ÷ 6 ½

Step-by-step explanation:

The formula  for the area of the base of the box is L * W.

The formula for the volume of the box is L * W * H

Therefore dividing 45 ½ (volume of box) by 6 ½ (area of base) will give you the height of the box

The value of k is 20.

An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, division, or exponents. The goal of solving an equation is to determine the value of the variable that makes the equation true. Equations are commonly used in algebra and other mathematical fields to model real-world situations and solve problems. They can be written in various forms, including standard form, slope-intercept form, point-slope form, and general form, among others.

Since the sum of two angles on a straight line is always 180 degrees, we can set up an equation:

First angle + Second angle = 180

112 + 3k + 8 = 180

Simplifying the equation, we get:

3k + 120 = 180

Subtracting 120 from both sides, we get:

3k = 60

Dividing both sides by 3, we get:

k = 20

Therefore, the value of k is 20.

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The slope and derivative of a vertical tangent are both undefined due to the vertical nature of the tangent line.

The slope/derivative of a vertical tangent.
A vertical tangent occurs when a curve has a point where its tangent line is vertical.

In terms of the slope and derivative, the following is true about the vertical tangent:
Slope:

The slope of a vertical tangent is undefined because the vertical line has no run (change in x). Slope is calculated as the rise (change in y) divided by the run (change in x), and division by zero is not possible.
Derivative:

The derivative of a function at a point represents the slope of the tangent line to the curve at that point.

When the tangent is vertical, the derivative is also undefined because the slope is undefined.

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a) The appropriate hypothesis testing are states as [tex]H_0 : p = 0.50[/tex]

[tex]H_a : p > 0. 50 [/tex]

b) The p-value for z-test is equals to the 0.000. Also, p-value < α.

c) Conclusion: Null hypothesis is rejected and there is evidence to support that more than 50% do not belief that such software unfairly targets students.

We have a sample of at an australian university that introduced the use of plagiarism-detection software.

Sample size = 178

Number of students who belief that such software unfairly targets student = 53

a) Null and alternative hypothesis are stated here as for right tailed t test.

[tex]H_0 : p = 0.05 [/tex]

[tex]H_a : p > 0.05[/tex]

sample proportion for students who does not belief that such software unfairly targets student [tex]\hat p = \frac {178- 53 }{178} [/tex] = 0.71

Now, test-statistic : [tex]t = \frac { \hat p - p} {\sqrt{ \frac{ p( 1- p)}{n}}}[/tex]

Substitute all the known values in above formula, [tex]= \frac {0.71 - 0.05} {\sqrt{ \frac{ 0.05( 1- 0.05)}{178}}}[/tex]

=> t = 41.25

b) Now, using Excel, the p-value for z

= 41.25 is 0.000. So, p-value < 0.05

Therefore, the Null hypothesis is rejected here.

c) Conclusion: there is evidence to support the claim that more than 50% do not belief that such software unfairly targets students.

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Complete question:

in a sample of 178 students at an australian university that introduced the use of plagiarism-detection software in a number of courses, 53 students indicated a belief that such software unfairly targets students. does this suggest that a majority of students at the university do not share this belief? test appropriate hypotheses at level 0.05.

a) State appropriate hypothesis

b) find p-value

c) draw conclusion

Answer:

3 + 7 = 10

Step-by-step explanation:

I hope this answers your question. :)

Answer: 3+7=10

Step-by-step explanation:

maybe this is it but this question is really unclear

The maximum amount of water that the tank can hold is 82,824 cubic inches, which corresponds to option (a) in the given answer choices.

To find the maximum amount of water that the tank can hold, we need to find the volume of the tank. The volume of a rectangular prism (which is what a fish tank is) can be found by multiplying the length, width, and height of the prism.

Volume = length x width x height

Plugging in the given dimensions of the fish tank, we get:

Volume = 34 in x 58 in x 42 in

Volume = 82,824 in^3

Therefore, Correct option is A.

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This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.

To apply the Mean Value Theorem, we need to check if f(x) is continuous on [0,2] and differentiable on (0,2).

[tex]f(x) = x^3 - 2x^2[/tex] is a polynomial function, so it is continuous and differentiable everywhere.

