A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
Part A: Dillon and Chelsey are discussing how to write the equation of a tangent line
to circle A through point B. Both agree that they start the problem by drawing the
radius AB and find the slope of that segment. They also know that a tangent line is
perpendicular to the radius.

Answers

Answer 1

The area of the shaded region is (9/500)π.

To find the area shaded below in circle K, we first need to find the radius of the circle.

Let O be the center of the circle, and let N be the midpoint of segment LM. We can draw a radius ON to segment LM such that it is perpendicular to LM, and then draw another radius OL to point L. This forms a right triangle LON with the hypotenuse equal to the radius of circle K.

Since segment LM is given to have a length of 11/9π, we can find the length of LN by dividing it in half:

LN = (11/9π)/2 = 11/18π

We can then use trigonometry to find the length of OL:

sin(55°) = OL / LN

OL = LN sin(55°)

OL = (11/18π) sin(55°)

Next, we can use the Pythagorean theorem to find the length of ON:

ON² = OL² + LN²

ON² = [(11/18π) sin(55°)]² + [11/18π]²

ON ≈ 1.022

Therefore, the radius of circle K is approximately 1.022.

The area of the shaded region can now be found by subtracting the area of sector LOM from the area of triangle LON:

Area of sector LOM = (110/360)π(1.022)² ≈ 0.317π

Area of triangle LON = (1/2)(11/18π)(1.022) ≈ 0.326π

Area of shaded region = (0.326π) - (0.317π) = (9/500)π

So the area of the shaded region is (9/500)π.

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Related Questions

The price of a shirt after 25% discount is R480 calculate the original price of the shirt

Answers

discount amount= CP-Disount percentage

or,480=CP-25/100

or480×100+25 =CP

48025 is the original price of shirt

Worth 50 points!!! a ball is dropped from a height of 32 meters. with each bounce, the ball reaches a height that is half the height of the previous bounce. after which bounce will the ball rebound to a maximum height of 25 centimeters?

Answers

The ball will rebound to maximum height of 25 centimetres or 0.25 meters after 7 bounces.

Firstly perform the unit conversion. As known, 1 meter is 100 cm. So, 25 centimetres is 0.25 meters.

Now, the formula to be used to find the number of bounces is -

New height × [tex] {2}^{n} [/tex] = old height, where n refers to number of bounces.

Keeping the values in formula

0.25 × [tex] {2}^{n} [/tex] = 32

Rearranging the equation

[tex] {2}^{n} [/tex] = 32/0.25

Divide the values

[tex] {2}^{n} [/tex] = 128

Converting the result into exponent form

[tex] {2}^{n} [/tex] = 2⁷

Thus, n will be 7 bounces.

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On a unit circle, the terminal side of Angle 0 intersects the circle at point (x,y). ?


Underline the expressions that would make the following statements true.


A) sin θ = (x,y, the ratio of x to y, the ratio of y to x)


B) tan θ = (x,y, the ratio of x to y, the ratio of y to x)


C) cos θ = (x,y, the ratio of x to t, the ratio of y to x)

Answers

The correct expressions are:

A) sin θ = y

B) tan θ = y/x

C) cos θ = x

How On a unit circle, the terminal side of Angle 0 intersects the circle at the point?

On a unit circle, the terminal side of Angle 0 intersects the circle at points (x,y). We can use trigonometric ratios to relate the coordinates (x,y) to the angle θ.

A) sin θ = the ratio of y to 1, or simply y.

B) tan θ = the ratio of y to x.

C) cos θ = the ratio of x to 1, or simply x.

Therefore, the correct expressions are:

A) sin θ = y

B) tan θ = y/x

C) cos θ = x

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π8
radians is the same as
degrees.

Answers

Answer:

π/8 radians is the same as 22.5°

Step-by-step explanation

π corresponds to 180 degrees.

so

180 : 8 = 22.5°

Given the following practical problem, what is the slope of the linear function?

Homer walked to school every day. He walked at a pace of 4 miles per hour

Answers

The slope of the linear function representing Homer's walking pace is 4 miles per hour.

