Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine! Payton is overcome with emotion and needs your help to save her dog. You can repel down and successfully rescue Willow, but you must calculate how much rope is needed.

The ravine is 153 feet deep the repel line will be the diagonal distance from the top of the ravine to Willow The anchor and repel line form a 35 degree angle; this is angle A in the image below.

(a) Calculate the length of the repel line using one of the 3 trigonometry ratios taught (sin, cos, tan) Round your answer to the nearest whole number. Show all needed math for calculating this length.

5+(7+x)

Finding an Equivalent Expression

The associative property of addition states that you can move the terms that are inside the parentheses and still have the expression remain true. So, in the answer above, I moved 5 out of the parentheses and x into the parentheses. No matter the value of x the value of the expression will remain the same

Examples and Proof

Another example of the associative property could be (1+6)+3 = 1+(6+3). To prove this statement we can evaluate each side of the expression.

First, let's do (1+6)+3

Next, let's do 1+(6+3)

As you can see both of these expressions are the same, thus proving that the associative property works in this situation.

Answer:

4 Nickles

Step-by-step explanation:

to find this out we can devide the total cost (20 ¢) by the worth of the coin we are using (1 Nickel = 5 ¢) as shown below

20 ÷ 5 = 4

what this equation shows is that 4 nickels are needed to add up to a total of 20 ¢

hope this helps

side note, i dont usually say this but at the moment i am 2 crowns away from my next level, so if the answer seems fit to you a crown would be, depending on the other answer, thank you

EDIT:
Additional Example

this method can be applied to most situations, even if you need multiple coin types

say Ron wants to buy a 57 ¢ apple pie slice in exact change, lets assume he has a surplus in the four common coins in his wallet book or pocket

first he uses a quarter and divides as follows

57 ÷ 25 = 2 with a remainder of 7

then he can take a coin of less value then the remainder (in this case a nickel since 5 < 7, and not a dime since 10 > 7)

7 ÷ 5 = 1 with a remainder of 2

and finally with the pennies

2 ÷ 1 = 2

with this info we know that Ron will need 2 quarters, 1 nickel and 2 pennies to have exact change in the least amount of coins

Answer:

5 feet

Step-by-step explanation:

So you know the cross-sectional area of the circle at the bottom of the cylinder is 28 square feet and you are told the volume of the cylinder is 140 cubic feet which means the height must be 5 feet as the 28 square feet must continue going up to fill the 140 cubic feet.

Answer:

During the Cold War, the political and economic tensions between the U.S. and the Soviet Union shaped Latin American political society. Named as 'Operation Condor', the political crackdown of revolutionary organizations and guerrilla groups on the continent was backed by the North American superpower.

Answer:

19.99 (rounded)

Step-by-step explanation:

We know that the formula to solve is:

[tex]V=\pi r^{2}h[/tex].

[tex]R = \sqrt{\frac{V}{\pi h } } = \sqrt{\frac{16328}{\pi 13} = 19.99493[/tex]

Answer:

[tex] x^2 -6^2[/tex]

x(x - 6) + 6(x - 6)

Step-by-step explanation:

Area of the white figure

= Area of external square - Area of internal square

[tex] x^2 -6^2[/tex]

This can also be written as:

x(x - 6) + 6(x - 6)

Answer:

6 units

Step-by-step explanation:

The questions states that the area = perimeter.

From this we can set up an equation:

[tex]x*y=2x+2y[/tex]

Since we know one of the sides is 3 we can substitue one of the variables for 3. In this case I choose [tex]y[/tex]

[tex]3*x=2x+2*3\\3x=2x+6[/tex]

Solving for x we get [tex]x=6[/tex].

That's our answer!

Answer:

degree x π/180 = radian

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

1) -290° × π/180 = -5.061rad

3) 970° × π/180 = 16.93rad

5) 510° × π/180 = 8.901rad

7) 210° × π/180 = 3.665rad

9) 240° × π/180 = 4.189rad

11) -945° × π/180 = -16.49rad

13) 315° × π/180 = 5.498rad

15) -520° × π/180 = -9.076rad

17) 300° × π/180 = 5.236rad

19) 555° × π/180 = 9.687rad

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

i hope this helps!

