You tie a spherical balloon that is 2 feet in diameter to a stake in the ground.The string is 15 feet long.The wind blows and you observe that the top of the balloon is 8 feet over from the stake,as shown in the diagram.what is the height,b,of the balloon?

You Tie A Spherical Balloon That Is 2 Feet In Diameter To A Stake In The Ground.The String Is 15 Feet

Answers

Answer 1

To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,8);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 8$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$8^2 + b^2 = 15^2$

$64 + b^2 = 225$

$b^2 = 161$

$b = \sqrt{161} = \boxed{12.8}$ feet

Therefore, the height of the balloon is approximately 12.8 feet.


Related Questions

Please helpppp me with thisss

Answers

Answer:

d = 0

Step-by-step explanation:

We have the equation

7.5d = 2.5d

We divided both sides by factors and get

d = 0

Value of d is 0.

According to question

7.5d=2.5d

Lin divides each side by 2.5d

∴7.5d÷2.5d=2.5d÷2.5d

⇒3=1

which is not possible and Lin is doing wrong

Elena subtract 2.5d from each side

∴7.5d-2.5d=2.5d-2.5d

⇒5d=0

⇒d=0

So Elena is right and the value of d is 0.

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Write a triangle congruence statement

Answers

Answer:

1. ΔCDE≅ΔJEH

2. ΔIHG≅ΔIHD

3. ΔIHJ≅ΔIXT

4. ΔIJT≅ΔJIH

5. ΔEFD≅ΔDKJ

6.ΔGWY≅ΔGHI

Elie built a large rectangular vegetable garden that i 9 meter long and ha an area of 72 quare meter. What i the perimeter of Elie’ vegetable garden

Answers

Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

if you use 1 pound of mirepoix in a recipe that yields 1 gallon of soup, how much mirepoix do you need to make 31/2 gallons of soup?

Answers

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so [tex]\frac{x}{100} * y = 31/2[/tex]

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Which sentence does NOT contain an error in pronoun-antecedent agreement?
a. A large herd of buffalo thundered across the plain and left a cloud of dust in their wake.
b. When the crowd reached the center of town, the mayor was surprised by their size.
c.Our gymnastics team proved their skills during the individual floor exercises.

Answers

Answer:

a

Step-by-step explanation:

suppose you want to encrypt the message 10101111 by encrypting the decimal number that corresponds to the message. what is the decimal number

Answers

To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.

By using the following formula:

decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]

binary = converting binary number

i = index of the current digit in the binary number

n = total number of digits in the binary number

[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2

use the following steps to convert the binary number "10101111"

Calculate the decimal value for each digit in the binary number:

binary[0] = 1, [tex]2^{(8-0-1)}[/tex]  = [tex]2^7[/tex] = 128

binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64

binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32

binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16

binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8

binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4

binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2

binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1

Adding decimal values for each digit

Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11

= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1

= 175

Hence, the decimal number that corresponds to the binary number "10101111" is 175.

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Angles 2 and 8 are what type of angles?

A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles

Help!!!

Answers

Answer:

B. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are angles that are outside two lines intersected by the transversal and are located on opposite sides of the transversal. Also, they have the same degree! So, the answer is B.

You just signed a 2 years lease for a one bedroom apartment in Brooklyn. The rent is $2,657 per month pulse $200 security deposit. Thinking long-term, you are wondering if it is better to rent or own a property. How will the total amount of rent you pay change over time?

Answers

After the end of the lease period the pay, the rent would increase to $3030.83 approx.

What is a Lease agreement?

A lease is a legal agreement by which the owner of a building, a piece of land, or something such as a car allows someone else to use it for a period of time in return for money.

Given here,  a 2-year lease is - $2,657 per month plus a $200 security deposit. Now, the average increase in the rate in the U.S is 14.07%

thus, at the end of the two-year lease period, the new rent would be

= (1+14.07/100) × $2,657

= $3030.83

Hence, the new rent with a security deposit is $3030.83 + security deposit.

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PLEASE HELP!!!!! 90 POINTS!!!!!