Now, we can use the Mean Value Theorem, which states that there exists a number c in (0,2) such that:
[tex]f'(c) = (f(2) - f(0))/(2-0)[/tex]

First, let's find f'(x):

[tex]f'(x) = 3x^2 - 4x[/tex]

Now, we can solve for c:

f'(c) = 3c^2 - 4c

f(2) = 2^3 - 2(2^2) = -4

f(0) = 0^3 - 2(0^2) = 0

(f(2) - f(0))/(2-0) = -4/2 = -2

So, we need to solve the equation 3c^2 - 4c = -2 for c.

Rearranging, we get:

3c^2 - 4c + 2 = 0

Using the quadratic formula, we get:

c = (4 ± sqrt(16 - 24))/6

c = (4 ± 2i)/6

Since the interval is [0,2], we only need to consider real solutions.
[tex]f'(c) = 3c^2 - 4c\\f(2) = 2^3 - 2(2^2) = -4\\f(0) = 0^3 - 2(0^2) = 0\\(f(2) - f(0))/(2-0) = -4/2 = -2\\[/tex]
Therefore, c = 4/3 is not a valid solution.

To choose between the remaining options, we can test if f'(c) is positive or negative.

For c = 0, f'(0) = 0 - 0 = 0.

For [tex]c = 1/2, f'(1/2) = 3(1/2)^2 - 4(1/2) = -1/2.[/tex]

For[tex]c = 1, f'(1) = 3(1)^2 - 4(1) = -1.[/tex]
Therefore, f'(c) is negative on the interval [0,1/2] and positive on the interval [1/2,2].

This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.

Therefore, the answer is (b) 1/2.

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the expected value of the sum of two fair 6-sided dice is 7.

The possible values of the sum of two fair 6-sided dice range from 2 (when both dice show a 1) to 12 (when both dice show a 6). The probability of each possible sum can be calculated using a probability distribution table or by listing all the possible outcomes and counting them.

Here is the probability distribution table:

Sum Number of Outcomes Probability

2 1 1/36

3 2 2/36

4 3 3/36

5 4 4/36

6 5 5/36

7 6 6/36

8 5 5/36

9 4 4/36

10 3 3/36

11 2 2/36

12 1 1/36

The expected value of the sum, denoted E(X), is the sum of each possible value of X multiplied by its probability, or:

E(X) = 2*(1/36) + 3*(2/36) + 4*(3/36) + 5*(4/36) + 6*(5/36) + 7*(6/36) + 8*(5/36) + 9*(4/36) + 10*(3/36) + 11*(2/36) + 12*(1/36)

E(X) = 7

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. A probability of 0.5 (or 50%) means the event is just as likely to occur as it is not to occur.

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The margin of error used in calculating the 90% confidence interval for the true proportion of customers who write a review is 0.043.

To calculate the margin of error, we first need to find the sample proportion of customers who wrote a review:

sample proportion[tex]\hat p =\frac{ 340}{560} = 0.607[/tex]

Next, we can use the following formula to calculate the margin of error:

margin of error [tex]= z* \sqrt{(\hat p * (1-\hat p) / n)[/tex]
where z* is the z-score associated with the desired level of confidence (90% in this case), and n is the sample size.

The z-score for a 90% confidence interval is 1.645. Plugging in the values, we get:

margin of error =[tex]1.645 * \sqrt{(0.607 * (1-0.607) / 560)[/tex]

= 0.043

Therefore, the margin of error used in calculating the 90% confidence interval for the true proportion of customers who write a review is 0.043.

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The circle graph that correctly represents the data in the table is that with:  A. four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent correctly represents the data in the table.

To find the percentage for each type of sandwich, we can divide the number of customers who ordered that sandwich by the total number of customers (100) and multiply by 100.

Using the data given in the table, we get:

Turkey: 30/100 x 100% = 30%

Ham: 20/100 x 100% = 20%

Chicken: 35/100 x 100% = 35%

Vegetarian: 15/100 x 100% = 15%

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The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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To find the absolute maximum and absolute minimum of a function using the closed interval method.

Determine the function, f(x), and the closed interval [a, b].
Calculate the critical points of the function by finding the derivative, f'(x), and setting it equal to zero.

