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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Pls help me
On June 1, Mary had a balance of $50 in her bank account. During June she made the four transaction below.
Deposited $25.62
Withdrew $19.76
Wrote a check for $56.29
Paid a bank fee of $25
If there were no other transaction, what was the balance in Mary's account at the end of the month?
Answer:
The balance in Mary's account at the end of the month is $14.09
Step-by-step explanation:
Step 1: 50+25.62=75.62
Step 2: 75.62+19.76=95.38
Step 3: 95.38-56.29=39.09
Step 4: 39.09-25= $14.09
Can someone plz help with this
Answer:
hexagonal prism
On a coordinate graph the following points of a rectangle are given. A(0,2) B (0,-2) C (3,-2) 4 Where do the coordinates of Dneed to be to form the rectangle? 0 (3,2) O (2, 3) 0 (1,3) 0 (3,1)
Answer:
(3, 2)
Step-by-step explanation:
Please mark me brainliest if this helped! :P
an electrician has 4.1 meters of wire.How many strips of 7 tenths can be cut?and how much wire will be left over?
Which expression represents the area of this figure in square feet?
Answer:
(3×2) + (3×4)
Step-by-step explanation:
One box's area is 3×2 and the other box's area is 3×4, so when you add them, you get the total area.
Drag the numbers to order them from least to greatest.
0.7
-4.5
0.3
-0.5
2.3
Answer:
-4.5, -0.5, 0.3, 0.7, 2.3
Step-by-step explanation:
The higher the negative number the lower it really is.
Answer:
-4.5, -.5, .3, .7,2.3
Step-by-step explanation:
y=1/4x + 4 input (x) = 4 find (y) output PLEASE HELP
Answer:
y = 5
Step-by-step explanation:
y = (1/4)x + 4
input (x) = 4
plug in 4 for x
y = (1/4)(4) + 4
y = 1 + 4
y = 5
URGENT!!!
Peggy sue decided to enter her famous “Five- Alarm chili” at her local chili cooking contest. Normally, she needs 5 tomatoes to make enough chili for her family of 7
A. How many tomatoes should she expect to use to make her famous recipe for 100 people?
b. When she gets to the contest, she realizes that she only packed 58 tomatoes. How many people can she expect to feed?
What is the range of f(x)?
Answer:
{ f(x)| -∞ < f(x) ≤ 4 }
Step-by-step explanation:
The range of a function is the interval of every y-value represented on the function. Since the highest this function goes on the y-axis is to y=4, we know that the upper limit of the range is 4, which is inclusive because the function actually reaches this value. The function also appears to go down indefinitely on the right side, so the lower limit is -∞, which is non-inclusive because we will never reach that value.
The range is -∞ < f(x) ≤ 4
How much would it cost to buy three medium sodas and two hotdogs
Answer:
depends how much they cost each
You have 4 cups of flour and you need to us 1 3/4 cups of flour for a cookie recipe.how much flour will you have left?
Will give brainliest no files plz
Answer:
x=3 and y= 4 / 3 (Fraction)
Step-by-step explanation:
Substitute x for 6y-5.
2(6y−5)−3y=2
Add 6y and 3y, and multiply 5 by 2/Simplify the equation.
9y−10=2
Add 10 to both sides, and then divide each side by 9.
9y−10+10=2+10
9y / 9 = 12 / 9
y = 4/3.
Repeat the process but replace y with 4/3!
Answer:
x=3
y= 4/3
Step-by-step explanation:
2(6y-5)-3y=2
y= 4/3
x=6x 4/3-5
x=3
Help needed, this is timed :’)
Answer:
Step-by-step explanation:
last answer
Which statement is an example of heat transfer by convection? Question 4 options: Jane's feet burned as she walked across the hot beach sand. Hot air from the sand rose and was replaced by cool air blowing in from the ocean as a sea breeze. The black asphalt of the parking lot was much warmer than the green grass surrounding the lot. People were scattered across the beach, sitting on chairs and towels, warming themselves in the bright sunshine.
Answer:
Step-by-step explanation
Hot air from the sand rose and was replaced by cool air blowing from the ocean as a sea breeze.
A regular polygon has 45 sides.
Find the size of each of its exterior angles.
100 POINTS
Answer:
8
Step-by-step explanation:
360/45 = 8
We know
Sum of exterior angles of any polygon is 360°Let every angle be x
[tex]\\ \sf\longmapsto 45x=360[/tex]
[tex]\\ \sf\longmapsto x=360/45[/tex]
[tex]\\ \sf\longmapsto x=8°[/tex]
can i have help on this q plz
Answer:
No, they will need an additional £34 to stay the planned 10 nights.
Step-by-step explanation:
Attached screenshot of a spreadsheet.
The cost for 10 nights for the 2 people is £100.
The tent site rental (over 10m^2) for 10 nights is £150.
Savings for the two over the 9 weeks is £216.
They will need an additional £34 to camp as planned.
I suggest fibbing about the extra 0.5m^2 needed for the tent site. That will reduce the bill by £30, so they are only £4 short. Time to make a couple of friends.
The measures of angles x and y in the above figure is:
Step-by-step explanation:
sum of 2 angles on a straight line = 180°
therefore,
y + 120 = 180
y = 180 - 120 = 60
y = 60°
now apply angle sum property of triangle
now,
50 + x + y = 180
50 + x + 60 = 180
110 + x = 180
x = 180 - 110
x = 70
therefore, x = 70 & y = 60
hope this answer helps you dear! take care
Answer:
x = 70°
y = 60°
Step-by-step explanation:
hope it helps u
plzz plzz pLZZ MARK AS BRAINLIEST
Help! Please! Help! Please!
Step-by-step explanation:
a midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments (that create the midsegment triangle). A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side (due to similar triangles and their constant scaling factors, when one side of the similar triangle is half of the sys of the original triangle, then all its sides are half of their original counterparts).
the 3 sides of the main triangle are
2x + 5
3x - 1
5x
the perimeter of the main triangle is the sum of these :
2x + 5 + 3x - 1 + 5x = 10x + 4
since the sides of the midsegment triangle are all exactly half the length of the sides of the main triangle, also the perimeter of the midsegment triangle is half of the perimeter of the original triangle :
(10x + 4) / 2 = 5x + 2
plz help on this question;WORK OUT,1+2+3(1+2+3)
Answer:
21
Step-by-step explanation:
1) Simplify 1 + 2 to 3.
1 + 2 + 3 × ( 3 + 3 )
2) Simplify 3 + 3 to 6.
1 + 2 + 3 × 6
3) Simplify 3 × 6 to 18.
1 + 2 + 18
4) Simplify 1 + 2 to 3.
3 + 18
5) Simplify.
21
in the inequality 4> -4 which number appears farther right on a number line and why?
Answer:
4
Step-by-step explanation:
It is a positive number meanwhile -4 in negative.
The theater manager needs to set up 54 chairs for a show each row can be holed up to eight chairs the manager puts as many chairs in each row as possible how many rolls will the manager set up
Answer:
7 not 7 full rows though
Step-by-step explanation:
HELP ME PLEASE
whats 9+10?
Answer:
21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
PLEASE HELP NEED TO GET THIS RIGHT WILL GIVE BRAINLIEST
Answer:
27 / 4x^6y^8.
Step-by-step explanation:
= 4 * 3^3 x^6 y^12 / 16 x^12 y^20
= 4*27 / 16 x^6y^8
= 4*27/ x^6y^8
= 27 / 4x^6y^8
reorder the steps of the proof to make sure that steps that are logically dependent on prior steps are in the proper order.
Given:
A
B
‾
≅
C
D
‾
AB
≅
CD
and
B
C
‾
≅
A
D
‾
.
BC
≅
AD
.
Prove:
A
C
‾
AC
bisects
B
D
‾
BD
.
Answer: a
Step-by-step explanation:
what is (x-2) (3x-4)=
a.3x² - 6x-8
b.3x² - 2x - 8
c.3x² + 10x + 8
d.3x² - 10x + 8
Answer:
D. 3x^2-10x+8
Step-by-step explanation:
[tex] \: \: \: \: \: [/tex]
D. 3x²- 10x + 8hope it helps
refer to the attachment
[tex] \: \: \: \: \: [/tex]
Solve the equation by completing the
square. Enter the smallest solution first
and round to the nearest tenth.
s2 - 10s - 23 = 0
-
s = [?]
=
Answer:
s ≈ - 1.9 , s ≈ 11.9
Step-by-step explanation:
s² - 10s - 23 = 0 ( add 23 to both sides )
s² - 10s = 23
To complete the square
add ( half the coefficient of the s- term )² to both sides
s² + 2(- 5)s + 25 = 23 + 25
(s - 5)² = 48 ( take square root of both sides )
s - 5 = ± [tex]\sqrt{48}[/tex] ( add 5 to both sides )
s = 5 ± [tex]\sqrt{48}[/tex]
Then
s = 5 - [tex]\sqrt{48}[/tex] ≈ - 1.9 ( to the nearest tenth ) ← smaller solution
s = 5 + [tex]\sqrt{48}[/tex] ≈ 11.9 ( to the nearest tenth ) ← larger solution
-3 and -5 what is less, greater than , and or equal
Answer:
-3 is less and -5 is greater
Step-by-step explanation:
Answer:
less than
Step-by-step explanation:
because -5 would be less than -3 because it is bigger
Answer this middle school math equation for 30 points lol
Answer:
n
Step-by-step explanation:
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Multiply both sides by -5:
[tex]-\frac{1}{5} (x-4)=-2[/tex]:
[tex]-\frac{1}{5} (x-4)*-5=-2*-5[/tex]
[tex]1(x-4)=10[/tex]
[tex]x-4=10[/tex]
Add 4 to both sides:
[tex]x-4+4=10+4[/tex]
[tex]x=14[/tex]
what is the unknown number to ( 6 x 2) + (6 x 3) = 6 x __
Answer:
6
Step-by-step explanation:
6
I need help please !
Answer:
y column: 1st = -7 , 2nd = -5 , 3rd = -3 , 4th = -1 , 5th = 1