a crew is setting up a zip line between two towers with support wires as shown in the figure (not to scale). they only know the heights of the towers and the angles that two of the supports make with the ground. what is the length of the zip line?

A Crew Is Setting Up A Zip Line Between Two Towers With Support Wires As Shown In The Figure (not To

Answers

Answer 1

Answer:

length of the zip line = 121. 63 ft

Step-by-step explanation:

The length of the zip line AB forms a triangle  ABC. To find the length AB we need to know the length of 2 sides of the triangle an angle.

Triangle ADC

We need to find the hypotenuse side AC using the SOHCAHTOA principle.

Therefore,

sin 41° = opposite/hypotenuse

opposite = 65 ft

sin 41° = 65/AC

cross multiply

0.65605902899 AC = 65

divide both sides by 0.65605902899

AC = 65/0.65605902899

AC = 99.0764506359  ft

AC ≈ 99.08 ft

Triangle BCE

We are looking for side BC. The triangle BCE is also a right angle triangle so we use the same methodology like the triangle ADC.

sin 62° = opposite/hypotenuse

opposite = 85 ft

sin 62° = 85/BC

cross multiply

BC sin 62° = 85

BC = 85/sin 62°

BC = 85/0.88294759285

BC = 96.2684543086

BC ≈ 96.27 ft

The angle ACB can be gotten when you subtract 62° and 41° from 180 (angle on a straight line).

Therefore,

∠ACB = 180° - 62° - 41°

∠ACB  = 77°

Now let us use the cosine law to find the zip line AB.

c² = a² + b² - 2ab cos C

a = 96.27 ft

b = 99.08 ft

c² = 96.27² + 99.08² - 2 × 96.27 × 99.08 cos 77°

c² = 9267.9129 + 9816.8464 - 19076.8632 cos 77°  

c² = 19084.7593 - 19076.8632 × 0.22495105434

c²  = 19084.7593 - 4291.36049041

c² = 14793.398810

square root both sides

c = √14793.398810

c = 121.628116856

c ≈ 121. 63 ft

length of the zip line = 121. 63 ft


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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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so

w=6

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Step-by-step explanation:

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Step-by-step explanation:

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theres 3 odd numbers not counting the 1 so thats 3/8  coverted to percent is %37.8

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Answers

Answer:

C

Step-by-step explanation:

If you look at the graph, you notice there is no data to determine the slope, but there (0,b) represents the y-intercept. So my guess is, they give you a clue what the slope is already, but if you notice the y-intercept lowers the linear line a few notches because (0,18) is lower than the (0,30). That is what I would choose as the answer

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Answers

Problem 11

Answer: -4x^2 - 6  (choice 3)

Work Shown:

P = 4x^2-x+1

Q = -6x^2+x-4

P+Q = sum of P and Q

P+Q = (4x^2-x+1)+(-6x^2+x-4)

P+Q = (4x^2-6x^2)+(-x+x)+(1-4)

P+Q = -2x^2+0x-3

P+Q = -2x^2 - 3

2*(P+Q) = twice the sum of P and Q

2*(P+Q) = 2*(-2x^2 - 3)

2*(P+Q) = 2(-2x^2) + 2(-3)

2*(P+Q) = -4x^2 - 6

======================================================

Problem 12

Answer: 6x^3 + 4x^2 - 34  (choice 1)

Work Shown:

y = 3x^3 + x^2 - 5

z = x^2 - 12

2(y+z) = 2(3x^3 + x^2 - 5      +   x^2-12)

2(y+z) = 2(3x^3 + 2x^2 - 17)

2(y+z) = 2(3x^3) + 2(2x^2) + 2(-17)

2(y+z) = 6x^3 + 4x^2 - 34

Answer:

11. 3

12. 1

Step-by-step explanation:

11.

[tex](4x^2-x+1)+(-6x^2+x-4)\\4x^2-x+1-6x^2+x-4\\-2x^2-3[/tex]

Double that

[tex](2)(-2x^2-3)\\-4x^4-6[/tex]

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

12.