Graph the following system of equations.

2x + 4y = 8
2x + 6y = 18

What is the solution to the system?

There is no solution.
There is one unique solution, (−6, 5).
There is one unique solution, (−4, 4).
There are infinitely many solutions.

Answers

Answer:

There is one unique solution, (−6, 5).

Step-by-step explanation:

2x + 4y = 8

2x + 6y = 18

2x + 4y = 8  ==> solve for 2x

2x + 4y - 4y = 8 - 4y

2x = 8 - 4y

2x + 6y = 18  ==> solve for 2x

2x + 6y - 6y = 18 - 6y

2x = 18 - 6y

8 - 4y = 18 - 6y  ==> 2x = 8 - 4y   and   2x = 18 - 6y

8 - 4y + 6y = 18 - 6y + 6y  ==> solve for y by first adding 6y on both sides to

                                                remove negative y

8 + 2y = 18  ==> simplify

8 - 8 + 2y = 18 - 8  ==> isolate y

2y = 10

y = 5

2x + 4(5) = 8  ==> substitute 5 for y in 2x + 4y = 8

2x + 20 = 8

2x - 20 + 20 = 8 - 20  ==> subtract 20 on both sides to isolate 2x

2x = -12

x = -6

x = -6, y = 5  ==> (6, 5)

Answer: There is one unique solution, (−6, 5).

Answer is in the graph, there is one unique solution (-6, 5)

The question asks you to graph and find the solution. I graphed this and attached it.

The solution is where the lines intersect, at (-6, 5)

(-10, -12), (-8, -8), (-6, -4), (-4, 0)

Find the slope of the line passing through the given points

Answers

Answer: the slope is [tex]\frac{4}{2}[/tex] which can be simplified to just 2.

Step-by-step explanation:

You can use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope of a line. In this case, I chose to use the coordinates (-4,0) and (-6,-4), it doesn't matter which you choose as the (x1,y1) and (x2,y2) coordinates. So, [tex]\frac{-4-0}{-6-(-4)}[/tex] becomes [tex]\frac{-4}{-2}[/tex] which is the same as [tex]\frac{4}{2}[/tex], which is equal to 2. you can repeat this with the other points given to check your answer.

The slope of the line passing through the given points is equal to 2 .

what is the slope of a line?

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the tangent of the angle made by the line with the x - axis. It is represented by m: m = y₂-y₁ / x₂ - x₁

Given here, are the points P (-10, -12), Q(-8, -8), R(-6, -4),S (-4, 0)

Now the slope of a line is constant for any two points that lie on a line.

therefore, slope of the line that passes through P,Q,R,S  is

m = -8-(-12) /-8-(-10)

    = 2

 or m= 0-(-4) /-4-(-6)

         = 2

clearly the slope is equal to 2 in either case that's because the line passes through all the four points.

Hence,  the slope of the line passing through the given points is equal to 2.

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Help asp thank you show your work if you want

Answers

Answer:

[tex]y=-\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Parallel means same slope.

[tex]y=-\frac{2}{3}x+b[/tex]

[tex]5=-\frac{2}{3} (-6)+b[/tex]

5 = 4 + b

b = 1

[tex]y=-\frac{2}{3}x+1[/tex]

What is the first quartile of the given data set?

Answers

The value of first quartile of the given data set is 2.5

What is first quartile?

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

Given is a data set,

According to the data,

The lower quartile is between 0 and 2.5, which under 25% of the data.

Hence, The value of first quartile of the given data set is 2.5

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pls help having trouble!

Answers

Answer:

a is 30 degrees.

Step-by-step explanation:

The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.

[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]

PLEASE HELP I AM SO BEHIND ON SCHOOL WORK !!!
Which equation represents the same line as the points in the table?

y=−3x+2y is equal to negative 3 x plus 2

y=−34x+83y is equal to negative 3 fourths x plus 8 thirds

y=2x−34y is equal to 2 x minus 3 fourths

y=−34x+2

Answers

Answer:

Use this site, it will help you in the long run.