Answer:

Step-by-step explanation:

area = 1/2 x base x height

Explanation:

➡ Pythagorean Theorem: a² + b² = c²

➡ We eliminate D - So the Pythagorean theorem is used for right triangles and that equation is a² + b² = c² and answer D doesn't have anything squared.

➡ Hypotenuse is what letter in the theorem? It is Letter C!

➡ 11² + 60² = 3721

Hope this helps! :)

Answer:

8%

Step-by-step explanation:

8 out of 100 are green

8/100  * 100% = 8 %

Answer:

8% of the beads are green

Step-by-step explanation:

Step 1:  Determine what percentage of the beads are green

This problem is known as a probability problem which basically tries to determine the proportionality between certain numbers.  In this example we are trying to figure out the proportionality between the green beads and the total sample.  

(8 green beads) / (100 total beads)

0.08

0.08 is the probability but if we want to determine what the percentage is of the number we just multiply it by 100.

0.08 * 100 = 8%

Answer:  8% of the beads are green

Answer:105

Step-by-step explanation:

area of rectangle (b*h) (7*12)

Area of triangle 1/2 (b*h) 1/2(7*6)

Rectangle=84

Triangle=21

84+42= 105

Answer:

105

Step-by-step explanation:

Well, this figure, as you can see, is made of two figures - a triangle and a rectangle.

To find it's area we will find the areas of the triangle and the rectangle separately and then sum them. I hope you get why we do that.

So, let's start with the rectangle.

The area of the rectangle is very easy to find simply just multiply the lenghts of its two sides:

A1 = 7 * 12 = 84

Now, the triangle.

You can see that one of the smaller sides of the rectangle is equal to 7. The side in front of it is also 7. Notice that this side is also equal to one of the sides of the triangle, its base.

So from the figure we can tell that the base of the triangle is equal to 7, we are also given its height.

There is a formula we can use here to find the area. The area of a triangle is equal to its base (a) multiplied by the height(h) and divided by 2. I'll call the area of the triangle A2.

We know the height

h = 6

I hope you noticed that we also know the base

a = 7

So we just use the formula:

A2 = (6 * 7) / 2 = 42 / 2 = 21

Now that we have the areas of the two figures, A1 and A2, all we have to do is to sum them to find the area of the big one.

So, let's do it:

A = A1 + A2

A = 84 + 21 = 105

Answer:

9 children and 0 adults, 6 children and 2 adults, 3 children and 4 adults, or 6 adults and 0 children went to the park

Step-by-step explanation:

2x + y = 7,  y is a function of x

Explanation:

2x + y = 7 is a function

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

Rewrite into slope intercept form

y = 7 - 2x

y = -2x + 7

The vertical line touches the graph only one time. Thus y is a function of x.

Answer:

Given equation:  [tex]2x+y=7[/tex]

Definition of a function

The given function is in the standard form of a linear equation: [tex]ax+by=c[/tex]

If the given equation is rearranged to make y the subject:

[tex]y=-2x+7[/tex]

it is now in the general form of a linear equation, [tex]y=mx+b[/tex] (where m is the slope and b is the y-intercept).

A linear equation is one of a straight line, and so, by definition, each value of y corresponds to one value of x.  Therefore, this is a one-to-one function.

Answer:

difference of 10 min

Step-by-step explanation:

Answer:

your correct answer is 15

i just did wrong so the person below me is correct

Step-by-step explanation:

Answer:

A: 15

Step-by-step explanation:

It is asking for the hypotenuse of the triangle. To find this, use pythaogreans theorem.

A^2 + B^2 = C^2

In this case,

9*9 + 12*12 = C*C

81 + 144 = C*C

225 = C*C

Now do the square root of both sides and you get

15 = C. Therefore the missing length is 15.