[tex]y=3x^3+x^2-5\\z=x^2-12[/tex]

[tex]2(y+z)\\2(3x^3+x^2-5+x^2-12)\\2(3x^3+2x^2-17)\\6x^3+4x^2-34[/tex]

Please help me it’s really important to me

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1. b
2. e
3. a
4. c
5. d
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The double number lines show the ratio of cups to gallons.
64
0
Cups 4+
Gallons +
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4
How many cups are in 3 gallons?
cups

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Answer:

Step-by-step explanation:

The answer is There are 3 gallons

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Answer:

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Step-by-step explanation:

Answer:

-2-(-0.7)

= -2-(-0.7)

= -2 + 0.7

= -1.3

Step-by-step explanation:

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A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games.
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Answer:

C. Estimate the probability using your simulation.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

What are the three cues to remember for dribbling with mature form in basketball?

Answers

Answer:

Thee three cues are

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2. Always dribble at waist level

3. One's eyes should be up to see the team members and defenders while dribbling

Step-by-step explanation:

To dribble a basketball requires, keeping one's head up to see the on going game around. Endeavor to shield defenders from the ball with the aid of the non dribbling arm and body

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2. Dribbling should be done only at the waist level  

3. When dribbling a ball, one should keep his eyes up to see the game ongoing.

Compute the requested value. Choose the correct answer.
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It is
%

Answers

Answer:

8% percent I think

Step-by-step explanation:

Elsie starts a food blog. In the first month, there are 46 new subscribers. Each month after that, the number of new subscribers
increases by 15 more than the number of new subscribers in the previous month. At this rate, what will be the total number of
subscribers after 8 months?

788

394

151

848

Answers

Answer:C 151

Step-by-step explanation:

7 * 15=105 + 46=151

Answer: 788

Step-by-step explanation:

The amount of money that Li spends on video games depends on how
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Answers

Answer:

x < 4

Step-by-step explanation:

The function is represented by this equation:

22.5x = y

Where x is the number of games he buys and y is the amount of money that he spends. We know that y cannot be greater than 90, because Li only has 90 dollars. So, if y is less than 90, 22.5x must be less than 90 as well.

22.5x < 90

x < 90/22.5

x < 4

A spinner has 5 equal sections labeled 1 through 5. The bar graph shows the results of spinning the spinner 100 times. Which statement is true about not spinning a 1?

Answers

Answer:

The experimental probability is less than the theoretical probability.

Step-by-step explanation:

The probability of not spinning a 1 is the complement is 0.8.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The theoretical probability of not spinning a 1 is 4/5 or 0.8.

This is because there are 4 sections labeled 2 through 5 that are not labeled 1, out of a total of 5 sections.

The probability of spinning a 1 is 1/5 or 0.2.

So the probability of not spinning a 1 is the complement of that, which is 4/5 or 0.8.

or

= 1 - 1/5

= 4/5

= 0.8

Thus,

The probability of not spinning a 1 is the complement is 0.8.

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If you answer a question put the number of the question in your answer. Thanks

Answers

Answer:

You'll find the answer below each.

Step-by-step explanation:

1-4 you can use this formula: [tex]V=l*h*w[/tex]

1.

[tex]V=l*w*h\\V=(6ft)(4ft)(1ft)\\V=24ft^3[/tex]

2.

[tex]V=l*h*w\\V=(2yd)(\frac{1}{2}yd )(2yd)\\V=2yd^3[/tex]

3.

[tex]V=l*h*w\\V=(12\frac{1}{2}mm)(3mm)(4mm)\\V=150mm^3[/tex]

4.

[tex]V=l*h*w\\V=(2cm)(8.5cm)(2cm)\\V=34cm^3[/tex]

5-7 you need these 2 formulas: [tex]A=\frac{bh}{2}[/tex] and [tex]V=Bh[/tex] or you can use one formula which is: [tex]V=\frac{bh}{2}*h[/tex]

Let me explain. The first formula is for finding the area of the base of the triangle and the second formula is for finding the volume of the prism using the area previously mentioned. The first h is with respect to the triangle and the second h is with respect to the prism.

5.