Moussa is younger than Sophia. Their ages are consecutive even integers. Find Moussa's age if the product of their ages is 24.

Answers

Moussa's age if the product of their ages is 24 is 4 years.

How to calculate their age?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Moussa is younger than Sophia. Their ages are consecutive even integers.

Let the ages be x and x + 2.

This will be illustrated as:

x(x + 2) = 24

x² + 2x = 24

x² + 2x - 24 = 0

x² + 6x - 4x - 24 = 0

x(x + 6) -4(x + 6) = 0

x - 4 = 0

x = 4

x + 2 = 4 + 2 = 6

The ages are 4 and 6 years.

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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.

How to find the Moussa's age?

Moussa is younger than Sophia.  Their ages are consecutive even integers.

The product of there ages is 24. Moussa's age can be found as follows:

Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Hence,

Let

x = age of Moussa

x + 2 = age of Sophia

Hence, the product of their age will be as follows:

x(x + 2) = 24

x² + 2x = 24

x² + 2x - 24 = 0

lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,

x² - 4x + 6x - 24 = 0

x(x - 4) + 6(x - 4) = 0

(x + 6)(x - 4) = 0

Therefore,

x = - 6 and x = 4

We can only use positive numbers.

Therefore, the age of Moussa is 4 years

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FILL IN THE BLANK. the _______ _______ is a statement we are trying to find evidence to support.

Answers

Answer:

Alternative Hypothesis

The tatue i 4. 6 meter high. The angle of elevation from the oppoite corner of the courtyard to the top of the tatue i 8

Answers

The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters

First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:

tan 8 = 4.6/opposite

Solving for the opposite, we get:

opposite = 4.6/tan 8 = 5.8 meters

This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.

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Help me quickly please! (I will mark brainliest)

Answers

The graphs in this problem that show continuous data are given as follows:

Top right.Bottom left.

What are continuous and discrete graphs?

Continuous and discrete graphs have different formats to show the data, which are presented as follows:

For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.

For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.

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(x + 2)(x+4)²
———————
(x+4)

Answers

Answer:

(x + 2)(x + 4)

Step-by-step explanation:

for the denominator we have (x + 2)(x + 4)(x + 4).

divide the denominator by (x + 4), you would be left with (x + 2)(x + 4).

In a board of directors composed of 14 people, how many different ways can one chief
executive officer, one director, and one treasurer be selected?

Answers

Answer:

2184

Step-by-step explanation:

This question involves permutations. We can solve it using the formula

[tex]\frac{n!}{(n-r)!}[/tex]

where n=14 (because we are choosing from 14 people)

and r=3 (because we are choosing 3 people)

and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)

14!/(14-3)!

= 14!/11!

= 14 x 13 x 12

= 2184

here is a famous problem: nn guests arrive at a party. each person is wearing a hat. we collect all hats and then randomly redistribute the hats, giving each person one of the nn hats randomly. what is the probability that at least one person receives his/her own hat?hint: use the inclusion-exclusion principle.

Answers

The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.

The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.

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f(x)=2x^2
g(x)=x+1
prove fg(x)=gf(x)

Answers

Answer:

here is the answer with proper steps.

HELP QUICK!!

An item on sale costs 35% of the original price. If the original price was $60, what is the sale price?

Answers

0.35 * 60 = 21, therefore $21


When dealing with percentages they are numerators (?wc) of 100, so 0.35 = 35/100.
In percentage calculations you want to make the original/starting value equivalent to the 100 denominator
35/100 * 6000/100
This sum is the same as the first line… sorry if this is more confusing ;-;
TL;DR: take the percentage as 0.XX and times by original value if going lower in value. If your going higher do 1.XX

thanks for helping me!

Answers

Answer:

<E=180-60=120

t=60 degrees

u=8

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E=180-60=130
T= 60
So U=8

Each year the value of a car decreases by 12% of its value at the beginning of that year. The original value of the car is $20000. Calculate the value of the car at the end of 3 years

Answers

Answer:

The value of the car at the end of 3 years will be $13707.

Step-by-step explanation:

If the original value of the car is $20000, then after the first year, the value of the car will be $20000 - (12/100)*$20000 = $17600.

