A goat (point G) is tied with a 6-foot rope to the corner of a shed. The floor of the shed is a
square whose sides are each 3 feet long. The shed is closed and the goat can't go inside.
The space all around the shed is flat, grassy, and the goat can't reach any other structures
or objects. What is the area over which the goat can roam?

Answer:

B) [tex]3\sqrt{3}[/tex]

Step-by-step explanation:

First simplify the radical on the right.

[tex]\sqrt{75}[/tex] is equal to [tex]\sqrt{25} *\sqrt{3}[/tex] , because 25 * 3 is 75, so we can separate the square roots into the product of these two square roots.

Then we know [tex]\sqrt{25}[/tex] is just equal to 25, which means the simplified version of [tex]\sqrt{75}[/tex] is [tex]5\sqrt{3}[/tex].

Then we can use this new representation to finish solving.

[tex]8\sqrt{3}-5\sqrt{3} =3\sqrt{3}[/tex], so the answer would be B

Answer:

x=1 and y=4/5

Step-by-step explanation:

Given system of equations

3x+5y=7

5x+10y=13

Multiply first equation by 2

2(3x+5y)=2(7)

6x+10y=14

Eliminate y-variable to get "x"

 6x+10y=14

- 5x+10y=13

         x = 1

Substitute x=1 into either equation and find "y"

3x+5y=7

3(1)+5y=7

3+5y=7

5y=4

y=4/5

Therefore, x=1 and y=4/5

i) less than

ii) greater than

iii) less than

iv) greater than

Step-by-step explanation:

do you need the calculations too?

Answer:

Miguel earned 37 points.

Step-by-step explanation:

32+5=37

To find the average divide total caught by total hours:

Leonard = 40 / 8 = 5 fish per hour

Charlotte = 32/8 = 4 fish per hour

Leonard caught more fish per hour.

Answer:

See Below.

Step-by-step explanation:

For Leonard: 40/8 = 5 fishes/hr

For Charlotte: 32/8 = 4 fishes/hr

From this, we can identify that Leonard caught more fishes per hour or faster.

Answer: if you simplify this it becomes 30=28 but this is a false statement so you would say 30≠28

Step-by-step explanation:

≠ means not equal

Right circular cylinder has its height as the straight line connecting centers of its top and bottom circle. The volume of given cylinder is: 5889.95 cubic feet.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi \times r^2 \times h \: \rm unit^3[/tex]

For the given case, the considered right circular cylinder has these dimensions:

Its base diameter = 17.5 ft

Its height = 24.5 ft

Since radius is half of diameter, thus, radius of considered cylinder = 17.5/2 = 8.75 ft

Thus, using the formula for volume of right circular cylinder, we get:

[tex]V = \pi \times r^2 \times h \: \rm unit^3\\V \approx 3.14 \times (8.75)^2 \times (24.5) \approx 5889.95 \: \rm ft^3[/tex]

Hence, the volume of given cylinder is: 5889.95 cubic feet.

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Answer:

72

Step-by-step explanation:

multiply 18 by 4,

since 100/4 is 25, and four quarters makes a dollar, multiply it by 4

18(4) = 72

Step-by-step explanation:

Key words:

Let's create an equation:

y is squared.

[tex] {y}^{2} [/tex]

Then, added to twice the same number.

[tex] {y}^{2} + {y}^{4} [/tex]

Lastly, minus by 74.

[tex] {y}^{2} + {y}^{4} - 74[/tex]

is your equation.

Answer: 27

Step-by-step explanation:

Convert 60% to a decimal

.60 * 45 = 27

Answer:

the answer is A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

I think it is

Answer:

Earth to the Moon I think

Answer:

x<_5

Step-by-step explanation:

first collect the like terms

4x<_28-8

4x/4<_20/4

=x<_5

Answer:

V=904.32 cubic centimeters

Step-by-step explanation:

V=4/3(Pi)x6^3

Answer:

11.6

Step-by-step explanation:

Divide the 23.20 by 2 to get 11.6 per fluid. So the answer is $11.6.

Hope this helped you out!!!

Answer:

$1.45 per fluid ounce

Step-by-step explanation:

There are 8 ounces in 1 cup

There are 16 ounces in 2 cups

Solve:

-Chetan K

The profit on the shares is $2180

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

Number of shares = 50

Cost price = $98.40

Current price = $142.00

The profit on the shares is then calculated as

Profit = (Current price - Cost price) * Number of shares

Substitute the known values in the above equation, so, we have the following representation

Profit = (142 - 98.40) * 50

Evaluate

Profit = 2180

Hence, the profit is $2180

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Answer:

y=3x+10 is the answer. I hope it is

Answer:

the answer  is 322

Step-by-step explanation:

Answer:

129.82

Step-by-step explanation:

I got the right answer

The cost to make the spinner is $132.50.