[tex]V=\frac{bh}{2}*h\\V=\frac{(8in)(6in)}{2}* 18in\\V=\frac{48in^2}{2}*18in\\ V=48in^2*9in\\V=432in^3[/tex]

6.

[tex]V=\frac{bh}{2}*h \\V=\frac{(11m)(5m)}{2}*35m \\V=\frac{55m^2}{2}*35m\\ V=\frac{1925m^3}{2}\\ V=962.50m^3[/tex]

7.

[tex]V=\frac{bh}{2}*h \\V=\frac{(5mm)(8mm)}{2}*12mm\\V=\frac{40mm^2}{2}*12mm\\ V=40mm^2*6mm\\V=240mm^3[/tex]

For the last one, we have a special case.

This formula is a bit odd and long.

[tex]V=\frac{1}{4}h(\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}[/tex]

a=8yd

b=15yd

c=17yd

h=11yd

[tex]V=\frac{1}{4}(11yd)(\sqrt{-(8yd)^4+2[(8yd)(15yd))]^2+2[(8yd)(17yd)]^2-(15yd)^4+2[(15yd)(17yd)]^2}[/tex][tex]-(17)^4[/tex]

As you can see this is long. I'll just jump to the answer.

Answer: [tex]660yd^3[/tex]

Answer:

He is correct

Step-by-step explanation:

Probability & Sampling:Question 4
If the probability of a chance event is 0, it is
to happen
when compared to a chance event with a probability of 1.
Select one:
both more and less likely
less likely
more likely
equally likely

Answers

Answer:

more likely

Step-by-step explanation:

Complete the equation of the line whose slope is 555 and yyy-intercept is (0,4)(0,4)left parenthesis, 0, comma, 4, right parenthesis.

Answers

Answer:

y = 5x + 4

Step-by-step explanation:

Equation of a line passing through a point (x', y') and having slope 'm' is represented by,

y - y' = m(x - x')

If the point through which the given line is passing is (0, 4) and slope of the line is '5'

Equation of the line will be

y - 4 = 5(x - 0)

y = 5x + 4

Therefore, equation of given line is y = 5x + 4

Answer:

y=4x-1

Step-by-step explanation:

This is right i promise, also add me on ig melanin_.leesha

How many batches of cookies can Robert make?

Answers

Answer:

5 batches

Step-by-step explanation:

For this you need to divide the 2 fractions, and what ever you get will be the answer.

[tex]4\frac{1}{2}[/tex]÷[tex]\frac{3}{4}[/tex]

First make the mixed fraction into a improper fraction.

[tex]\frac{9}{2}[/tex]×[tex]\frac{4}{3}[/tex]=[tex]\frac{36}{6} =\frac{5}{1} =5[/tex]

Final answer

5 batches

A basketball has a volume of 23047 cm
What is the diameter of this basketball?
4 of 5 QUESTIONS
24 cm
16.6 cm
27.7 cm
12 cm
SUBMIT

Answers

Answer:

17.65693585 = r

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

23047 = 4/3 (3.14) r^3

23047 = 4.1866666666 r^3

Divide by 4.186666 on each side

23047/4.18666666 = 4.1866666666/4.18666666 *r^3

5504.856688 = r^3

Take the cubed root on each side

(5504.856688)^1/3 = r^3^(1/3)

17.65693585 = r

can someone help me with algebra 2 with an explanation?

Answers

Answer: This took me a long time to type, hope you read it and find it helpful and easy to understand...

1. [tex]x=1[/tex]

2. [tex]x=\frac{3}{2}[/tex]

3. [tex]x=1[/tex]

4. [tex]x=\frac{6}{5}[/tex]

Step-by-step explanation:

1.

[tex]\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}[/tex]

To make it easier to add / subtract fractions, we are looking for common denominators. I can see that if I move the fraction on the left with a denominator 3x to the right, I'll be able to add two equations with like denominator.

Let's add [tex]\frac{x-2}{3x}[/tex]

[tex]\frac{1}{x}=\frac{4}{3x}+\frac{x-2}{3x}[/tex]

Add the numerators and keep the same denominator.