How can the slope of Homer's linear function be determined?

In the given practical problem, we are told that Homer walked to school at a pace of 4 miles per hour. The slope of the linear function can be determined by considering the relationship between the distance he walked and the time it took.

In this case, the slope represents the rate of change of distance with respect to time, which is equal to the speed at which Homer is walking. Since Homer's pace is given as 4 miles per hour, the slope of the linear function representing his distance as a function of time would be 4.

Therefore, the slope of the linear function in this practical problem is 4, indicating that for every hour that passes, Homer walks 4 miles.

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30 % of a number is 14.99 . Set up an equation and solve to find the original number

Answers

Answer:

The original number is approximately 49.97.

--------------------

Let the original number be n.

We are given that 30% of n is 14.99.

Set up an equation to reflect this relation:

30% of n = 14.99

Solve it for n:

0.3*n = 14.99n = 14.99/0.3n = 49.97 (rounded)

This mysterious hand went to the mall and saw a massage chair


that he would have to take a loan out to purchase. The total of the


loan was $6600. The bank said that he could get a simple interest


rate of 8% for 5 years. What is the total amount that the mysterious


hand will pay for the chair?

Answers

Since the loan is at a simple interest rate of 8% for 5 years, the total amount that the mysterious hand will pay is:

Total amount = Principal + Interest

where Principal is the initial amount of the loan, and Interest is the amount of interest charged on the loan.

The interest charged on the loan can be calculated using the simple interest formula:

Interest = Principal x Rate x Time

where Rate is the interest rate per year, and Time is the time period in years.

Plugging in the given values, we get:

Interest = 6600 x 0.08 x 5 = 2640

So the total amount that the mysterious hand will pay is:

Total amount = 6600 + 2640 = 9240

Therefore, the total amount that the mysterious hand will pay for the massage chair is $9,240.

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Explain why a runner completes a 6.2 mi race in 32 min , then he must be running 11m/hr at the entire race

Answers

The runner's average speed is approximately 11.63 mph, which is slightly faster than 11 mph. So, the runner doesn't maintain exactly 11 mph throughout the entire race, but they are close.

If a runner completes a 6.2 mile race in 32 minutes, we can calculate their average speed by dividing the total distance by the total time.

6.2 miles ÷ 32 minutes = 0.194 miles per minute

To convert this to miles per hour, we need to multiply by 60 (the number of minutes in an hour):

0.194 miles per minute x 60 minutes = 11.63 miles per hour

So the runner must be running at an average speed of 11.64 miles per hour throughout the entire race in order to complete it in 32 minutes. This is an impressive pace and shows that the runner is very fit and capable of sustaining a fast speed for a relatively long distance.

A runner completes a 6.2-mile race in 32 minutes, and we are to determine if they maintain an 11 mph pace throughout the race. To do this, we need to convert the race time to hours and then divide the race distance by the time.

First, convert 32 minutes to hours:
32 minutes / 60 minutes/hour = 0.5333 hours

Next, calculate the average speed:
6.2 miles / 0.5333 hours ≈ 11.63 mph


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How do i solve this?

Answers

RSQ= 126 degrees

both angles are cooresponding angels therefore

5x+86=10x+46

86-46=10x-5x

40=5x

x=8

substitute

10(x)+46

10(8)+46

80+46

126

Camden and violet are reading the same book. at the beginning of the month, camden was on page 18 and violet was on page 39. camden will read 11 pages per day and violet will read 8 pages per day. let c represent the page of the book that camden is on at the end of t days into the month. write an equation for each situation, in terms of t. and determine whether camden or violet is farther along in 2 days.​

Answers

For Camden the equation is c = 18 + 11t and for Violet the equation is v = 39 + 8t. After 2 days, Camden will be on page 40 and Violet will be on page 55.

Let's represent the situation with two equations, one for Camden (c) and one for Violet (v), using the given information and the variable t for the number of days.

