A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $14 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
Answer:
Width = 166.7 ft
Length = 250 ft.
Step-by-step explanation:
From the diagram at the ATTACHMENT
Let us denote the the length of the rectangular area as "x" and
the width of the rectangular area as "y"
Since, cost of the fence on the western side is shared with a neighbor, we can say it is $7 per foot. Otherwise, it is $14 per foot. The northern length is not fenced.
From the question, we know that the cost is not to exceed $7000, therefore we can expressed it as
7y + 14x + 14y = 7000
14x + 21y = 7000
Divide through by 14, we have
(x + 1.5) = 500 ------------- eqn (*)
But the area of the fenced
= A = (x×y) -------------- eqn (**)
Substitute (*) into (**) we have
A = (500 - 1.5y)*y
= 500y - 1.5y²
In other to maximize the Area, we can find the differential of A
A'(y) = 500 - 3y
At A'(y) = 0.
500-3y= 0
3y=500
y= 166.67 ft
From eqn(*)
(x+ 1.5) = 500
x = 500 - 1.5y
500-1.5(166.67)
= 250ft
Therefore, the dimensions for the plot that would enclose the most area are
Width of 166.67 ft and Length = 250 ft.
Solve: with full workings
(32/243)^-4/5
Answer:
[tex](\frac{32}{243})^{-\frac{4}{5}}=39.0625[/tex]
Step-by-step explanation:
Given
[tex](\frac{32}{243})^{-\frac{4}{5}}[/tex]
Required
Solve
[tex](\frac{32}{243})^{-\frac{4}{5}}[/tex]
Express 32 as 2^5 and 243 as 3^5
[tex](\frac{2^5}{3^5})^{-\frac{4}{5}}[/tex]
The exponent can be expressed as 1\5 * -4
So we have:
[tex](\frac{2^5}{3^5})^{\frac{1}{5} * -4}[/tex]
Apply law of indices:
[tex](\frac{2^{5*1/5}}{5^{5*1/5}})^{-4}[/tex]
[tex](\frac{2}{5})^{-4}[/tex]
In indices:
[tex](\frac{a}{b})^{-c} = (\frac{b}{a})^{c}[/tex]
So, the expression becomes
[tex](\frac{5}{2})^{4}[/tex]
[tex](\frac{5^{4}}{2^{4}})[/tex]
[tex]\frac{625}{16}[/tex]
[tex]39.0625[/tex]
Hence:
[tex](\frac{32}{243})^{-\frac{4}{5}}=39.0625[/tex]
Write the equation, show all your work, and circle your answer. ** The
square and the equilateral triangle at the bottom have the same
perimeter. Find the length of the sides of the triangle.
X + 5
3x
Please help it’s due Jan 8, 2021
Answer:
The length of the triangle is 3x given
The no of sides is 3x 3x 3x so 3x+3x+3x= 180
9x=180 x= 20
3x =3*20=60
3x=3*20=60
3x=3*20=60
HELP ME PLEASE!!!!!
The midpoint of PQ is M=(3, -1). One endpoint is P=(8, -7). Find the coordinates of the other endpoint, Q.
Answer:
I think the answer (-2, 6)
Amanda has four plastic shapes, a circle, a square, a triangle, and a pentagon, In how many ways can she lineup the four shapes if the circle cannot be next to the square
Do NOT have an explanation that isn't just writing all the combinations of shapes.
====================================================
Explanation:
Let's say we have the following code names for each shape
C = circleS = squareT = triangleP = pentagonWe have 4! = 4*3*2*1 = 24 ways to arrange them without any restrictions
Some permutations have C and S together, while others do not.
Example of them together: CSTP
Example of them separated: CTSP
--------------------------
Let's say Amanda used a rubberband or glue to connect the circle to the square. This way the two shapes would always be together. They combine to form a new shape of sorts.
Let's call this new shape "polygon" and define it as
L = polygon
The codename L is just a placeholder for CS or SC.
So instead of the set of these codenames {C,S,T,P}, we have this reduced set {L,T,P}
No matter how we arrange the items in {L,T,P}, the circle and square are always going to be together. Again, anywhere you see an L, you replace it with CS or SC.
--------------------------
There are 3 letters in {L,T,P} so there are 3! = 3*2*1 = 6 ways to arrange those 3 letters. There are 2 ways to arrange S and C within any of those 6 arrangements mentioned earlier.
So there are 2*6 = 12 different ways to arrange the four shapes such that S and C are together somehow.
Recall earlier we found 24 ways total to arrange the shapes without restriction. This must mean there are 24 - 12 = 12 permutations such that S and C are not together. This is the final answer we're after.
What is the expression of 5 times the difference between 19 and 13
Answer:
5 x 6
Step-by-step explanation:
9 lb 4 oz - 2 lb 12 oz with regrouping
Answer:
6 LB 12 OZ
Step-by-step explanation:
16 OZ in a LB
9 LB - 2 LB = 7 LB
4 OZ - 12 OZ difference of 8 OZ
4 - 4 = 0 then 16 OZ in a LB
4 remaining - 16 = 12 dropping the 7 LB to 6 LB
Answer:
6lb 8oz
Step-by-step explanation:
9lb 4oz
+16
8lb 20 oz
-2 lb 12oz =
Which inequality represents this sentence?