Answer:

Area = 3x^2 +x -14 units^2

Step-by-step explanation:

Area of a rectangle is (width x height)

Area = (x-2)*(3x+7)

Area = 3x^2 +x -14

Answer:

2502.10526316

≈ 2502.11

Step-by-step explanation:

Hope this helps!

Answer:

Part A: I disagree, because when shading the regions of inequalities, only the shaded area that overlaps with the other shaded area is the solution, not every single point shaded. 5x - 3y > 1 and 3x + 4y ≤ 18 have an overlapping shaded region, that is where the solutions are.

Part B: picture attached

Part C: All points located on the overlapped shaded region (the darkest part)

Step-by-step explanation:

hope this helps, good luck!

Answer:

I am pretty sure it's 312ft^2

Step-by-step explanation:

If you do 12x13/2 its 78

then you would do 78 x 4

and you get 312

so its 312ft^2

Answer:

A. x^2 + y^2 = 4^2

Step-by-step explanation:

The equations of a circle is x^2 + y^2 = r^2

Therefore, the equation of this circle is x^2 +y^2 = 4^2

Answer:

A

Step-by-step explanation:

Remark

The formula for a circle is

x^2 + y^2 = r^2

The number associated with x^2 and y^2 must always be 1. If it's not then you do not have a circle.

Answer

The answer to this question is x^2 + y^2 = 4^2 where r = 4 and it is squared.

Answer:

Your answer is B

Step-by-step explanation:

6 x 13 +11 = 89

13 x 6 + 11 = 89

TRUE

Answer:

Anwer is B

Step-by-step explanation:

13×6+11=89

so 6×13+11=89

so the true answer is B

Answer:

20079.05 cm^2,

Step-by-step explanation:

Surface area of the box without the lid

=  90*42 + 2(90*34) + 2(42*34) = 12756.

Now find Surface area of the half cylinder:

The diameter of the 2 half circles = 42 so the radius = 21.

The area of the lid  

= 2 + 1/2 π (21)^2 + π r * 90

= 7323,052

Total = 20079.052

Applying the distance formula, the distance from from Tia's home to Lei's home = 14.4 units.

The distance formula helps us to find the distance between two given coordinate points. It is expressed as, [tex]\mathbf{d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} }[/tex].

Tia = (4, 8) = (x1, y1)

Lei = (12, 20) = (x2, y2)

Apply the distance formula to find the distance from Tia's home to Lei's home:

d = √[(12−4)² + (20−8)²]

d = √[(8)² + (12)²]

d = √(64 + 144)

d = √208

d ≈ 14.4 units

The distance from from Tia's home to Lei's home = 14.4 units.

Learn more about the distance formula on:

https://brainly.com/question/661229

#SPJ4

Answer:

x [tex]\geq[/tex] 5 ( the last one)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The inequality of C says the amount of hours of tv that kenny can watch (x) can be exactly or anything below 5 hours

Answer:

-8°C Degrees in Toronto

Step-by-step explanation:

Just calculate it.

If you minus 3 from -5, then you will get -8, so hence, your answer is -8.

Answer:

-8 (degrees)C

Step-by-step explanation:

-5-3=-8

Answer:

Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula,

Answer:

option C

Step-by-step explanation:

area of rectangle = length * width

12x^2 - 5x - 3 = (4x - 3) * width

12x^2 - 9x + 4x - 3 = (4x - 3)* width

3x(4x - 3) + 1(4x - 3) = (4x - 3)*width

(3x + 1)(4x - 3) / (4x - 3) = width

3x + 1 = width

Using the binomial distribution, it is found that there is a 0.16 = 16% probability of choosing a gray button, replacing it, and choosing gray again.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability of two gray buttons is:

P(X = 2) = (0.4)² = 0.16.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

Answer:

68m2

Step-by-step explanation:

First you can split the shape into three different ones (as shown in my incredibly awful sketch ><)

Then you can multiply the length x width.

so 3x3 and 3x3 and 5x10

The sum of all the answers in 68 ^^

hope this helps for further problems <33