Camden:
At the beginning of the month, Camden was on page 18 and will read 11 pages per day. So, his equation will be:
c = 18 + 11t

Violet:
At the beginning of the month, Violet was on page 39 and will read 8 pages per day. So, her equation will be:
v = 39 + 8t

Now, we need to determine who is farther along in the book after 2 days. To do this, we will substitute t = 2 into both equations.

Camden's equation (c):
c = 18 + 11(2)
c = 18 + 22
c = 40

Violet's equation (v):
v = 39 + 8(2)
v = 39 + 16
v = 55

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PLSS HELPP!! The diagram shown is two intersecting lines. The measure of ∠2 is 29 degrees.

(a) What is the measure of ∠4? how do you know? Explain your answer in complete sentences.

(b) Suppose the measure of ∠3 can be represented by (3x - 8). What equation can be written to solve for the value of x?

(c) What is the value of x? show all work

Answers

The measure of ∠4 is 151°.

The equation that can be used to solve for the value of x is: 3x - 8 = 151°

The value of x is 53.

What is the measure of ∠4?

(a) The measure of ∠4 is found as follows:

∠2 + ∠4 = 180° ( sum of angles on a straight line)

However, ∠2 = 29°

29° + ∠4 = 180°

∠4 = 180° - 29°

∠4 = 151°

(b) The equation that can be used to solve for the value of x is found as follows:

∠3 = ∠4 ( vertical angles are equal)

Substituting for ∠3 = 3x - 8 and ∠4 = 151°,

3x - 8 = 151°

(c) The value of x is detremined as follows:

3x - 8 = 151°

3x = 159°

x = 53

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Question content area top
Part 1
A riverboat travels 69 km downstream in 3 hours. It travels 76 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.

Answers

The speed of the boat is 21 km/h and the speed of the stream is 2 km/h.

Select the correct answer.
Which is the minimum or maximum value of the given function?
of
44 N₂
O A.
OB.
O.C. The function has a minimum value of -4.
OD. The function has a maximum value of -4.
The function has a minimum value of -3.
The function has a maximum value of -3.

Answers

Answer:

C

Step-by-step explanation:

The lowest point on the graph on the y-axis is -4

Use your mouse or finger to split the


trapezoid into two triangles and a rectangle.


I ready

Answers

Trapezoids can be split into two triangles and a rectangle.

Trapezoid is also known as a trapezium which is a closed shape having 4  sides with one pair of parallel sides. Trapezium is quadrilateral with 4 sides The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. A trapezium can also have parallel legs. The parallel sides can be horizontal, vertical, or slanting. Few real-life objects example of trapezium is a lamp, popcorn box etc.

A trapezoid consists of two triangles and one rectangle figure shows how can we cut the trapezium to split the trapezium.

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How much interest has accrued after one month at a rate of 15. 5%? Use the formula I=Prt. *


A $19. 24


B $18. 71


C $18. 81

Answers

The interest accrued after one month at a rate of 15.5% on a principal amount of $1,000 is $12.92.

To use the formula I=Prt to calculate the interest accrued after one month at a rate of 15.5%, we need to know the principal amount (P) and the time period (t) in years.

Assuming that the principal amount is $1,000, and the time period is one month, which is equivalent to 1/12 of a year, we can calculate the interest as follows:

[tex]I = Prt[/tex]

[tex]I[/tex] [tex]= 1000 x 0.155 x (1/12)[/tex]

[tex]I = $12.92[/tex]

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3 cm
H
8 cm
12 cm
What is the volume of the table tent?

Answers

The volume of the table tent 3 cmH8 cm12 cm is 288 cubic cm.

How to determine the volume of the table tent

The volume of the table tent can be found by multiplying the length, width, and height of the tent.

Volume = length x width x height

In this case, the length is 12 cm, the width is 8 cm, and the height is 3 cm.

Volume = 12 cm x 8 cm x 3 cm

Volume = 288 cubic cm

Therefore, the volume of the table tent is 288 cubic cm.

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EMERGENCY HELP NEEDED!! WILL MARK BRAINLIEST!!!
f (X) = 2X + 3
g (X) = 3X + 2
What does (F + G) (X) equal

Answers

Answer:

To find (f + g)(x), we need to add the two functions f(x) and g(x), and then evaluate the sum at x.

