Goat on a Rope
Farmer Smith has a goat named Mel. He hasn’t had time to put up a fence to contain Mel, so he has Mel tied to a rope in his field. The rope is attached to a pole, allowing Mel to wander within a circular area. The rope is 10 feet long. Farmer Smith remembers that the formula for the area of a circle is A = r2 , and that “r” means the radius of the circle. He wants to know how much grass Mel can eat, so he uses 3.14 for , and calculates the area of the circle. How many square feet of grass can Mel reach while still on his rope? (It might help to draw a picture.)

Answer:

Step-by-step explanation:

Let a, b, c represent the amounts received by the first, second, and third person, respectively.

  2a-1 = b

  c = b+11

  a + b + c = 224

Substituting for c, we have ...

  a + b + b+11 = 224

  a +2b = 213

Substituting for b, we have ...

  a +2(2a -1) = 213

  a +4a -2 = 213 . . . . . eliminate parentheses

  5a = 215 . . . . . . . . . . add 2

  a = 43 . . . . . . . . . . . . .divide by 5

  b = 2a -1 = 2(43) -1 = 85

  c = b +11 = 85 +11 = 96

The amounts received were ...

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Since two negative sign  = positive sign

Therefore,

7 + 11 = 18

hope it helps

Answer:

It's called a straight angle, it's a straight line.

Step-by-step explanation:

Literally a straight line.

Answer:

Straight angle ..

Answer:

x = -2

y = -4

Step-by-step explanation:

Graph the systems of equations. Then analyze the graph for the intersection. The point of intersection will be your solution set.

Answer:

[tex]x = -2\\y = -4[/tex]

Step-by-step explanation:

Question

[tex]\left \{ {{-2x + 2y = -4} \atop {3x + 3y = -18}} \right.[/tex]

Multiply throughout the equation to eliminate a variable:

[tex]-2x + 2y = -4[/tex] becomes [tex]-6x + 6y = -12[/tex] when multiplied by 3

[tex]3x + 3y = -18[/tex] becomes [tex]6x + 6y = -36[/tex] when multiplied by 2

Then add the values of the variables together:

[tex]-6x + 6x = 0\\6y + 6y = 12y \\-12 - 36 = -48[/tex]

And a new equation forms:

[tex]0 + 12y = -48[/tex]

[tex]y = -4[/tex]

Plug in [tex]y[/tex] to any of the previous equations to solve for [tex]x[/tex] :

[tex]-2x + 2y = -4[/tex]

[tex]-2x + 2(-4) = -4[/tex]

[tex]-2x - 8 = -4[/tex]

[tex]-2x = 4[/tex]

[tex]x = -2[/tex]

Answer:

When factorizing one number, what you get are other numbers that, when they get multiplied, the result of the product is the first number.

In our case, the pair of 3, 12 and the pair of 4, 9 are factors of 36, as it's the number we get when multiplying them:

We can factroize 36 like this: 2*2*3*3, and:

The factor pairs belong to the number 36.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

As per the given data:

The factor pairs are as follows:

3, 12

4, 9

We have to find out that of which number these factor pair belongs.

When the factors of any number are multiplied with each other, we get that number.

For finding out the number, we need to multiply the factor pairs:

3 × 12 = 36

4 × 9 = 36

The factor pairs belong to the number 36.

Hence, The factor pairs belong to the number 36.

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Answer:

169

Step-by-step explanation:

14 + 162 - 7 = 169

hoped this helped:)

Answer:

Option (2)

Step-by-step explanation:

If m(x) and n(x) are the functions inverse of each other,

Then the following condition should be fulfilled,

m[n(x)] = n[m(x)] = x

Here, m(x) = [tex]\frac{3x}{x+7}[/tex] and n(x) = [tex]\frac{7x}{3-x}[/tex]

m[n(x)] = [tex]\frac{3(\frac{7x}{3-x})}{(\frac{7x}{3-x})+7}[/tex]

          = [tex]\frac{21x}{7x+21-7x}[/tex]

          = x

n[m(x)] = [tex]\frac{7(\frac{3x}{x+7})}{3-\frac{3x}{x+7}}[/tex]

           = [tex]\frac{21x}{3x+21-3x}[/tex]

           = x

Therefore, [tex]\frac{3(\frac{7x}{3-x})}{(\frac{7x}{3-x})+7}=\frac{7(\frac{3x}{x+7})}{3-\frac{3x}{x+7}}=x[/tex] will be the correct option.

Option (2) will be the answer.