Six plus two is less than nine plus three.
9+3 9+3
Answer: it doesn’t make sense why you have random numbers underneath that inequality sentence. But if anything it would look like 6+2 < 9+3
Step-by-step explanation:
This < equals less than, or more than depending on what number it’s facing. Think of it as an alligator that eating the specific number (or larger number bc its hungry) so whatever the open side is facing is a more than but the number the closed side is facing is less than.
Aaron made a $400 purchase using his credit card. The credit card has a simple interest rate of 12% each year. How much will Aaron owe in total at the end of the year?
Answer: 448 dollars
=============================================
Work Shown:
P = 400 is the balance
r = 0.12 is the decimal form of the interest rate
t = 1 is the number of years
Use those values to get the simple interest to be
i = P*r*t
i = 400*0.12*1
i = 48
The amount of interest charged is $48
Add this onto the balance of 400 dollars and the total amount Aaron owes is P+i = 400+48 = 448 dollars.
Evaluate the expression 15x + 4 for x = -1 1/2
Answer:
18.5
Step-by-step explanation:
First we plug in the number
-1 1/2 is the same as -1.5
Plugging this in we will have:
15(-1.5) + 4 =
-22.5 + 4 =
-18.5
I’ll make you brainliest:Which shows the equation 12x + 4y = 480
in general form?
Answer:
y = -3x + 120
Step-by-step explanation:
Hope this helps!
Select the correct answer.
Which complex number is equivalent to this expression?
1/3(6 + 3i) – 2/3(6 - 12i)
OA. 6- 7i
B. 6 + 9i
C. -2 + 9i
D.
-2 - 7i
Answer:
-2 + 9i
Step-by-step explanation:
Consider the line y=5x-3.
Find the equation of the line that is parallel to this line and passes through the point (2, -5).
Find the equation of the line that is perpendicular to this line and passes through the point (2, -5).
Answer:
y=5x-15, y=-1/5x-23/5
Step-by-step explanation:
Parallel lines have the same slope, so we know the line that is parallel to y=5x-3 must have slope 5.
We now have y=5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=5x+b
-5=5(2)+b
-5=10+b
b=-15
So the equation of the parallel line is y=5x-15.
Perpendicular lines must have slopes that multiply to -1, so we know the line perpendicular to y=5x-3 must have slope -1/5.
We now have y=-1/5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=-1/5x+b
-5=-1/5(2)+b
-5=-2/5+b
b=-23/5
So the equation of the perpendicular line is y=-1/5x-23/5.
Eddie's Evergreens sells Christmas trees and wreaths. Trees cost 3 dollars more than 4 times the price of each wreath. It costs $ 99 buy 2 wreaths and 1 tree . How much does each wreath cost? How much does each tree cost?
Answer:
[tex]W = 16[/tex]
[tex]T = 67[/tex]
Step-by-step explanation:
Represent trees with T and wreaths with W
Given
[tex]T = 3 + 4 * W[/tex]
[tex]2 * W + T = 99[/tex]
Solving (a): Cost of W
Substitute 3 + 4 * W for T in the second equation
[tex]2*W + 3 + 4 * W = 99[/tex]
[tex]2W + 3 + 4 W = 99[/tex]
Collect Like Terms
[tex]2W + 4 W = 99 - 3[/tex]
[tex]6W = 96[/tex]
Divide through by 6
[tex]W =\frac{96}{6}[/tex]
[tex]W = 16[/tex]
Hence, each wreath costs $16
Solving (b): Cost of T
[tex]T = 3 + 4 * W[/tex]
Substitute 16 for W
[tex]T = 3 + 4 * 16[/tex]
[tex]T = 3 + 64[/tex]
[tex]T = 67[/tex]
Hence, each tree costs $67
The slope of a line perpendicular to y = 2x + 1 is -2.
False
True
Answer:
incorrect.
Step-by-step explanation:
the slope of the line perpendicular is the negative reciprocal, which in this case is -1/2
Answer:
False
Step-by-step explanation:
To find the slope of a perpendicular, flip the slope and change the sign.
The slope pf the given line is 2.
The slope of a line perpendicular to y = 2x + 1 is -1/2.
Answer: False
help me pleaseeeeee!!!!!
Answer:
61
Step-by-step explanation:
3x + 28
5x + 52
+ 2x - 10
10x + 70 = 180º
x = 11
3(11) + 28 = 61º
Find the area of the triangle.
PLEASE HELP ASPA
Answer:
(B). 12.9 cm²
Step-by-step explanation:
a = 8 cm , b = 5 cm , c ≈ 12.259 cm
P = 25.259 , s = P/2 ≈ 12.63
[tex]A_{ABC}[/tex] ≈ 12.856 ≈ 12.9 cm²
Solve the following equations | 3x + 3/7 | = 2 1/3
Answer:
X∈[tex]\frac{5}{63}, -\frac{23}{63}[/tex]
Step-by-step explanation:
Jill paid a sales tax of $1.40 when she bought a vest.What was the price of the vest not including the tax?