So, we have:

(f + g)(x) = f(x) + g(x)

Substituting the given functions, we get:

(f + g)(x) = (2x + 3) + (3x + 2)

Simplifying the expression, we get:

(f + g)(x) = 5x + 5

Therefore, (f + g)(x) is equal to 5x + 5.

a teacher has an annual salary of 98,500. how much does that teacher make biweekly?

Answers

If a teacher has an annual salary of 98,500, the teacher makes  $947.12 per biweekly period.

To calculate the teacher's biweekly salary, we need to divide their annual salary by the number of weeks in a year, and then divide that result by 2 (since there are 2 weeks in a biweekly period).

There are a few different ways to approach this calculation, but one common method is to use the following formula:

Biweekly Salary = (Annual Salary / Number of Weeks in a Year) / 2

Using this formula, we can calculate the teacher's biweekly salary as follows:

Biweekly Salary = (98,500 / 52) / 2

Biweekly Salary = (1,894.23) / 2

Biweekly Salary = 947.12

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17/3 yd = how many ft

Answers

Answer:

w

Step-by-step explanation:

w


17 ft



1yd = 3 ft

17/3 yd = (17/3) x 3 ft
= 17 ft

11. On a basketball court, the free throw lane is marked off geometrically. This area of the court is called the


key and is topped by a semicircle that has a diameter of 12 feet. Find the arc length of the semicircle to the


nearest foot. Find the area of the semicircle to the nearest square foot.

Answers

The area of the semicircle is approximately 57 square feet.

The arc length of the semicircle can be found using the formula:

arc length = (θ/360) × 2πr

where θ is the angle in degrees, r is the radius, and π is approximately 3.14.

In this case, the diameter of the semicircle is 12 feet, so the radius is half of that, or 6 feet. The angle of the semicircle is 180 degrees, since it is a semicircle. Plugging these values into the formula, we get:

arc length = (180/360) × 2π(6) ≈ 18.85 feet

Therefore, the arc length of the semicircle is approximately 19 feet.

To find the area of the semicircle, we can use the formula:

area = (πr^2)/2

Plugging in the value of the radius from before, we get:

area = (π(6^2))/2 ≈ 56.55 square feet

Therefore, the area of the semicircle is approximately 57 square feet.

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Two sides of a parallelogram are 9. 5 feet and 6. 1 feet. The measure of the angle between these sides is 20°. Find the area of the parallelogram to the nearest 10th of a square foot

Answers

The area of the parallelogram is approximately 21.2 square feet, rounded to the nearest tenth of a square foot.

To find the area of a parallelogram, we need to multiply the base by the height. In this case, the two sides given (9.5 feet and 6.1 feet) are the base and height respectively, because they are perpendicular.

To find the area, we first need to find the length of the other two sides. Since a parallelogram has opposite sides that are equal in length, we know that the other two sides are also 9.5 feet and 6.1 feet.

Next, we can use the given angle (20°) to find the height of the parallelogram. We can use trigonometry, specifically the tangent function, to do this:

tan(20°) = height / 6.1 feet

height = 6.1 feet * tan(20°)

height ≈ 2.23 feet

Now we can find the area:

area = base * height

area = 9.5 feet * 2.23 feet

area ≈ 21.185 square feet

Rounding to the nearest tenth of a square foot, the area is approximately 21.2 square feet.

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The ratio of boys to girls in mrs. Cunninghams class is 2 to 3, there are 18 girls in the class. What is the total number of students in mrs. Cunninghams class

Answers

The total number of students in Mrs. Cunningham's class is 30.

From the question we know that the ratio of boys to girls in Mrs. Cunningham's class is 2 to 3 so we can write

no.of boys: no.of girls = 2:3

The total number of girls in the class is given as 18 so with this we can find out the number of boys in the class that is :

no.of boys= (2/3)*no.of girls in class

now after substituting the values in the equation, we get

no. of boys = (2/3) * 18

no.of boys = 12.

