A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.
He's tied to a corner of the barn with a 12 ft rope. Find the grazing area of the goat.

Answer:

{ - 3, 0 ]

Step-by-step explanation:

parenthesis ( ) is used when the interval does not include the end values

brackets [ ] are used when the interval includes the end values

The end values here are - 3 and 0 so brackets are used, that is

[ - 3, 0 ]

Answer:

total = 99m² + 39.4m²

= 148.4m²

Here we go !!

Since it's a regular pentagon, all it's sides are equal so let's solve for x

[tex] \hookrightarrow \: 3(x - 1) = 5x - 6[/tex]

[tex] \hookrightarrow \: 3x - 3 = 5x - 6[/tex]

[tex] \hookrightarrow \: 3x - 5x = - 6 + 3[/tex]

[tex] \hookrightarrow \: - 2x = - 3[/tex]

[tex] \hookrightarrow \: x = \dfrac{ - 3}{ - 2} [/tex]

[tex] \boxed{\boxed{x = \dfrac{3}{2} }}[/tex]

now let's find the measure of each side, i.e

[tex] \hookrightarrow \: 5x - 6[/tex]

[tex] \hookrightarrow \: (5 \times \dfrac{3}{2}) - 6[/tex]

[tex] \hookrightarrow \: \dfrac{15}{2} - 6[/tex]

[tex] \hookrightarrow \: 7.5 - 6[/tex]

[tex] \mathrm{\hookrightarrow \: 1.5 \: units}[/tex]

perimeter = 5 × side length ( for a regular pentagon )

[tex] \hookrightarrow \: 1.5 \times 5[/tex]

[tex] \boxed{ \boxed{ \: \: \: \: \: \: \: \: 7.5 \: \: units \: \: \: \: \: \: \: }}[/tex]

Step-by-step explanation:

all steps are done in the picture

Answer:

The cost of the printer is x=288 and cost of computer is 3x=864

Step-by-step explanation:

Let the cost of the printer be x and cost of computer be 3x

ATQ, x+3x=1152, x=288.

The cost of the printer is x=288 and cost of computer is 3x=864

Answer:

see explanation

Step-by-step explanation:

For the triangle to be isosceles it must have 2 equal sides.

Calculate the length of the sides using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = B (3, 5)

AB = [tex]\sqrt{(3-(-1))^2+(5-2)^2}[/tex]

     = [tex]\sqrt{(3+1)^2+3^2}[/tex]

     = [tex]\sqrt{4^2+9}[/tex]

     = [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5

Repeat with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = C (3, - 1)

AC = [tex]\sqrt{(3+1)^2+(-1-2)^2}[/tex]

      = [tex]\sqrt{4^2+(-3)^2}[/tex]

      = [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5

Consider B (3, 5) and C (3, - 1)

Since both x- coordinates are 3, this is a vertical line and its length is the difference of the y- coordinates, that is

BC = | - 1 - 5 | = | - 6 | = 6

Then

AB = AC = 5 , BC = 6

Since AB = AC = 5 then the triangle is isosceles

Answer:

6+10×4=40+6=46 number

Answer:

(x−2)2+(y+1)2=100

Explanation:

the standard form of the equation of a circle is  

2 2 ( x − a ) 2 + ( y − b ) 2 = r 2 2 2  where  ( a , b )  are the coordinates of the center and r is  the radius  to find the center we require the  midpoint of the  2 given points  center  = [ 1 2 ( − 4+ 8 ) , 1 2 ( 7 − 9 ) ]  center = ( 2 , − 1 )  the radius is the distance from the center to either of  the 2 given points  calculate the radius using the  distance formula ∙  d = √ ( x2 − x 1 ) 2 + ( y 2 − y 1 ) 2  let  ( x 1 , y 1) = ( 2 , -1 )  and  ( x 2 , y 2 ) = ( − 4 , 7 ) r = √ = √ ( − 4 − 2 ) 2 + ( 7 + 1 ) 2 = √ 36 + 64 = 10 ⇒ ( x − 2 ) 2 + ( y − ( − 1 ) ) 2 = 10 2 ⇒ ( x − 2 )2 + ( y + 1 ) 2 = 100 ←  equation of circle

Answer:22

Step-by-step explanation:

4*(2) + (6) +12 - 2*(2)=

8 +6 +12 -4=

14 +8= 22

Answer: 22

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We are given the function:

[tex]f(x) = x^2 - 4x[/tex]

And we want to find:

[tex]\displaystyle f(2b^2)[/tex]

Substitute:

[tex]\displaystyle f(2b^2) =(2b^2)^2 -4(2b^2)[/tex]

And evaluate:

[tex]\displaystyle \begin{aligned} f(2b^2) &=(2b^2)^2 -4(2b^2) \\ &=(4b^4) +(-8b^2) \\ &= 4b^4 - 8b^2 \end{aligned}[/tex]

In conclusion, our answer is A.

