2[tex]\frac{3}{5}[/tex] × 3[tex]\frac{1}{3}[/tex]

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83.[tex]\underline{\overline 3}[/tex] feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

the fence, we have;

Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

[tex]\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x[/tex]

[tex]y = \mathbf{250 - \dfrac{3}{2} \cdot x}[/tex]

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

[tex]\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2[/tex]

[tex]\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}[/tex]

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, [tex]\dfrac{dA}{dx} = 0[/tex]

Finding the value of x at the maximum point, we get;

[tex]\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0[/tex]

Therefore;

[tex]\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}[/tex]

[tex]\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125[/tex]

The length of the plot that will give the most area, y = 125 feet

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The length of the rectangular field is 164 yards and the width is 41 yards

From the question,

We are to determine the fields dimensions

From the given information

A rectangular field is four times as long as it is wide

That is

l = 4w -------- (1)

The perimeter of a rectangle is given by

P = 2(l + w)

Where

P is the perimeter

l is the length

and w is the width

From the given information

The perimeter of the field is 410 yards

∴ 2(l + w) = 410 ------ (2)

Substitute equation (1) into equation (2)

2(4w + w) = 410

2(5w) = 410

10w = 410

∴  w = 410 ÷ 10

w = 41 yards

Substitute the value of w into equation (1)

l = 4(41)

l = 164 yards

Hence, the length of the rectangular field is 164 yards and the width is 41 yards.

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Step-by-step explanation:

x + y = 17/18

x = 5/24

5/24 + y = 17/18

to bring both fractions to the same denominator (I see it is 72, but let's do it formally correct for you to learn), we look for the LCM, the lowest common multiple of both.

for this we split both numbers into their prime factors and then build the the combination of the longest chains per prime factor :

24 = 2×2×2×3

18 = 2×3×3

the LCM (and the new denominator) is then

2×2×2×3×3 = 8×9 = 72

so,

15/72 + y = 68/72

y = 53/72

53 is a prime number, so the fraction cannot be further refined.

Answer:

y - 2 = -1/3 (x + 3)

Step-by-step explanation

Sorry!

 Point-slope form )

Slope = (-1 -2)/(6 - (-3)

Slope = -3/9

Slope = -1/3

 Using the point-slope formula and point (-3, 2)

y - 2 = -1/3(x - (-3)

y - 2 = -1/3 (x + 3)  This is = to y = -1/3(x + 3) +2

Answer:

116

Step-by-step explanation:

Fast and loose: The two triangles are congruent by SSS (they are both right triangles, the hypotenuse is in common, one of the sides is congruent as a given, the second has to be because of pythagorean theorem). The two angles are thus congruent, and their measure is the same:

[tex]2x+20 = 5x-37 \rightarrow 3x=57 \rightarrow x=19[/tex]

Found x, we can find the measure of the larger angle which is [tex](2\times 19 + 20 )\times 2 = 58 \times 2 = 116[/tex]

Answer:

Angle fgh=116

Step-by-step explanation:

Since segments FI and HI are congruent and angles H and F are congruent we can safely assume that angles FGI and HGI are congruent too. Since they are congruent we're going to set up our equation like so:

(2x+20)=(5x-37)

Now we set the equations equal to each other to solve for x

-3x=-57

Divide the -3 by both sides

x=19

Now we have to plug the x into the equations

2(19)+20 and 5(19)-37

Our answer is 58 for both equations

Now we have to add 58+58 because we're solving for FGH not just FGI or HGI.

SO our final answer is 116

(Hope this helps! If I did this wrong someone please correct me and respond to this answer so that I can delete it. Have a great day!)

Answer:

Vertex form:  y = -2(x - 1)²

Standard form: y = -2x² + 4x - 2

Step-by-step explanation:

Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:

We can determine the equation by substituting these given values into the vertex form of the quadratic equation:

y = a(x - h)² + k

where:

a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.

(h, k) = vertex

Use vertex: (1, 0) and y-intercept, (0, -2):

y = a(x - h)² + k

-2 = a(0 - 1)² + 0

-2 = a(-1)²

-2 = a(1)

-2 = a

The quadratic equation in vertex form that matches the graph is:

y = -2(x - 1)² + 0 or  y = -2(x - 1)² ⇒ This is the quadratic equation in vertex form.

To transform the vertex form into the standard form, y = ax² + bx + c:

Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:

y = -2(x - 1)²

y = -2(x - 1)(x - 1)

y = -2(x² -2x + 1)

y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.  