[tex]\frac{1}{x}=\frac{4+x-2}{3x}[/tex]

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

To get rid of the denominator x on the left side, we can multiply by x.

[tex](x)\frac{1}{x}=\frac{2+x}{3x}(x)[/tex]

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

Now multiply by 3.

[tex](3)1=\frac{2+x}{3}(3)[/tex]

[tex]3=2+x[/tex]

Subtract 2.

[tex]3-2=x\\1=x[/tex]

The value of x is 1.

Proof.

[tex]\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}[/tex]

[tex]\frac{1}{1}-\frac{1-2}{3(1)}=\frac{4}{3(1)}[/tex]

[tex]1-\frac{-1}{3}=\frac{4}{3}[/tex]

[tex]1+\frac{1}{3}=\frac{4}{3}[/tex]

[tex]\frac{1*3+1}{3} =\frac{4}{3}\\\frac{4}{3}=\frac{4}{3}[/tex]

I can't show the proof to the following problems because I have a 5000 character limit.

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

2.

[tex]\frac{5x-5}{x^2-4x} -\frac{5}{x^2-4x}=\frac{1}{x}[/tex]

Again, we have like denominators, therefore, we can simply subtract the numerators and keep the same denominator.

[tex]\frac{5x-5-5}{x^2-4x}=\frac{1}{x}[/tex]

[tex]\frac{5x-10}{x^2-4x}=\frac{1}{x}[/tex]

Again, we can multiply by x to get rid of the x in the denominator.

[tex](x)\frac{5x-10}{x^2-4x}=\frac{1}{x}(x)[/tex]

Do not distribute the x in the numerator yet because we're gonna eliminate it later.

[tex]\frac{(x)(5x-10)}{x^2-4x}=1[/tex]

Factor the denominator.

[tex]\frac{(x)(5x-10)}{(x)(x-4)}=1[/tex]

Simplify x's.

[tex]\frac{5x-10}{x-4} =1[/tex]

Multiply by x-4 to get rid of the denominator.

[tex](x-4)\frac{5x-10}{x-4} =1(x-4)[/tex]

[tex]5x-10=x-4[/tex]

Add 10

[tex]5x=x-4+10[/tex]

Subtract x

[tex]5x-x=-4+10[/tex]

Combine like terms;

[tex]4x=6[/tex]

Divide by 4.

[tex]\frac{4x}{4}=\frac{6}{4}[/tex]

[tex]x=\frac{6}{4}[/tex]

Simplify by 2.

6/2 = 3

4/2 = 2

[tex]x=\frac{3}{2}[/tex]

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

3.

[tex]\frac{x^2-7x+10}{x}+\frac{1}{x}=x+4[/tex]

Same denominator, add numerators.

[tex]\frac{x^2-7x+10+1}{x}=x+4[/tex]

[tex]\frac{x^2-7x+11}{x}=x+4[/tex]

Multiply by x to get rid of the x.

[tex](x)\frac{x^2-7x+11}{x}=(x+4)(x)[/tex]

[tex]x^2-7x+11=x^2+4x[/tex]

Subtract [tex]-x^2-4x[/tex]

[tex]x^2-7x+11-x^2-4x=0[/tex]

Combine like terms;

[tex]-11x+11=0[/tex]

Subtract 11.

[tex]-11x=-11[/tex]

Divide by -11

[tex]x=\frac{-11}{-11} \\x=1[/tex]

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

4.

[tex]\frac{x^2+7x+10}{5x-30}+\frac{x}{x-6}=\frac{x^2-13x+40}{5x-30}[/tex]

It's easier if you move the operation with denominator x+6 to the right side with negative sign and bring the operation on the right side to the left side with negative sign as well.

[tex]\frac{x^2+7x+10}{5x-30}-\frac{x^2-13x+40}{5x-30}=-\frac{x}{x-6}[/tex]

Now, since we have the same denominators, we can simply subtract numerators.

[tex]\frac{x^2+7x+10-(x^2-13x+40)}{5x-30} =-\frac{x}{x-6}[/tex]

Distribute the negative sign.

