A 60-foot zip line from a tree to the ground forms a 45 degree angle of elevation from the ground. How high above the ground is the top of the zip line? Round your answer to the nearest tenth of a foot.

Answer-

a. no

b. yes

c. no

Answer:

[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]

Step-by-step explanation:

We want to write the equation of a line that passes through the point (3, -1) and is perpendicular to the line:

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

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given equation is 6.

So, the slope of our perpendicular line is the negative reciprocal of 6, which is -1/6.

Next, we are given that it passes through the point (3, -1). Since we are given a point and know the slope, we can use the point-slope form. Point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point.

We will substitute -1/6 for m and (3, -1) for (x₁, y₁). Hence:

[tex]\displaystyle y-(-1)=-\frac{1}{6}(x-(3))[/tex]

Simplify:

[tex]\displaystyle y+1=-\frac{1}{6}(x-3)[/tex]

Our answer is valid as it as, but we can simplify this into slope-intercept form. Distribute:

[tex]\displaystyle y+1=-\frac{1}{6}x+\frac{1}{2}[/tex]

And subtract one from both sides. Therefore, our equation is:

[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]

Answer:

(a+b)/2(a-b)

Step-by-step explanation:

Explained in the paper

Goodluck

Answer:

It would be 9π

Step-by-step explanation:

(x-1)²π

(x-1)(2x-4)

Answer:

Step-by-step explanation:

sin A = [tex]\frac{opposite side}{Hypotenuse}[/tex]

Sin 29 = [tex]\frac{y}{500}[/tex]

0.4848 * 500 = y

y = 242.4 ft

Answer:

Y=242.4

Step-by-step explanation:

due to the association property the angle at the bottom left is 29 degrees

since sine property is oposite over hypothesis we get

sine(29)=y/500

500sin(29)=y

Y=242.4

Answer:

$856.91  after 7 years

Step-by-step explanation:

Initial investment, P = 500

Interest rate, i = 8% (compounded once a year, i.e. annually)

Number of years, t = 7

Substitute in compound interest formula

Future value,

A = P (1 + 0.08/1) ^(1*7)

= 500 (1.08)^7

= 856.91 (to the nearest cent)

Answer:

x² + 7x + 10 = 0

Subtract 10 from both sides

x² + 7x = -10

Use half the x coefficent (7/2) as the complete the square term

(x + 7/2)² = -10 + (7/2)²

   note: the number added to "complete the square" is (7/2)² = 49/4

(x + 7/2)² = -10 + 49/4

(x + 7/2)² = 9/4

Take the square root of both sides

x + 7/2 = ±3/2

Subtract 7/2 from both sides

x = -7/2 ± 3/2

x = {-5, -2}

Answer:

Step-by-step explanation:

Answer:

366

Step-by-step explanation:

A garden table and bench cost 816 when combined together

The garden table cost 84 less than the bench

Therefore the price of the bench can be calculated as follows

x + (x+84)= 816

2x+84= 816

2x= 816-84

2x= 732

Divide both sides by 2

x= 732/2

= 366

Hence the price of the bench is 366

https://youtu.be/QnydfcNVJoQ

sypport my channel pls pls

channel name sabrina clodia

Answer:

x + y = 60

Step-by-step explanation:

[tex]2x + 2y + 60 = 180 \\ 2x + 2y = 180 - 60 \\ 2x + 2y = 120 \\ \frac{2x + 2y}{2} = \frac{120}{2} \\ x + y = 60 \\ [/tex]

Answer:

Answer is 3 because

Step-by-step explanation:

a=2

20*2= 40

40-1 = 39

b = 13

so 39/13 = 3

Answer:

this two graph is not same because they have different slopes for this they are not same

Answer:

[tex]81[/tex]

Step-by-step explanation:

The average of a set of [tex]n[/tex] values is equal to the sum of the values in that set divided by [tex]n[/tex].

Therefore, the average of your 5 scores is equal to [tex]\frac{73+86+91+88+67}{5}=\boxed{81}[/tex]. Since evidently your grade is represented by the average of all your scores, your new grade is 81.

Answer:

A   y ≥ (1/2)x + 5

Step-by-step explanation:

The shaded area is above the solid line

the correct symbol is ≥

Answer:

x = 16

Step-by-step explanation:

These are corresponding angles meaning they are equal to each other.

4x + 30 = 94

4x = 64

x = 16

Answer:

f(0) = g(0)

Step-by-step explanation:

The functions intersect at x =0, which means they have the same y value at x=0

f(0) = g(0)

Answer:

Angle F

Step-by-step explanation:

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

Explanation:

We see that angle A = angle E as shown by the arc marking. The tickmark says that side AB is the same length as side EF.

In the letter sequences "AB" and "EF", erase the first letters A and E to be left with B and F. This is one way to show how angle B pairs with angle F, and that is enough to show the two angles are congruent.

Answer:

the answer is c

Step-by-step explanation:

juice would be 1 variable and magazines would be another. u would put each variable next the things that they represent, so j for juice would be put with 3.25 because that's how much 1 bottle costs. The variable m would be with 8.5 because that's how much the magazines cost.

Answer: Hi the Range is 4

Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

18, 16, 19, 15, 17

19,18,17,16,15

19-15= 4

Answer:

[tex]\text{A. }\frac{5}{6}\pi x^2[/tex]

Step-by-step explanation:

The area of a sector with measure [tex]\theta[/tex] is equal to [tex]r^2\pi\cdot \frac{\theta}{360}[/tex]

Since there are 360 degrees in an angle, the measure of sector K must be 360-60=300 degrees.

What we know:

Thus, the area of the sector is [tex]x^2\pi\cdot \frac{300}{360}=\boxed{\text{A. }\frac{5}{6}\pi x^2}[/tex]

Answer:

x = 2

Step-by-step explanation:

In a vertical line, all x-coordinates are the same.

x = 2

Answer:

x =2

Step-by-step explanation:

A vertical line means the x value remains constant

The x value is 2

x =2

Answer:

288 pi yds^3

Step-by-step explanation:

First find the volume of the cylinder

V = pi r^2 h = pi (6^2) * 24 = pi (36)*24 =864 pi

Then find the volume of one sphere

V = 4/3 pi r^3 = 4/3 pi (6)^3 = /43 pi (216) =288 pi

There are 2 sphere so multiply by 2

288 pi *2 =576 pi

Subtract the spheres from the cylinder

864 pi - 576 pi =288 pi

Answer:

1/6

Step-by-step explanation:

A dies has six sides

1,2,3,4,5,6

There is 1 three

P(3) = number of threes/ total numbers

      = 1 / 6

Answers:

It looks like you have the correct order. To get those answers above, we simply multiply the original length by the scale factor 6.

Example: 7*6 = 42