So, now we know the number of boys in the class that is 12 and the number of girls in the class is 18.

We can calculate the total number of students in the class which is equal to

= no.of boys + no.of girls.

= 12+18

=30

Therefore, the total number of students in Mrs. Cunningham's class is 30.

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The likelihood that a child will attend a live musical performance can be modeled by
q = 0.01(0.0005x2 + 0.38x + 35) (15 ≤ x ≤ 100).
Here, q is the fraction of children with annual household income x thousand dollars who will attend a live musical performance during the year. Compute the income elasticity of demand E at an income level of $30,000. (Round your answer to two significant digits.)
E =
Interpret the result.
At a family income level of $_______ , the fraction of children attending a live musical performance is increasing by ________% per 1% increase in household income.

Answers

E = 0.01(0.0005(30)^2 + 0.38(30) + 35)(2*0.0005(30) + 0.38) ≈ 0.63

Interpretation: The income elasticity of demand is 0.63, which means that for every 1% increase in household income, the fraction of children attending a live musical performance increases by 0.63%.
At a family income level of $30,000, the fraction of children attending a live musical performance is increasing by 0.63% per 1% increase in household income.
To compute the income elasticity of demand E at an income level of $30,000, we need to find the derivative of q with respect to x, and then evaluate it at x=30. The derivative of q with respect to x is:

dq/dx = 0.01(0.001x + 0.38)
Now, let's evaluate this derivative at x=30:
dq/dx = 0.01(0.001(30) + 0.38) = 0.004
To calculate the income elasticity of demand E, we use the formula:
E = (dq/dx)(x/q)
First, let's find q at x=30:
q = 0.01(0.0005(30)^2 + 0.38(30) + 35) = 0.178
Now, we can find E:
E = (0.004)(30/0.178) ≈ 0.67

Interpret the result:
At a family income level of $30,000, the fraction of children attending a live musical performance is increasing by approximately 67% per 1% increase in household income.

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Consider triangle ABC with vertices A(0,0), B (0,6), and C (4,0). The image of triangle ABC after a dilation has vertices A'(0,0), B' (0,21), and C' (14,0).
What is the scale factor of the dilation?
k = ?

Answers

Answer:

k=0.3

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get  2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8

At the beginning of the summer, a camp has 540 campers and 36

counselors. part a: by midsummer, an additional 0 campers join the camp. how many additional counselors are needed to keep the same ratio of campers to counselors? write a proportion and solve. part b: by the end of the summer, 2/3 of the campers plan to come back next year. how many campers can they expect back next year? write a proportion and solve. part c: how many counselors will they need next year for the estimated returning campers? write a proportion and solve.

Answers

The camp would need 24 counselors for the estimated returning campers.

Midsummer is typically around the middle of the summer season, which is usually around the end of July. In this scenario, at the beginning of the summer, there are 540 campers and 36 counselors at a camp.

Part a asks us to determine how many additional counselors are needed to maintain the same ratio of campers to counselors if 0 additional campers join the camp by midsummer.

To solve this problem, we can set up a proportion:

540 campers / 36 counselors = (540 + 0) campers / x counselors

We can simplify this proportion by cross-multiplying and solving for x:

540x = 36(540 + 0)
x = 36(540 + 0) / 540
x = 36

Therefore, the camp would need an additional 36 counselors to maintain the same ratio of campers to counselors if no additional campers joined by midsummer.

Part b asks us to determine how many campers can be expected to return the following year if 2/3 of the current campers plan to come back. We can set up a proportion for this problem as well:

2/3 (current campers) = x (expected returning campers) / 540 (current campers)

We can solve for x by cross-multiplying and simplifying:

2/3 (540) = x
x = 360

Therefore, the camp can expect around 360 campers to return the following year.

Part c asks us to determine how many counselors will be needed for the estimated returning campers. We can set up a proportion once again:

540 (current campers) / 36 (current counselors) = 360 (expected returning campers) / x (needed counselors)

We can solve for x by cross-multiplying and simplifying:

540x = 36(360)
x = 24

Therefore, the camp would need 24 counselors for the estimated returning campers.

