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The dimensions of the region which enclose the maximal area is 61.5 feet by 41 feet .

Let the length of the rectangular plot be "L" and width be "w"

It is given that farmer wants to do fencing of 246 feet which means all the boundary will be covered which is given by

            [tex]L+L+w+w+w=246\\2L+3w=246\\2L=246-3w\\\\L=\frac{246}{2} -\frac{3w}{2} \\\\L=123-\frac{3w}{2}[/tex]  ...(2)

Putting the value of "L" in equation (1) , we get

       [tex]A=({123-\frac{3w}{2}}) \times w\\\\A=123w-\frac{3w^2}{2}[/tex] ....(3)

 Now , we are asked to find the maximum area then , put

            [tex]\frac{dA}{dw}=0[/tex]

           [tex]123-\frac{6w}{2} =0\\123-3w=0\\123=3w\\w=41[/tex]

Putting w = 41 in equation (3) , we will get the maximum area

  [tex]A=123(41)-\frac{3(41)^2}{2} \\\\A=5043-2521.5\\\\A=2521.5[/tex]

Putting w = 41 in equation (2) , we will get the length

   [tex]L=123-\frac{3(41)}{2} \\L=123-61.5\\L=61.5feet[/tex]

Hence , the dimensions will be 61.5 feet by 41 feet .

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Answer:

  15 : 20 : 8

Step-by-step explanation:

Given ratios a:b = 3:4 and b:c = 5:2, you want the ratio a:b:c in simplest form.

The extended ratio you want can be written only when the number of ratio units associated with 'b' is the same in both ratios. Multiplying the first ratio by 5, we get ...

  a:b = 3:4 = 15:20

Multiplying the second ratio by 4 gives ...

  b:c = 5:2 = 20:8

Now, 20 "ratio units" represent 'b' in both ratios, so we can combine them:

  a:b:c = 15:20:8

__

Additional comment

The value we chose to represent 'b' is the least common multiple (LCM) of the values that represent 'b' in the given (reduced) ratios.

According to the plot, it looks like [tex]y=3.5[/tex] when [tex]x=4[/tex], and [tex]y=7[/tex] when [tex]x=5[/tex]. Then the average rate of change from [tex]x=4[/tex] to [tex]x=5[/tex] is

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{7 - 3.5}{5 - 4} = 3.5[/tex]

The proof based on the triangle was done based on the fact that they are congruent triangles.

In this question we have  ΔABC ≅ ΔBAD

We have the following congruent sides in this triangle.

These are:

AB ≅ BA;

AC ≅ BD;

BC ≅ AD

These are corresponding angles too

∠ABC ≅ ∠BAD;

∠BCA ≅ ∠ADB;

∠CAB ≅ ∠DBA.

From the question we can see that the angles A and D can be said to be common. Hence we can say that

AE ≅ EB

Then CD would bisect AB

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Answer:

No

Step-by-step explanation:

substitute x = - 4 and y = - 17 into the left side and compare the result obtained to the right side.

2y - 3x

= 2(- 17) - 3(- 4) = - 34 + 12 = - 22 < 12

thus (- 4, - 17 ) is not a solution of the inequality

Monthly income and expenditure of Ganesh will be-16680

Let Ganesh's monthly income be x

The problem can be solved using linear equation

The amount of 60% of his salary is spent which can be written as 60% of x or 0.6x

The amount of money saved by Ganesh = total salary - amount spent

                                                                     = x - 0.6x

                                                                     = 0.4x

The amount of savings made by Ganesh  as per the question = 11120

Lets equate both the equation

                          0.4x = 11120

                               x = (11120 × 100)/ 40

                              x = 27800

Hence, Ganesh's monthly salary comes out to be 27800

Ganesh's monthly expenditure = 0.6 x= 0.6 × 27800 =16680

What is a linear equation in math?

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line

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Answer:

Step-by-step explanation:

a Whar grsde are u even in >:/

Answer: the one that cross -7 and -7

Step-by-step explanation:

f(x)= -x-7

y=mx+b m is the slope and the b for y-intercept form

y-intercept  (0,-7)   m= -1

-1 the line go  down from left to right

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

.........................................................

Step-by-step explanation:

.................................................