Solve for x to find the critical points.

Keep in mind that only the critical points within the closed interval are relevant to this problem.
Evaluate the function, f(x), at the critical points and the endpoints of the closed interval, a and b.
Compare the function values obtained in step 3.

The highest value corresponds to the absolute maximum, and the lowest value corresponds to the absolute minimum.
Identify the points (x, f(x)) corresponding to the absolute maximum and absolute minimum.

These points represent the locations and values of the absolute maximum and absolute minimum on the given closed interval.

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A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50.

We will find the score that separates the lower 60% of ratings from the top 40% of ratings.

Let x be the score that separates these two portions. We can find the corresponding z-scores using the standard normal distribution, since the ratings are normally distributed with mean 200 and standard deviation 50.

The z-score corresponding to the 60th percentile is the value z such that

P(Z ≤ z) = 0.6

With the help of standard normal tables, we can find that z = 0.25. Therefore, we have

(x - 200)/50 = 0.25

For x, we get

x - 200 = 0.25 * 50

x - 200 = 12.5

x = 212.5

Similarly, the z-score corresponding to the 40th percentile is the value z such that

P(Z ≤ z) = 0.4

With the help of standard normal tables, we can find that z = -0.25. Therefore, we have

(x - 200)/50 = -0.25

For x, we get

x - 200 = -0.25 * 50

x - 200 = -12.5

x = 187.5

Hence, the score that separates the lower 60% from the top 40% is between 187.5 and 212.5.

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Answer: 5 (first round) + 25 (second round) + 125 (third round) + 625 (fourth round) = 780

So, at the end of 4 rounds, including Jacob himself, 780 people will have gotten fliers.

Step-by-step explanation: In the first round, Jacob hands out fliers to 5 people.

In the second round, each of the 5 people from the first round hands out 5 fliers to 5 other people. So, there are now 5 x 5 = 25 people with fliers (including the original 5).

In the third round, each of the 25 people from the second round hands out 5 fliers to 5 other people. So, there are now 25 x 5 = 125 people with fliers (including the original 5 and the 25 from the second round).

In the fourth round, each of the 125 people from the third round hands out 5 fliers to 5 other people. So, there are now 125 x 5 = 625 people with fliers (including the original 5, the 25 from the second round, and the 125 from the third round).

The linear approximation of [tex]f(x) = x^2 at x = 3.5 is f(3.5)[/tex]  ≈ 9.5.

To write a linear approximation (equation of the tangent) and use it to approximate the value of a function, we can follow these steps:

Choose a point on the function where you want to approximate the value.

Let's call this point (a, f(a)).

Find the slope of the tangent line at that point using the derivative of the function at that point.

The slope of the tangent line is equal to the derivative of the function at that point, which is denoted by f'(a).

Write the equation of the tangent line using the point-slope form, which is given by: y - f(a) = f'(a)(x - a)

Use this equation to approximate the value of the function at a nearby point.

Plug in the value of x that is close to a into the equation and solve for y. The resulting y-value will be an approximation of the value of the function at the nearby point.

For example, suppose we want to approximate the value of [tex]f(x) = x^2 at x = 3.[/tex]

We can follow these steps:

Choose the point (3, f(3)) = (3, 9) on the function.

Find the slope of the tangent line at x = 3 using the derivative: f'(x) = 2x, so f'(3) = 6.

Write the equation of the tangent line using the point-slope form: y - 9 = 6(x - 3), which simplifies to y = 6x - 9.

Use this equation to approximate the value of f(x) at x = 3.5: f(3.5) ≈ 6(3.5) - 9 = 9.5.

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Given the above conditions in the word problem above, x is also equal to 6.5°.

The angle x is the angle between this perpendicular line and the Earth's surface. It is also equal to the angle between the tangent line and the horizontal axis.

Since the reentry angle is 6.5°, we know that the tangent line makes an angle of 6.5° with the horizontal axis. We also know that the tangent line and the perpendicular line form a right angle, so the angle between the perpendicular line and the horizontal axis is 90° - 6.5° = 83.5°.

Finally, we can subtract this angle from 90° to find x:

x = 90° - 83.5° = 6.5°

Therefore, x is also equal to 6.5°.

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