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Keisha's teacher gives her the following information: • m, n, p, and q are all integers and p = 0 and q + 0 m and B= 4 What conclusion can Keisha make? A + B = so the sum of two rational numbers is a rational number. AB= so the product of two rational numbers is a rational number. A + B = so the sum of a rational number and an irrational number is an irrational number. A. BE so the product of two irrational numbers is an irrational number. ​

Answers

Option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

Given integers are m, n, p and q

And q ≠ 0 and p ≠ 0

A = m / p

B = n/ q

Adding A and B

A + B = m / p + n / q

A + B = (mq + np) / pq

as p ≠ 0 and q ≠ 0 so, pq ≠ 0

So, A + B = (mq + np) / pq is a rational number

Therefore, option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

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Given question is incomplete, the complete question is below:

Keisha's teacher gives her the following information:

• m, n, p, and q are all integers, and p≠ 0 and q≠0

•A= m/q and B= n/p

What conclusion can Keisha make?

A: A +B = (mp + nq)/pq, so the sum of a rational number and an irrational number is an irrational number.

B: A•B= (mp + nq)/pq, so the product of two irrational numbers is an irrational number.

C: A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

D: A•B= (mp + nq)/pq, so the product of two rational numbers is a rational number.​

5. A salesman bought a computer from a manufacturer. The salesman then sold the computer for


$15 600 making a profit of 25%. Unfortunately, he suffered a 5% loss due to damages when


assembling


a. What was his actual profit earnings? (10 marks)

Answers

The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.

Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.

Let the cost price of the computer be x.

Selling price = 125% of cost price

$15,600 = 1.25x

Solving for x, we get:

x = $12,480

So, the salesman's cost price of the computer was $12,480.

Now, the salesman suffered a loss of 5% due to damages when assembling the computer.

Loss = 5% of cost price

Loss = 5% of $12,480

Loss = $624

So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.

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A plane rose from take-off and flew at an angle of 11° with the ground. When it reached an

altitude of 500 feet, what was the horizontal distance the plane had flown?​

Answers

A plane rose from take-off and flew at an angle of 11° with the ground, the horizontal distance the plane had flown when it reached an altitude of 500 feet is approximately 2755.3 feet.

To solve this problem, we can use trigonometry. We know that the angle between the ground and the plane's path is 11°, and the altitude of the plane is 500 feet. Let x be the horizontal distance the plane has flown.

We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle, to find x. In this case, the opposite side is the altitude (500 feet) and the adjacent side is x. So we have:

tan(11°) = 500/x

To solve for x, we can multiply both sides by x and then divide by tan(11°):

x = 500 / tan(11°)

Using a calculator, we get:

x ≈ 2755.3 feet

Therefore, the horizontal distance the plane had flown when it reached an altitude of 500 feet is approximately 2755.3 feet.

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A standard number cube is rolled to play a certain board game. What is the Sample Space? Use proper notation as necessary and no extra spaces.

Answers

Answer: 1.3

Step-by-step explanation:

Can I have help with this question, Please?
"Write an equation for the ellipse."
Center: (1, -3)

Answers

The equation of the ellipse with center (1, -3), and a semi major axis of 4, and a semi minor axis of 3 is; (x - 1)²/4² + (y + 3)²/3²

What is the standard form of the equation of an ellipse?

The standard form equation of an ellipse can be presented as follows;

(x - h)²/a² + (y - k)²/b² = 1

Where;

(h, k) = The coordinates of the center of the ellipse.

The length of the semi major axis = a

Length of the semi minor axis = b

The center of the specified ellipse is; (h, k) = (1, -3)

The semi major axis = 4

The length of the semi minor axis = 3

The equation of the ellipse is therefore;

(x - 1)²/4² + (y - (-3))²/3² = 1

(x - 1)²/4² + (y + 3)²/3² = 1

Learn more on the equation of an ellipse here: https://brainly.com/question/29016892

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