The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.

The area of each triangle is (1/2) * base * height = (1/2) * 2 * 5 = 5 square centimeters.

The total area of the spinner is 2 * 5 = 10 square centimeters.

The cost to make the spinner is 10 * $13.25 = $132.50.

Rounded to the nearest cent, the cost is $132.51.

Here is the calculation:

Area of each triangle = (1/2) * base * height = (1/2) * 2 * 5 = 5 square centimeters

Total area of the spinner = 2 * 5 = 10 square centimeters

Cost to make the spinner = 10 * $13.25 = $132.50

Rounded to the nearest cent, the cost is $132.51

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Answer:

Slope: 3

Step-by-step explanation:

There are two ways to solve this, one is more algebraically, and one is more logically.

Algebraically:

When only a graph is available to us as a resource, we can use a method called rise-over-run, which looks like this [tex]\frac{y}{x}[/tex].

Now, we select 2 points on the graph that are real integer values, meaning they aren't decimals. I will use (3,-2) and (4,1)

When we use rise-over-run we subtract the y-values and the x-values from each over before dividing. [tex]\frac{1-(2)}{4-3} = 3/1=3[/tex]

Logically:

We can use something called a "slope triangle" to find the slope. We will connect the same 2 points mentioned before.

We will draw a triangle to the right of the two points. I will attach a screenshot.

Answer:

Hey there!

When we are given what one of our variables is equal to, we can easily solve the system of equations via substitution, which is where we take the variable value, plug it into the other equation, and solve for the other variable.

In this case, we just take our value for y and plug it in for the value for y in the first equation and solve for x.

2(-x+7)=14-2x

-2x+14=14-2x

-2x=-2x

x=x

As we can see, there are infinitely many solutions to this first equation, which means that there is no possible way to solve for y because x has infinitely many solutions, so there are infinitely many solutions to this system of equations, because they are both the same line.

I hope this helps! :D

Diagonals of paralleogram bisect eachother

[tex]\\ \rm\longmapsto 5x=30[/tex]

[tex]\\ \rm\longmapsto x=30/5[/tex]

[tex]\\ \rm\longmapsto x=6[/tex]

As we know that, Diagonal of parallelogram bisect each other. That means the two halves of the diagonal are equal. According to this property;

[tex]5x = 30[/tex]

Now, Solve for x by dividing both sides of equation by 5 to eliminate the coefficient of x

[tex]x = 6[/tex]

[tex]5x = 30[/tex]

[tex]5 \times 6 = 30 \\ 30 = 30[/tex]

Answer:

Step-by-step explanation:

8.2×10^9 ×4.5×10^{-5}=36.9×10^4

Answer:

its c 3.69x105

Step-by-step explanation:

Step-by-step explanation:

12 in long requires 96 pounds.

inversely proportional means that if I double the length of the handle, I need only half of the force.

so,

24 in long requires 48 pounds.

the product of both factors is constant for the system.

c = 12×96 = 1152 = 24×48 = ...

c is called "work". it is force times distance and usually expressed in joules.

(a)

so, the force is then work / distance.

force = 1152 / length

(b)

60 = 1152 / length

60 × length = 1152

length = 1152/60 = 288/15 = 96/5 = 19.2 in

the handle must be 19.2 in long to do the same work with 60 pounds of force (i.e. to loosen the bolt with 60 pounds of force).

The rate at which the ball drops from the height is an illustration of an geometric sequence

The height of the 9th bounce of the ball is 0.4 feet

The given parameters are:

Initial height, a = 4.75

Rate, r = 75%

Bounce, n = 9

The function that represents the height of the ball is:

[tex]H = ar^{n[/tex]

So, we have:

[tex]H = 4.75 * (75\%)^{9[/tex]

Evaluate

[tex]H = 0.4[/tex] --- approximated

Hence, the height of the 9th bounce of the ball is 0.4 feet

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Answer: B.

Step-by-step explanation: 2x² + x - 6x - 3

= 2x² - 5x - 3

Tell me if you get the answer right.

Answer:

diameter =20 inches

radius = d÷ 2

=20 ÷2

r. = 10 inches.

Answer:

10 inches

Step-by-step explanation:

radius is half of the diameter and half of 20 is 10

Answer:

B

Step-by-step explanation:

This is all 1/3 of the number of times the experiment was tried to put in perspective john has 10 apples and he gives 3 away that's about 1/3 of the amount of apples