Answer:
Price of tne Vest + $40 - 1.40 = $38.6
Step-by-step explanation:
3.5% * n = $1.40
0.035 * n = $1.40
0.035/0.035 * n = $1.40/0.035
n = $40
The price of the vest not including the tax is, $40
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Since, Tax is a sum levied by the government or an agency of the government on goods and services. taxes increases the price of products
Now,
Let p = price of a vest
Hence, from the question, this equation can be formed,
⇒ 35% of p = $1.40
⇒ 0.035 x p = $1.4
divide both sides of the equation by 0.035;
⇒ p = $40
Thus, The price of the vest not including the tax is, $40
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ2
Complete question is this;
Jill paid a sales tax of $1.40 when she bought a vest. What was price of vest not including tax? Sales tax = 3.5%
Use the equation machine to help you solve the
addition equation.
O k=8
Ok=9
O k=17
O k=2
For 100 points
Answer: k=8
Step-by-step explanation:
Answer:
k=8
Step-by-step explanation:
Complete this item.
Identify _1 and 22. Select all that apply of the following terms: acute, right, obtuse, adjacent, vertical,
complementary, supplementary.
Answer:
Angle 1 is obtuse, and adjacent. Angle 2 is obtuse, and is also adjacent.
Step-by-step explanation:
Both seem to be obtuse since they're not right triangles, and they're both adjacent because they have two angles that share the same vertex. Hope this helped :)
When x=5, which is x3?
Answer:
125
Step-by-step explanation:
5 cubed is literally 5 x 5 x 5
So 5 x 5 = 25
multiply 25 with 5 and you get 125 as the answer.
The Answer Is 8
Your Welcome!♠
The range of (fog)(x) is
Answer:
The range of [tex]f\circ g \,(x) = 2^{x+1}[/tex] is [tex]Ran\{f\circ g\,(x)\} = (0, +\infty)[/tex].
Step-by-step explanation:
Let [tex]f\circ g \,(x) = 2^{x+1}[/tex], [tex]\forall\, x \in \mathbb{R}[/tex]. The graphic represents a power function, whose lower bound is the horizontal asymptote [tex]y=0[/tex]. From the graphic we find the range of the composite function corresponds to the values of the function associated with the vertical axis (y-axis).
Hence, the range of [tex]f\circ g \,(x) = 2^{x+1}[/tex] is [tex]Ran\{f\circ g\,(x)\} = (0, +\infty)[/tex].
Answer:
✔ y > 0.
Step-by-step explanation:
edg 2021
The price of a 40-inch television is $268 plus 8% sales tax rate. What is the amount of the sales tax for the television, in dollars and cents?
Write an equation in slope intercept form for the line that passes through the points (6,-3)and (0,2)
Answer:
y = [tex]\frac{5}{-6}[/tex]x + 2
Step-by-step explanation:
Given coordinates: (6,-3) (0,2)
y = mx + b
y = mx + 2
[tex]\frac{2+3}{0-6}[/tex] = [tex]\frac{5}{-6}[/tex]
y = [tex]\frac{5}{-6}[/tex]x + 2
The equation of the line that has a slope of 3 and passes through the point (2, 1) is y = 3x - 5.
True
ОО
False
Answer:
True
Step-by-step explanation:
y = 3x - 5 does have slope 3.
Let's test point (2, 1).
y = 3x - 5
1 = 3(2) - 5
1 = 6 - 5
1 = 1
Point (2, 1) does work in the equation.
Answer: True
Where did the 45% come from. It states 55% in question
Answer:
is this a question......
9+x=12 Can you guys please tell me the answer
Answer:
X=3
Step-by-step explanation:
9+x=12
x=12-9
so x is 3
Answer:
3
Step-by-step explanation:
Let's go through this together.
Step 1) Rearrange Terms (Optional)
9 + x = 12
x + 9 =12
Step 2) Subtract 9 from both sides of the equation
x + 9 = 12
-9 -9
Step 3) Simplify
If we subtract 9 on both sides, we end up with:
x + 0 = 3
Since 0 no longer has any part in the equation, we can conclude that:
x = 3
PLS HELP ME
It takes Li 1 hour to drive 65 miles, 2 hours to drive 130 miles, and 3 hours to drive 195 miles. How many miles can he drive in 5 hours?
Answer:
310
Step-by-step explanation:
65 x 5
What is the domain and range of the following ordered pairs: {(-6, -7), (-1, 1), (0,
9), (3,-2)}? *
Wh
Domain: {-6, -1,0, 3} Range: (-6, -1, 0, 3}
Domain: {-7,1,9, -2} Range: {-7,1,9,-2}
Domain: {-7,1, 9, -2} Range: (-6,-1, 0,3}
Domain: {-6,-1, 0,3} Range: {-7, 1, 9, -2}
Answer:
The answer is the last option (d.)
Step-by-step explanation:
The domain is the X values and the range is the Y values.
Answer:
Answer: Domain {-6,-1,0,3} Range: {-7,1,9,-2}
Step-by-step explanation:
I took the test and it was correct.