After the second year, the value of the car will be $17600 - (12/100)*$17600 = $15552.

After the third year, the value of the car will be $15552 - (12/100)*$15552 = $13707.

Therefore, the value of the car at the end of 3 years will be $13707.

Subtract the expressions.

(7.43n − 2.2) − (6 + 10.5n)

−30.70n − 4.5
−3.07n − 8.2
9.63n − 4.5
17.93n + (−8.2)

Answers

The solution to the expression is (b) -3.07n - 8.2

How to subtract the expressions?

From the question, we have the following parameters that can be used in our computation:

(7.43n − 2.2) − (6 + 10.5n)

Remove the brackets

So, we have

(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n

Evaluate the like terms

(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2

Hence, the solution is (b) -3.07n - 8.2

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At a school there are six lessons in a day.
In total, the six lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working

Answers

Answer:

40mins

Step-by-step explanation:

4hrsx60

=240mins

240mins/6 lessons

=40mins per lesson

Given g(x)=-5x+2 find g(-4)

Answers

Answer:_18

replace _4 instead of x

-5*-4=_20

_20+2=_18

Step-by-step explanation:

use the graphs of f and g to graph h(x) = (f + g)(x). (graph segments with closed endpoints.)

Answers

Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.

In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).

A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

The graph is given below:

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

The function h(x) can be written as

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

Different x values must be taken into account in order to graph h (x).

h (0) = f (0) + g (0) = 2 - 1 = 1

h (1) = f (1) + g (1) = 3 + 0 = 3

h (2) = f (2) + g (2) = 1 + 0.5 = 1.5

h (3) = f (3) + g (3) = 2 + 0 = 2

So the graph of the h(x) is given below:

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solve each equation by completing the square
[tex]x^{2} -34x+289=0[/tex]
After completing the square, the equation is ____ and the solution is _________
WHOEVER ANSWERS CORRECTLY WILL BE MARKED BRAINLIEST

Answers

Answer:

x = 17

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

Complete the square as follows:

x² - 34x + 289 = 0x² - 2*17*x + 17² = 0                      Identity  (a ± b)² = a² ± 2ab + b²(x - 17)² = 0x - 17 = 0                                       Square root both sidesx = 17
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Manners and Etiquettes Ethio engineering Corporation has signed a road construction agreement contract with Ethiopian Road Authority to renew and construct-the main road from Addis Ababw to Diredawa with a contract amount of 250million, 80% of the contract amount will be financed from the loan released by Commercial Bank of Ethiopia at an annual nual interest rate of 13% to be paid as per the following terms of payment At the end of the 1 At the end of the 2 At the end of the 3 At the end of the 4 At the end of the 5th year year year year year At the end of the 6th year 10% of the principal 20% of the principal 30% of the principal 20% of the principal ....15% of the principal 5% of the principal Task 4.1. Determine A Amount of loan from Commercial Bank Of Ethiopia B. Amount of Principal and interest repayment for the 20 year C Amount of outstanding balance at the end of the year including interest expenses D Total interest of the loan paid all loan Find the kinetic energy of arotating body with moment of inertia 0.003 kgm^2 and angula velocity of 0.6 radius how did the hawley-smoot tariff passed by the u.s. congress contribute to the great depression? suppose juanita modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds; that is, she chooses combination c. the average annual return for this type of portfolio is 7.5%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of to a loss of . Brainly please don't delete my question it's not even breaking your guideline I even checked I just need my questions answered! scientists discovered that the difference between blond and dark hair in humans and other mammals comes down in part to a single nucleotide difference in the dna sequence of an enhancer that lies more than 350,000 base pairs upstream from the coding region of the gene it controls. on average, blonds transcribe this gene less efficiently than people with dark hair. which of the following statements about this blond/dark hair enhancer is correct? elementary surveying two ridges b and c forms a valley having a at the bottom part in between the ridges. elevation difference between b nad c is 111..356 m. observing at point a, the angle of elevation is Plot all ordered pairs for the values in the domain.