[tex]\frac{x^2+7x+10-x^2+13x-40}{5x-30} =-\frac{x}{x-6}[/tex]

Combine like terms;

[tex]\frac{20x-30}{5x-30}=-\frac{x}{x-6}[/tex]

Factor.

I can see that I can factor a 5 on both numerator and numerator. This will allow me to simplify them.

[tex]\frac{(5)(4x-6)}{(5)(x-6)} =-\frac{x}{x-6}[/tex]

Simplify.

[tex]\frac{4x-6}{x-6}=-\frac{x}{x-6}[/tex]

Multiply by x-6

[tex](x-6)\frac{4x-6}{x-6}=-\frac{x}{x-6}(x-6)[/tex]

This will simplify the denominators.

[tex]4x-6=-x[/tex]

Add x and 6.

[tex]4x+x=6\\[/tex]

Combine like terms;

[tex]5x=6[/tex]

Divide by 5.

[tex]x=\frac{6}{5}[/tex]

I need this done please help in the picture

Answers

Answer

7.85

but I not sure JutMon21 know the problem

Answer:

I got 7.85

Step-by-step explanation:

First, I took the center angle which is 90 degrees in this case and divided by 360 and I got 0.25 Then, I multiplied that number by the radius which is 5 and I got 1.25. After that I multiplied 1.25 with 2π and the final answer that I got is 7.85

Johnny had a math test and he started at 2:18 p.M. It took 75 minutes to complete the test. He had a dentist's appointment at 4:30 p.M. How much time, in minutes, did he have between the end of the test and his appointment time

Answers

Answer:

57 minutes

Step-by-step explanation:

First, add 75 minutes to the time he started the test. Then, subtract the time you get from the time for his dentist appointment.

75 minutes is the same as 1 hour 15 minutes (1 hour = 60 minutes)

  H    M

  2   :  18

+  1   :  15

   3  :  33

He ended the test by 3:33 PM.

 H    M

 4  :  30

- 3  :  33

 0 :  57

Therefore, he had 57 minutes between the end of the test and his appointment.

Which expressions are equivalent to One-half + 3 c + StartFraction 4 Over 5 EndFractionCheck all that apply. 3 c + StartFraction 4 Over 5 EndFraction + one-half 1 + 2 + 3c + 4 +5 StartFraction 4 Over 5 EndFraction + one-half + 3 c 2 + 3c + 4 One-half + StartFraction 4 Over 5 EndFraction + 3 c

Answers

Question:

Which expressions are equivalent to ½ + 3c + ⅘.

Check all that apply.

Answer:

½ + 3c + ⅘ is equivalent to

1. ⅒(30c + 13)

2. 3c + 13/10

Step-by-step explanation:

The options are not well presented.

However, I'll give simplify the given expression in the question above.

Given: ½ + 3c + ⅘.

Required: Simplify

We start by collecting like terms

3c + ½ + ⅘

From this point, the expression can be solved in two ways

1. Solve fractions

This gives [Find LCM]

3c + (5 + 8)/10

3c + 13/10

3c + ⅒(13)

This can still be solved further [Find LCM]

(30c + 13)/10

⅒(30c + 13)

Hence ⅒(30c + 13) is equivalent to ½ + 3c + ⅘.

2. Convert fractions to decimal

½ + 3c + ⅘ becomes

0.5 + 3c + 0.8

Collect like terms

3c + 0.5 + 0.8

3c + 1.3

Convert decimal to fraction

3c + 13/10

3c + ⅒(13)

This can still be solved further [Find LCM]

(30c + 13)/10

⅒(30c + 13)

Hence ⅒(30c + 13) is equivalent to ½ + 3c + ⅘.

This is as far as the expression can be evaluated

Answer:

1,3.and 5

Step-by-step explanation:

11-n÷3 for n=6 Please solve

Answers

Answer: 9

11-6 (over fraction) 3

11-2 = 9

Round your answer to the nearest hundredth_
A
?
6
4

Answers

Answer:

Step-by-step explanation:

arc sin (4/6) = 41.81

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