Answer:

Slope = (4/5)

Step-by-step explanation:

Point 1: (-2, 0); Point 2: (3, 4)

            (x₁, y₁)               (x₂, y₂)

       y₂ - y₁         4 - 0             4            4

m = ----------- = ------------ = ------------ = ------

       x₂ - x₁         3 - (-2)        3 + 2         5

y - y₁ = m(x - x₁)

y - 0 = (4/5) (x - (-2)

y - 0 = (4/5) (x + 2)

y - 0 = (4/5)x + (8/5)

y = (4/5)x + (8/5)

I hope this helps!

The original length of the square garage is 19.1 ft.

The length of the new garage is 23.4 ft and the percentage increase in length is 81.6 %.

Yossi used to have a square garage with 364ft of floor space.

Recently, built an addition to it.

The garage is still a​ square, but now it has​ 50% more floor space

Therefore,

area of a square = l²

where

Therefore,

364 = l²

l = √364

l = 19.0787840283

l = 19.1 ft

Therefore, the original length of the square garage is 19.1 ft.

After 50% increase in the area,

New area = 50 / 100(364) + 364

New area = 546 ft²

Therefore,

546 = l²

l = √546

l = 23.3666428911

l = 23.4 ft

Hence,

percentage increase in length = 19.1 / 23.4 × 100

percentage increase in length = 1910 / 23.4

percentage increase in length = 81.6239316239

percentage increase in length = 81. 6 %

Therefore, the length of the new garage is 23.4 ft and the percentage increase in length is 81.6 %.

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Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ 2- (-4)~~)^2 + (~~ 3- 0~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 6 )^2 + ( 3)^2}\implies \boxed{AB=\sqrt{45}}[/tex]

[tex]B(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) ~\hfill BC=\sqrt{(~~ 6- 2~~)^2 + (~~ 0- 3 ~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4)^2 + ( -3)^2}\implies \boxed{BC=5} \\\\\\ C(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad D(\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) ~\hfill CD=\sqrt{(~~ 0- 6~~)^2 + (~~ -3- 0~~)^2} \\\\\\ ~\hfill CD=\sqrt{( -6)^2 + ( -3)^2}\implies \boxed{CD=\sqrt{45}}[/tex]

[tex]D(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) ~\hfill DA=\sqrt{(~~ -4- 0~~)^2 + (~~ 0- (-3)~~)^2} \\\\\\ ~\hfill DA=\sqrt{( -4)^2 + ( 3)^2}\implies \boxed{DA=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{\sqrt{45}~~ + ~~5~~ + ~~\sqrt{45}~~ + ~~5 ~~ \approx ~~ \text{\LARGE 23.42}}[/tex]

Answer: 1 inch 7/8

Step-by-step explanation: 65 1/4 inches is the same and 65 2/8 inches. its now just as simple as finding the difference.

                  <-----------take 8/8 or 1 away from the 65 and add it to the 2/8                 65 2/8

-  63 3/8

----------------          

   64 10/8           <------now the equation looks like this

-   63 3/8             <----10-3 is 7    ----   64 - 63 is 1

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

  1 inch and 7/8

The volume of the given three-dimensional figures are:

So, the volume of the cube: a³

(1) a³ = 4³ = 64ft³

The volume of the cuboid: whl

(2) whl = 4 × 6 × 3 = 72ft³

(3) whl = 2 × 3 × 5 = 30ft³

(4) whl = 2 × 5 × 8 = 80ft³

Therefore, the volume of the given three-dimensional figures are:

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The required equation that is a representation of the associative property of addition is 5 + (6 + 2) = (5 + 6) + 2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

-15 + 0

The associative property of addition states that

(x + y) + z = x + (y + z)

This means that

(x + y) + z = x + (y + z) is a representation of the associative property of addition

From the list of given options, we have

5 + (6 + 2) = (5 + 6) + 2

The above is a perfect illustration of (x + y) + z = x + (y + z)

So, 5 + (6 + 2) = (5 + 6) + 2 is a representation of the associative property of addition

Hence, the required equation that is a representation of the associative property of addition is 5 + (6 + 2) = (5 + 6) + 2

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Answer:

5 + (6 + 2) = (5 + 6) + 2

Step-by-step explanation:

Answer:6.75 miles per half hour

Step-by-step explanation:6..75 miles per half hour

Answer:

The function which has a slope of 4 will be that function or line which is going through the points (2, 0) and (3, 4).