Rewrite the equation:

1/3  ⋅  ( πr2 ( 3r−h )) =  V.

Answer:

  $6

Step-by-step explanation:

Between 1 and 2 miles, the charge is $6.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 578 yds

The statement

The length is one more than three times the width is written as

l = 1 + 3w

Substitute the expression into the above formula and solve for the width

That's

578 = 2(1 + 3w) + 2w

578 = 2 + 6w + 2w

8w = 576

Divide both sides by 8

w = 72

Substitute w = 72 into l = 1 + 3w

That's

l = 1 + 3(72)

l = 216 + 1

l = 217

Therefore the dimensions are

length = 217 yd

width = 72 yd

Hope this helps you

Answer:

it's in the picture

Step-by-step explanation:

it's in the picture

Answer:

Here is a solution: (since idk the length or width of the pryamid)

Step-by-step explanation:

use the solution for volume.

V=L*W*H

(V= volume

L=Length

W=Width

H=Height)

Answer: Use distributive practice rather than massed practice. ...

Study in triads or quads of students at least once every week. ...

Don't try to memorize formulas (A good instructor will never ask you to do this). ...

Work as many and varied problems and exercises as you possibly can. ...

Look for reoccurring themes in statistics.

Answer:

Explained below.

Step-by-step explanation:

The value of different types of coins are as follows:

1 penny (p) = 1 cent

1 nickel (n) = 5 cents

1 dime (d) = 10 cents

1 quarter (q) = 25 cents

It is provided that Taylor has 18 cents in dimes and nickels in her pocket.

This is not possible.

Because the sum of any number of dime and nickel coins will always be a multiple of 5.

a·d + b·n = 10a + 5b = 5 (2a + b)

The value 18 cents can be formed as follows:

8p + d = 18 cents

3p + n + d = 18 cents

3n + 3p = 18 cents

Answer:

Step-by-step explanation:

This is a ratio problem and Sophia is expected to simplify the ratio by finding the smallest possible values and not to compound it by multiplying by some values

We can represent the given ratio 60:36 as a fraction.

60/36

we proceed to reduce the fraction by dividing both the numerator and the denominator by a common factor say 6

10/6

We can further reduce with a common factor of 2

5/2

re-writing the ratio we have 5:2

Answer:

Step-by-step explanation:

There is no solution for system of equations:  [tex]a_1x+b_1y=c_1\\a_2y+b_2y=c_2[/tex]

if:     [tex]a_1=a_2\quad and\quad b_1=b_2\quad and\quad \bold{c_1\ne c_2}[/tex]

so first, we we need to transform the equations to the form where the coefficients at y will be the same:

[tex]kx-3y=4\\ 4x-5y=7\\\\ (kx-3y)\cdot5=4\cdot5\\ (4x-5y)\cdot3=7\cdot3\\\\ 5kx-15y=20\\ 12x-15y=21[/tex]

Now we have  b₁=b₂ and c₁≠c₂ so the system has no solution if a₁=a₂

5k = 12

÷5     ÷5

k = ¹²/₅

The mean is affected by the skewness, whereas the median is not.

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

Let's go through the answer choices to see which are true and which are false.

You can use the commutative property to rearrange the problem like this, 18 + 28 * 28 * 28 * 28 = 130

Basically, you can use the properties of operations to solve 18 + 4(28) in various ways. Though whichever operation you apply must give you the same result. The result of 18 + 4(28) is 130.

   The four basic types of properties of operations are commutative, associative, distributive and identity. These properties only apply to the operations of addition and multiplication.

   According to the purplemath site, "The word 'commutative' comes from 'commute' or 'move around', so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is 'a + b = b + a'; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is 'ab = ba'; in numbers, this means 2×3 = 3×2."

   According to the splashlearn site, "the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped. Here's an example of how the sum does NOT change irrespective of how the addends are grouped. Here's another example. ( 75 + 81 ) + 34."

   According to the mathwarehouse site, "In general, this term refers to the distributive property of multiplication which states that the. Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products."

   According to the math site, "Identity property. The identity property for addition tells us that zero added to any number is the number itself. Zero is called the 'additive identity.' The identity property for multiplication tells us that the number 1 multiplied times any number gives the number itself."

Answer:

Sample response: Use the distributive property and expand 28, then distribute the 4 to 20 and the 4 to 8. Then you have 18 + 80 + 32. Use commutative property to reverse the order of 32 and 80 so that 18 and 32 are friendly numbers to add.

Step-by-step explanationWhich reasons did you include in your response? Check all that apply.

The distributive property can be applied to multiply 4(28) mentally.

The number 28 can be expanded to 20 + 8.

The commutative property can be applied to reverse the order of numbers.:

hope this helps \_(-^-)_/

Answer:

h=0.8

Step-by-step explanation:

Steps

$h+\frac{6}{5}=2$

$\mathrm{Subtract\:}\frac{6}{5}\mathrm{\:from\:both\:sides}$

$h+\frac{6}{5}-\frac{6}{5}=2-\frac{6}{5}$

Show Steps

$\mathrm{Simplify}$

$h=\frac{4}{5}$

Answer:

The answer would be 2h

Step-by-step explanation:

please let this be helpful

Answer:

m = 3/40

Step-by-step explanation:

4 = 3/4m - 6

m*4 = m(3/4m -6)

4m = m*3/4m + m*-6

4m = 3/4 - 6m

6m + 4m = 3/4

10m = 3/4

m = (3/4)/10

m = 3/40

check:

4 = 3/(4*3/40) - 6

4 = 3/(12/40) - 6

4 = (3*40)/12 - 6

4 = 120/12 - 6

4 = 10 - 6

Answer:

45

Step-by-step explanation:

So we have the expression:

[tex]ab^2-d[/tex]

And we want to evaluate it for a=3/4, =-8, and d=3.

Thus, substitute in these values:

[tex]=(\frac{3}{4})(-8)^2-3[/tex]

Do the exponent first. -8 squared is positive 64:

[tex]=(\frac{3}{4})(64)-3[/tex]

And 3/4 times 64 is 48:

[tex]=(48)-3[/tex]

Subtract:

[tex]=45[/tex]

Answer:

There is 243.84 cm in 8 feet.

Step-by-step explanation:

We have:

1 inch = 2.54 cm

1 feet = 12 inch  

We can find the number of centimeters (n) present in 8 feet as follows:

[tex] n = \frac{2.54 cm}{1 inch}*\frac{12 inch}{1 ft}*8 ft = 243.84 cm [/tex]

Therefore, there is 243.84 cm in 8 feet.

I hope it helps you!

Answer:

243.84

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

[(3+5)⋅2−5]⋅3

[8·2−5]⋅3

[16−5]⋅3

11⋅3

33

Answer:

33

Step-by-step explanation:

Lets break it down. Remember PEMDAS

[(3+5)⋅2−5]⋅3

[(8)⋅2-5]⋅3 start with the parenthisis

[16-5]⋅3 multiply

[11]⋅3

33

hope this helps :)

Answer:

There will be 24 boys, 32 -8 = 24

Step-by-step explanation:

In the class there is 20 boys.

All these are alzebraic expressions. A monomial consists of only one term, binomial contains two terms and a polynomial is when the number of terms is two or more than two.

In the given question

There are 8 more boys than girls in a class of total 32 students

let the number of girls be x according to the given data boys will be (x + 8)

∴ {x + (x+8)} = 32

 2x + 8 = 32

 2x = 24

   x = 12

∴ the no. of girls = 12 and no. of boys = 12+8 = 20.

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Answer:

45231 = [tex]4 \times 10000 + 5\times 1000 +2 \times 100 + 3\times 10 +1 \times 1[/tex]

Step-by-step explanation:

Given the number:

45,231

We have To write the given number in the expanded form.

Solution:

First of all, let us write the different digits of the number:

Unit's digit = 1

Ten's digit = 3

Hundred's digit = 2

Thousand's digit = 5

Ten thousand's digit = 4

Unit's digit has to be multiplied with 1.

Ten's digit has to be multiplied with 10.

Hundred's digit has to be multiplied with 100.

Thousand's digit has to be multiplied with 1000.

Ten Thousand's digit has to be multiplied with 10000.

And then they have to be added so that the number gets formed.

45231 = [tex]4 \times 10000 + 5\times 1000 +2 \times 100 + 3\times 10 +1 \times 1[/tex]

Answer:

5y = -5

Step-by-step explanation:

-2(3y+5)= -4

Divide each side by -2

-2/ -2  (3y+5)= -4/-2

3y+5 = 2

Subtract 5 from each side

3y +5 -5 = 2-5

3y = -3

Divide by 3

3y/3 = -3/3

y = -1

5y = 5*-1 = -5

Answer:

100(1/a + 1/b)

Step-by-step explanation:

Machine A takes a hours to make 100 bolts

Machine B takes b hours to make 100 bolts

Two machines will make:

bolts in one hour