Answer:

the coomon factor is 3xy³

by factoring we get

3xy³(4y-7xy²z+12)

Answer:

Step-by-step explanation:

please help me 8x-3+4x+3​

8x - 3 + 4x + 3​ =

8x + 4x  - 3 + 3 =

12x

Answer:

12x

Step-by-step explanation:

1. To simplify this expression, we must group like terms.

Therefore, the answer is 12x.

Answer:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, and 72.

Answer:

8, 16, 24, 32, 40, 48, 56, 64, 72

Step-by-step explanation:

8, 16, 24, 32, 40, 48, 56, 64, 72

Answer:

AC is straight line.

72°+3x=180°[linear pair]

3x=180°-72°

3x=108°

x=108°/3

x=36°

option c.

Answer:

solutions are all values greater than 6

Step-by-step explanation:

add 15 to each side to get:

3x > 18

divide each side by 3 to get:

x > 6

solutions are all values greater than 6

if I did it right then it's $32.38.

Answer:

2550

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

A = 1/2bh for a triangle.

36 = 1/2b(12)

36 = 6b

----    ----

6        6

b = 6

Answer:

y ÷ 4 ≥ 22

Step-by-step explanation:

I can't find the greater than symbol, but just write the "≥" without the line underneath

Answer:

44

Step-by-step explanation:

Let the number be X

B/P,

X/4=22  Or, X=22*4

X=88

X/2=88/2=44

So the quotient of the number when divided by 2 is 44.

Hope it help and if it its correct please give brainliest

Stay Safe and healthy

Thank You

Answer:

Step-by-step explanation:

8/9    8 is a cube but 9 is not.  8/9 is not a cube

27      27 = 3^3, a perfect cube

30      Not a cube

8/27   Both 8 and 27 are perfect cubes, and so 8/27 is one also.

1/27    This is equivalent to 1^3 / 3^3 and is a perfect cube.

27/64  Both 27 and 64 are perfect cubes, so 27/64 is one also

64        64 = 4^3, a perfect cube

1/9        9 is not a cube, so 1/9 is not one either.

Answer:

the slope of the equation

Step-by-step explanation:

Answer:

y = 1/3x +1

Step-by-step explanation:

y intercept is 1 and the rise is one with a run of 3

Answer:

39

Step-by-step explanation:

Lets solve for x:

We know the ratio is 1:3

1x+3x = 52

4x = 52

x = 13

Since the ratio is 1:3:

13(3) = 39

13:39

Which makes 39 the larger number

Answer:

$6 per cat, $10 per car

Step-by-step explanation:

I guess and checked my work.

Answer:

54 marbles

Step-by-step explanation:

7+2=9(amount Eric had in all)

9×6=54

so in all, he bought 54 marbles which he shared among his friends and brother.

ANS:54 marbles

Answer:

[tex]1 + 2 = [/tex]

answer

Answer:

x = 3

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that's supplementary to the third interior angle:

15x + 5 + 22x + 4 = 120 add like terms

37x + 9 = 120 subtract 9 from both sides

37x = 111 divide both side by 37

x = 3 and to find the angles replace x with 3 in given expressions

Answer:

Either B. 'The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him' or A. 'He did not trust the woman not to trust him. And he did not want to be mistrusted now.'.

Step-by-step explanation:

The passages from the story "Thank You, Ma'am" that support the theme that respectful treatment encourages mutual respect are: "The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him." "The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next." and "Then, Roger, you go to that sink and wash your face,” said the woman, whereupon she turned him loose—at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink." Correct options are 2, 3 and 4.

These passages highlight how the woman treats the boy, Roger, with kindness and respect despite his attempt to steal her purse. Her understanding and respectful treatment lead Roger to reflect on his actions and ultimately decide to follow her guidance. This illustrates how respectful treatment encourages mutual respect between the characters.

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Answer:

the answer is 87 keep trying also the answer 45 aha tricked you

Step-by-step explanation:

um not sure of the answer but loo-kit u p on o just keep trying quay

Answer:

Hey I got you!

Step-by-step explanation:

These are the correct answers I use another easier platform you could say

Answer:

the answer is d

Step-by-step explanation:

I hope youre asking for the y=mx+b kind of equation… if so its y=2x-1

Answer:

Step-by-step explanation:

A. If you need proof message me.

Answer:

D

Step-by-step explanation:

its correct

Answer:

Answer 1

Because the alphabet can end,it is not unlimited