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

In the given question is saying for the second case the line goes through points  (2, 0) and (3, 4) so the slope will be

(4 - 0)/(3 - 2) = 4 hence, it will be the correct answer because it is the only line that has a slope of 4.

Answer:

On a coordinate plane, a line goes through points (2, 0) and (3, 4).

Step-by-step explanation:

In a normal distribution, x = 9 and z = −1.21. This tells you that x = 9 is 1.21 standard deviations to the left the mean.

The z-score is a mathematical measure that allows us to see how much above or below the mean a value in a distribution is in terms of standard deviation.

When the value is above or right of the mean, the z-score would be positive and when the z-score is left or below the mean, the z-score would be negative.

In this instance, x = 9 has a z-score of -1.21 which means that it is 1.21 standard deviations to the left of the mean.

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Answer:

f'(x) = 0

Step-by-step explanation:

the derivative of a constant is zero , that is

f(x) = 5 ( a constant ) , then

f'(x) = 0

Answer:

(2m+5)

2

=

Use binomial theorem (a+b)

2

=a

2

+2ab+b

2

 to expand (2m+5)

2

.

4m

2

+20m+25

Answer - 4m + 2 + 20m + 25

Step-by-step explanation:

help

The fraction of those who were cast got major roles is 1 / 5.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.

Given that ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles.

The fraction will be calculated as below:-

Fraction of the students cast = 90 / 3 = 30

Fraction of the students selected for major roles = 6 / 30 = 1 / 5

Therefore, the fraction of those who were cast got major roles is 1 / 5.

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The amount that will be left based on the information will be 60100 - 23s - 28t - 14r.

Total number of soles = 60100

From the information, she bought 23 stoves, 28 television, and 14 refrigerators.

Therefore, the amount that will be left based on the information will be:

= 60100 - 23s - 28t - 14r

where s = stove

t = television

r = refrigerator

Therefore, the amount that will be left based on the information will be 60100 - 23s - 28t - 14r.

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Answer:

3x, where x = the price of a football ticket

-1/2 = 3/8y
Answer:

y = -4/3

answer is y= -4/3

step by step

-1/2 = 3/8y

divide both sides by 3/8 to solve for y

-1/2 divided by 3/8 = 3/8 divided by 3/8y

when you divide fractions you flip the divisor and multiply

-1/2 x 8/3 = y

-8/6 or simplified to -4/3

you can check your work by substituting your y value of -4/3 into your original equation

-1/2= 3/8y

-1/2 = (3/8) (-4/3)

-1/2 = -12/24

-1/2 = -1/2

They equal so problem solved!

Based on the number of hours in the work week, the cost of the laborers and masons, worth of the materials and the profit, the estimated cost of the job can be written as a mathematical statement of A. 3 x $15 x 40 + 4 x $25 x 40 + $3,268 + $700 = $

The total estimated cost is $9,768

The total estimated cost of the job can be found by the formula:

= (Number of laborers needed x Cost of laborers x Number of hours in work week) + (Number of masons x cost of masons x number of hours in work week) + materials worth + Required profit

The total estimated cost is therefore:

= (3 x $15 x 40) + (4 x $25 x 40) + $3,268 + $700

= 1,800 + 4,000 + 3,268 + 700

= $9,768

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Question: Hello: )✨A masonry contractor is preparing an estimate for building a stone wall and gate. He estimates that the job will take a

40-hour work week. He plans to have three laborers at $15 per hour and four masons at $25 per hour. He'll need $3268

worth of materials and wishes to make a profit of $700. Write a mathematical statement that will give the estimated cost of

the job. Then calculate this total.

Select the correct choice below and fill in the answer box to complete your choice.

Answer: Checked to see if this was right* Based on the number of hours in the work week, the cost of the laborers and masons, worth of the materials and the profit, the estimated cost of the job can be written as a mathematical statement of A. 3 x $15 x 40 + 4 x $25 x 40 + $3,268 + $700 = $

The total estimated cost is $9,768

What is the total estimated cost?

The total estimated cost of the job can be found by the formula:

= (Number of laborers needed x Cost of laborers x Number of hours in work week) + (Number of masons x cost of masons x number of hours in work week) + materials worth + Required profit

The total estimated cost is therefore:

= (3 x $15 x 40) + (4 x $25 x 40) + $3,268 + $700

= 1,800 + 4,000 + 3,268 + 700

= $9,768

Have an awesome day/night<3

Answer:

17.37

Step-by-step explanation: