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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On the first day, a shoe shop sold 40 pairs of shoes and every day after it sold 20 more pairs of shoes.
Write an equation in slope-intercept form that describes the number of shoes sold.
Answer:
Step-by-step explanation:
Write 27% as a fraction.
Answer:
27/100
Step-by-step explanation:
27%= 0.27= 27/100 which cannot be reduced
Answer:
27/100
Step-by-step explanation:
27% = 27/100
a square lot has a side of 8 5/8 meters,what is the area of the lot?
Need some help for Exponents.
1) Five squared
2) Eight to the 5th power
3) Nine cubed
4) 2 x 2 x 2 x 2
5) 7 x 7 x 7 x 7 x 7 x 7
6) 2.3 x 2.3
Find the value of each of the following:
7) 54
8) 132
9) (1.2)2
10) 180
11) 10002
12) 72 x 70
Critical Thinking Applications
13) Mali bought a new car. She drove 63 miles the first month and 64 miles the second month. How much further did she drive the second month? Explain each step.
14) Create an application problem similar to the one above. Solve your problem. Explain each step.
15) In your own words, write three or four sentences explaining what exponents are and how they are used in math.
16) Create and solve 5 problems using exponents.
Answer:
1) 25
2) 32,768
3) 729
4) 16 or 2^4
5) 117,649 or 7^6
6) 5.29 or 2.3^2
Not sure what 7-12 mean
13) 1 mile 64-63=1
14) Mali bought a new car. She drove 63 miles the first month and 100 the second month. How much further did she drive the second month? Explain each step. 37 miles 100-63=37
15) An exponet is a number raised to a power, which means that number times itself that many times. It is used because it's alot easier to go 7^6 than 7x7x7x7x7x7.
16) 8^5= 32,768 6^6= 46,656 5^7= 78,125 5^5= 3,125 4^10= 1,048,576
Step-by-step explanation:
1 Analyze Alana used the table of values to find the slope of the graph for this function.
Analyze her work and explain why you do or don't agree with her.
x
х
N
4.
6
00
у
4.
5
6
7
m= 6-2 - or2
=
Step-by-step explanation:
From the table of values, it is clear that Alana chose the points (2,4) and (6,6). She also used this formula to find the slope:⤵⤵⤵
(sorry if it's a bit small btw)
[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]
She plugged in her values like so:
[tex] \frac{6 - 2}{6 - 4} [/tex]
But, right away we can tell that she put the values in the wrong places, because the y-values are supposed to be on top while the x-values are supposed to be on the bottom. Yet in this case, you can see that the 2 is an x-value, meaning she put it on the top, and thus the slope is wrong.
The correct way would be if she switched them around, where the y-values are on top and the x-values are on the bottom. With this in mind, the slope would actually be 2/4 which if you simplify it, it would be 1/2.
This is essentially your answer, feel free to use some of my words, if need.
Hope this helps :)
easy one - giving brainly if correct - show work.
my teacher said this was wrong so what's the correct answer? answer both!
Answer:
a = 9.6 b = 11.2
Step-by-step explanation:
10 percent of 8 is .8
8 + (8 x .1) = 8.8
8.8 + .8 = 9.6
She will be paid 9.6 dollars after 1 full year of working, because working for one year is 12 months, and thats 10 percent of 8 twice. You can also put that as 20 percent of 8, aka 1.6
When you do 8+1.6 it equals 9.6
For the second part, that is 24 months, so 10 percent of 8 4 times. .8+.8+.8+.8 = 3.2
8+3.2 = 11.2
She will be paid 11.2 dollars after 2 full years of working.
Your answer isnt wrong, I dont know why your teacher is saying it is.
Members of a soccer team raised $1428 to go to a tournament. They rented a bus for $955.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine pp, the number of players the team can bring to the tournament.
Answer:
16 players can be brought to the tournament. The equation is written within my step-by-step explanation.
Step-by-step explanation:
Variable p = number of players
Set up an equation:
974.50 + 60.75p = 1946.50
Isolate variable p:
60.75p = 972
Divide:
p = 16
Check your work:
974.50 + 60.75(16) = 1946.50
974.50 + 972 = 1946.50
1946.50 = 1946.50
(6,1),(7,2),(8,3) what is the range
Answer:
the range is 1, 2, 3
Step-by-step explanation:
please someone help me answer this question. file is attached.
Answer:
ok so im pretty sure it is 6 pans with 2 cups left over
Step-by-step explanation:
so 2 1/2 times 6 is 15 since we cant get it exactly, so you use 6 which is 15 and you figure out what was leftover which is 2
what i can do what can i do
Answer:
thanks for the points have a nice day
help algebra 2 look at all the pictures please multiple choice
Relation given:-
{(-2,5),(-1,3),(0,-1),(1,-3),(2,-5),(3,-7)}Inverse
{(5,-2),(3,-1),(-1,0),(-3,1),(-5,2),(-7,3)}#2
f(x)=2x-3Let it be y
[tex]\\ \tt\hookrightarrow y=2x-3[/tex]
[tex]\\ \tt\hookrightarrow 2x=y+3[/tex]
[tex]\\ \tt\hookrightarrow x=y+3/2[/tex]
Write in terms of x
[tex]\\ \tt\hookrightarrow f^{-1}(x)=\dfrac{x+3}{2}[/tex]
Tim bought 3.6 pounds of flour for a cake and paid $8.50. What was the cost per pound?
Answer:
$2.36
Step-by-step explanation:
To find the price per pound is super easy. Just divide the price by the given pounds:
8.50/3.6=2.361=$2.36
Hope This Helps!
Which term of the arithmetic sequence 1, 5, 9, 13, ... is 169?
It is the
th term.
Answer:
43rd term
Step-by-step explanation:
Arithmetic sequences are basically linear functions, so the same value is added every time. So, knowing that Asub1 is equal to one, and Asubn is equal to 169 we can take 169-1 and divide by our common difference. This is four as 5-1=4 and 9-5=4.
So, (169-1)/4=42.
This is however 42 terms after Asub1, so this would be the 43rd teen of the sequence!
Can someone please help will mark brainliest.
Answer:
3 square miles
Step-by-step explanation:
If the area of rectangle is x^2+5x+6, what expressions represent the length and width of the rectangle?
Answer:
length = x + 3
width = x + 2
Step-by-step explanation:
Hope it helps:)
the diagonal of a cube is root 12. What is the edge?
Step-by-step explanation:
Given length of diagonal of a cube = √12 cm Recall that length of diagonal of a cube = √3 × Length of edge of the cube ⇒ √12 = √3 × Length of edge of the cube ∴ Length of edge of the cube = √12 / √3 = 2√3 / √3 = 2 Thus the edge of the given cube is 2 cm
what is 5000000000000 divided by 11
Answer:
45.454
Step-by-step explanation:
The length, breadth and height of a cuboid are in the ratio 6:3:5. If the total surface area is 504cm2, calculate area of 4 walls
please answer quick (i will mark as brainliest)
thank u
Step-by-step explanation:
metallic when has is equipment death of amiloride open interval a b payment to see payment payment details
What times -1/2 x what = -20?
Answer:
40
Step-by-step explanation:
Let the number be y
-1/2 × y = -20
y = -20 ÷ -1/2
y = 20 × 2
y = 40
¿Cuál es el recíproco de 3 3/7
Answer:
[tex]3 \frac{3}{7} \\ = \frac{24}{7} \\ [/tex]
[tex]The \: reciprocal \: of \: \frac{24}{7} = \frac{7}{21} .[/tex]
A computer virus infects files very quickly. The number of files triples every minute. After the first minute, five files are infected. (pls answer)
Options in the pic
Answer:
C
Step-by-step explanation:
The answer is C because r =3 I got that because it says triples. a=5 it comes from when it says five files are infected. an=3an-1. an=5(3)n-1. Hope this helps!
quellle expression algébrique représente l'aire totale d'un cude dont chauqe coter messure 1,5x
Answer:
sorry bro I don't understand your language
Solve for f.
1≤2–f
89 points pls help
Answer:
f ≤ 1
Step-by-step explanation:
1) Subtract 2 from both sides.
1 - 2 ≤ - f
2) Simplify 1 - 2 to - 1.
- 1 ≤ - f
3) Multiply both sides by - 1.
1 ≥ f
4) Switch Sides.
f ≤ 1
[tex]\\ \sf\longmapsto 1\leqslant 2-f[/tex]
Take 2 to right[tex]\\ \sf\longmapsto 1-2\leqslant -f[/tex]
[tex]\\ \sf\longmapsto -1\leqslant -f[/tex]
Multiply -1 on both sides
[tex]\\ \sf\longmapsto f\leqslant 1[/tex]
How did the Twenty-fourth Amendment to the Constitution affect African Americans?
A. By defining citizenship, it meant all African Americans were entitled to due process.
B. By allowing citizens to directly elect senators, it gave African Americans a greater voice in the government.
C. By banning slavery, it meant millions of African Americans were free from bondage.
D. By eliminating poll taxes, it meant more African Americans could vote.
Answer:
The answer is D,..................
Step-by-step explanation:
D
help me please!!!!!! 20 points!
Answer:
Step-by-step explanation:
2x = x + 40
2x - x = x - x + 40
x = 40
∠I = ∠Q = 33°
∠H = ∠P = 80°
∠J = ∠R = 67°
Rusty's hair grows at the rate of 1 inch per month.
4
How many months will it take Rusty's hair to grow 5 inch?
5
8
Explain your answer using words, and show your work using division of fractions.
Answer:=> 10 months
Given :
Step-by-step explanation:
Given :
1 / 4 inches = 1 month
Find :
5 / 8 inches = ? months
According to the question :
1 month = 1 / 4 inches
5 / 8 inches = ' x ' months
=> ( 5 / 8 ) / ( 1 / 4 ) = x
=> ( 5 / 8 ) × ( 4 / 1 ) = x
=> ( 5 × 2 ) / 1 = x
=> 10 / 1 = x
=> x = 10.
So, it takes 10 months.
Answer:
it would be 5 months for his hair to grow 5 inches.
Step-by-step explanation:
well, if his hair grows 1 inch per month, and it take 5 months for his hair to grow.
so multiple 1 times 5 and you get you answer
What list shows these in order from least to greatest?
Square W: A= √325 in.2
Square X: A= 3π/.5 in.2
Square Y: A= 5.5π in.2
Square Z: A= 17.92 in.2
1. Z, Y, W, X
2. X, W, Z, Y
3. Y, Z, W, X
4. W, X, Y, Z
Answer:
4 i am not sure for this answer guess
5(2x + 1) = 50
Help me plsss
Answer:
x=9
Step-by-step explanation:
shape it helps
byeeeeee
What’s the slope or fraction?
A company is considering purchasing the mineral rights to two different mountains. The probability that it will purchase the mineral rights to the first mountain is 0.55. The probability that it will purchase the mineral rights to the second mountain is 0.4. Assuming the decisions to purchase the mineral rights to each mountain are made independently, what is the probability that it will purchase the mineral rights to exactly one of the two mountains?
a. 0.4
b. 0.45
c. 0.51
d. 0.49
Using probability of independent events, it is found that the probability that it will purchase the mineral rights to exactly one of the two mountains is given by:
c. 0.51
If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, these following two events result in the rights of exactly one of the two mountains being bought:
First bought(0.55 probability), second not(0.6 probability).First not bought(0.45 probability), second bought(0.4 probability).Hence:
[tex]p = 0.55(0.6) + 0.45(0.4) = 0.51[/tex]
Thus, option c is correct.
A similar problem is given at https://brainly.com/question/24174994