Answer:

[tex]\huge\boxed{\sf SG = 31}[/tex]

Step-by-step explanation:

Given:

SW = 3x + 1

WA = 6x

AG = x + 6

SW = AG

Required:

Length of SG = ?

Solution:

Given that:

SW = AG

3x + 1 = x + 6

Combining like terms

3x - x = 6 - 1

2x = 5

x = 5/2

x = 2.5

Now,

SG = SW + WA + AG

SG = 3x + 1 + 6x + x + 6

SG = 3x + 6x + x + 1 + 6

SG = 10x + 6

Put x = 2.5

SG = 10(2.5) + 6

SG = 25 + 6

SG = 31

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

D) 9.8

Step-by-step explanation:

The geometric mean of two numbers x and y is

[tex]\sqrt{xy}[/tex]

so [tex]\sqrt{8*12}[/tex] = [tex]\sqrt{96}[/tex] [tex]\approx 9.7979[/tex]

Which, since the 9 in the hundredths place is greater than 5, we can round up to 9.8

Answer:

65÷5(18-5)

=65÷5×13

=13×13

=169

Answer:

[tex]13\leq x<4[/tex]

Explanation:

If a side has a bracket [] then it is less than or equal to, meaning that it can reach that exact number.

However, if a side has a parentheses () then it is simply less than. It cannot be that exact number, but it can be even slightly less than that number.

Answer:

The cover has diameter of:

a.

Area of the pool cover:

b.

The length of the rope:

Answer:

Step-by-step explanation:

Add the length of the pool and the extent the pool cover [ 12in = 1ft ] has over the pool.

20 + 2 = 22ft

Part A:

The formula for the area of a circle is πr².

To find the radius just divide by two; 22 / 2 = 11ft

= π(11)²

= 121π

≈ 379.94ft

Part B:

We can use the circumference formula [ dπ ] to find how long the rope is.

= 22(3.14)

= 69.08ft

Best of Luck!

The length of the shorter piece is 45 inches.

Let's represent the length of the shorter piece as "x" inches.

According to the information given, the length of the longer piece would be three times the length of the shorter piece, which means it's 3x inches.

Since the total length of the pipe is 180 inches, we can set up an equation:

x (shorter piece) + 3x (longer piece) = 180

Now solve for x:

4x = 180

x = 45

Therefore, the length of the shorter piece is 45 inches.

Learn more about length at https://brainly.com/question/26589728

#SPJ3

I'm not sure if this is what you meant - 3.12.5.8.6.6, but I'm operating based on that

mean - 6.7

median - 6

mode - 6

range - 9

Answer:

The answer is C

Step-by-step explanation:

since the left side reads k times a, the only way to get a by itself is by dividing both sides by k

Answer:

D 37.64

Step-by-step explanation:

C=2πr

so 2✘3.14 ✘6

Answer:

84%

Step-by-step explanation:

you cross multiply 42/50 by 2 and then u get 84/100

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

25958400

Step-by-step explanation:

[tex] {8}^{2} \times 6(4 + {8}^{2} \times (10 - 6) {)}^{2} [/tex]

[tex] = 64 \times 6(4 + {2}^{6} \times 4 {)}^{2} [/tex]

[tex] = 64 \times 6(4 + {2}^{6} \times {2}^{2} {)}^{2} [/tex]

[tex] = 64 \times 6(4 + {2}^{8} {)}^{2} [/tex]

[tex] = 64 \times 6(16 + 2048 + 65536)[/tex]

[tex] = 64 \times 6 \times 67600[/tex]

[tex] = 25958400[/tex]

Answer:

The selling price of 21 articles is equal to the cost price of 18 articles. Find the loss percent. Answer: answer is 100/7 %

Answer:

t = 10

Step-by-step explanation:

z^t ⋅ z^5 = z^15

We know that a^b*a^c = a^(b+c)

z^(t+5) = z^15

Since the bases are the same, the exponents are the same

t+5 = 15

t = 15-5

t = 10

Step-by-step explanation:

maybe I am wrong sorry for that but try to understand it

have a great day

Answer:

27 Days

Step-by-step explanation

The rate of her gas consumption is inverse to the time she is driving. This means that if her time spent driving is increased by 66.66% (5/3 of the original rate), then it would inverse to create her decreased gas consumption by 3/5.

3/5 of 45 = 27

27 days

hope this helps :)

Each term has a common factor of x + y + z, so

a (x + y + z) + b (x + y + z) + c (x + y + z) = (a + b + c) (x + y + z)

Answer:

Step-by-step explanation: