a farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to seperate the regions) are made up of fencing, as shown below. If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the maximal area?
Answers
The dimensions of the region which enclose the maximal area is 61.5 feet by 41 feet .
The area of a rectangle is the area occupied by the rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle which is given by [tex]AREA=L \times w[/tex] ....(1)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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Related Questions
60 divided by the sum of 5 and 2
Answers
Answer: 3.75
Step-by-step explanation:
60/(5+11)
60/16
3.75
what's the answer for. Solve for the variable. Round your answer to the nearest hundredth. -8p-9=8-5p-9
Answers
-8p-9=8-5p-9
-8p+5p=9-9+8
=3p=8
=3p÷3=8÷3
=p=2.6666
=p=2.67
turn sentence into an equation: eight times the sum of a number and 6 equals 4. hurry pleas!
Answers
The sum of a number is 92 which is not equal to 4.
8(N+6) = 4
N+6 = 4/8
N=1/2-6
=11/2
plug that into the original equation to check the solution
8(11/2 + 6) = 4
8(23/2) = 4
8 x23/2 = 4
92 = 4, which is not equal to 4.
An equation is simply a number sentence with a variable in the place of an unknown value. A variable is a letter that is substituted in place of the unknown value. It can be any letter you want, although x or n is most commonly used.There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
The term “linear”, though derived from the idea that a linear equation in two variables represents a line, has been generalized from that to mean that the equation involves a polynomial with degree 1. That is, the variable(s) are only multiplied by constants and added to other terms, with nothing more (squaring, etc.)
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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The children got out of the pool when their mother said it was time to leave.
Identify the independent variable.
The children got out of the pool
The mother said it was time to leave
The pool
The mother
Answers
The independent variable in the children got out of the pool when their mother said it was time to leave is D. The mother.
What is an independent variable?It should be noted that an independent variable simply means a variable that can stand alone without being changed by the other variables.
It should be noted that from the information given, the statement is that the children got out of the pool when their mother said it was time to leave.
Therefore, the independent variable in the children got out of the pool when their mother said it was time to leave is the mother as she's not influenced by others.
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Answer:
You should redo your user name
Find area of these two figures
Answers
From what i can see c will be in the middle so 14cm and d i cant see really but going off what i can see 3cm
please help asap. 100 points
Answers
Answer:
1,524,211 square miles is equal to 3,947,688 square km
i'm not sure about the second part but i think this is actually the right answer to the first part
Step-by-step explanation:
Look at the four numbers below.
a) 7.9 X 10-3
b) 7.9 X 104
c) 7.9 X 103
d) 7.9 X 10-4
Test item courtesy of Ontario's College Sector Committee for Adult Upgrading.
Which is equal to 0.0079 in scientific notation?
a)
b)
c)
d)
Answers
The answer that is equal to 0.0079 in scientific notation will be C. 7.9 × 10^-3.
How to illustrate the information?It should be noted that scientific notation are the way that are used to express the numbers given that are either too small or too large.
Therefore, it should be noted that 0.0079 will be written as:
0.0079 = 7.9 × 10^-3
Therefore, the answer that is equal to 0.0079 in scientific notation will be 7.9 × 10^-3.
In conclusion, the correct option is C.
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A four-foot tree was planted. It will grow 2.5 feet each year. The relationships between x, the number of years since the tree has been planted, and y, the projected height of the tree is a linear relationship.
Write an equation to represent this relationship.
Answers
The equation to represent the relationship between number of years and height of tree is y = 2.5x + 4
How to write equation?The tree was planted at 4 feet.
It will grow 2.5 feet each year.
x = the number of years since the tree has been planted.
y = the projected height of the tree
Therefore, the relationships between x, the number of years since the tree has been planted, and y, the projected height of the tree can be represented as follows:
The equations is linear.
Hence, it will be in the format below
y = mx + b
where
m = slope b = y-intercepty = 2.5x + 4
Therefore, the equation to represent the relationship is as follows:
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Which set of ordered pairs represents a function?
O
A. {(3, 1), (3, 2), (3, 3), (3, 4), (3,5)}
B. {(2, 3), (3, 4), (4, 3), (3, 2), (2, 1)}
O C. {(0, 5), (2, 5), (4, 5), (6, 5), (8, 5)}
O D. {(1,4), (2, 4), (3, 4), (4, 3), (4, 2)}
Answers
i have to put more than 20 things don’t mind this
Answer: C
Step-by-step explanation: the comment box said so so it must be right
Find an ordered pair that satisfies the equation 3x + y = 11.
Answers
Answer:
(1, 8)
many possible answers
Step-by-step explanation:
to find an ordered pair to satisfy the equation means to find x and y to make the equation true
we can start off by putting x as 1
3(1) + y = 11
3 + y = 11
then subtract 3 to both sides
y = 8
you must put them in (x, y) form
so
(1, 8) is one of many possible answers
The sum of an integer and 3 times the next consecutive integer is -29. Find the value
of the lesser integer.
Answers
Answer:
[tex]x = -8[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the integer, then the consecutive integer is [tex]x + 1[/tex]. "3 times the next consecutive integer" means we should multiply [tex]x + 1[/tex] (the consecutive integer) by 3, giving us [tex]3 ( x + 1)[/tex].
We are told that the sum of [tex]x[/tex] and [tex]3(x + 1)[/tex] gives -29. Therefore, we can build an equation.
The sum of [tex]x[/tex] and [tex]3(x + 1)[/tex] can be expressed as [tex]x + 3(x + 1)[/tex].
Therefore,
[tex]x + 3(x + 1) = -29 \text{ // Distribute 3(x + 1)}\\x + 3 \times x + 3 \times 1 = -29\\\to x + 3x + 3 = -29 \text{ // Simplify}\\\to 4x + 3 = -29 \text{ // Subtract 3 from both sides}\\4x + 3 - 3 = -29 - 3\\\to 4x = -32 \text{ // Divide by 4 on both sides}\\\frac{4x}4 = -\frac{32}4\\\to x = -8[/tex]
The question is in the screenshot
Answers
Answer:
The limit is equal to 0.
Step-by-step explanation:
f(x) will approach a much larger value than g(x) as x approaches infinity, meaning the fraction will approach 0.
please help will give lots of points
Answers
Answer:
what is x
Step-by-step explanation:
what is x then ill know
In which function is x = 2 mapped to 32?
Answers
B is the answer
Arithmetic sequence is described by the formula a
Answers
Arithmetic sequence is described by the formula aₙ=a₁+(n-1)d.
Arithmetic sequence or Arithmetic progression is a series of numbers where the difference between each number and the number preceding is equal.
Arithmetic sequence is described by the formula aₙ=a₁+(n-1)d.
where aₙ is the n-th term of the sequence
a₁ is the first term of the sequence , n is the number of terms in the sequence and d is the common difference.
The terms of the arithmetic sequence are of first term a and common difference d are a , (a + d), (a + 2d) , (a + 3d)....
The sum of n terms of an arithmetic sequence is given by
Sₙ=a₁+aₙ where aₙ is the last term of the AP.
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Divied muti-diget numbers 174 divied by 6
Answers
Answer:29
Step-by-step explanation: 174 divided by 6 is 49 becuase 6x49=174
Which equation represents a line which is parallel to the line ?3x+4y=-4?
A : Y=4/3 x +6
B: Y=4/3 x +8
C: y=3/4x-3
D: Y = -3/4x +7
Answers
What is the missing coefficient?
(15x²+11y²+8x)-(7x²+5y² + 2x) = [ ] x² +6y² +6x
=8
How do we get to 8 ?
Answers
The missing coefficients of x² is 8.
According to the question we have been given the expression which is :
[tex](15x^{2} + 11y^{2} + 8x) - (7x^{2} + 5y^{2} + 2x) = [ ]x^{2} + 6y^{2} + 6x\\[/tex]
In this we have to find the missing coefficient.
To find the missing coefficients we will solve the L.H.S that is
[tex]= (15x^{2} + 11y^{2} + 8x) - (7x^{2} + 5y^{2} + 2x)[/tex]
First we will eliminate the brackets we get
[tex]= 15x^{2} + 11y^{2} + 8x - 7x^{2} - 5y^{2} - 2x\\[/tex]
Solving the coefficients of x² terms , y² terms and x terms we get
= 8x² + 6y² + 6x
Which is equal to the R.H.S
Combining both the equation we get the coefficient of the x² is 8.
Hence the missing coefficient is 8.
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The linear function that is represented by which table has the same slope as the graph? (the tables are the choices)
Answers
Answer: Table 3,
x : -9 -7 -5 -3 -1
y: -25 -21 -17 -13 -9
has same slope as line given equal to 2.
Step-by-step explanation:
Slope between two points having coordinates, (x1, y1) (x2,y2) which lie in a coordinate plane is given by:
coordinate plane is given by:
= (y2 - y1) / (x2 - x1)
Slope of linear function given in table 1, can be calculated byWe can see table 1,
Then we can write,
= (-7 - (-9) ) / (-21 - (-25) )
= (-7+9) / (-21+25)
= 2/4
= 1/2
Slope of linear function given in table 2, can be calculated byWe can see table 2,
Then we can write,
= (7-9) / (-21 - (-25) )
= -2/-21+25
= -2/4
= -1/2
Slope of linear function given in table 3, can be calculated byWe can see table 2,
Then we can write,
= (-21 - (-25) ) / (-7 - (-9) )
= (-21+25) / (-7+9)
= 4/2
= 2
Now, slope of line which passes through (0,-3) and (3,3) is
= (3 - (-3)) / 3-0
= 3+3/3
= 6/3
= 2
Table 3,
x : -9 -7 -5 -3 -1
y: -25 -21 -17 -13 -9
has same slope as line given equal to 2.
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Write a linear equation in standard form that satisfies the given set of conditions. passes through (4, –1) and (8, 3)
Answers
The linear equation in standard form that satisfies the given conditions is
x - y = -5
Given,
Points that the line passes through:
(x₁, y₁) = (4, -1)
(x₂, y₂) = (8, 3)
Let's find the slope of the line,
m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{3-(-1)}{8-4}[/tex] = [tex]\frac{3+1}{4}[/tex] = [tex]\frac{4}{4}[/tex] = 1
Now, we can write the equation in point slope form:
y - y₁ = m(x - x₁)
y - (-1) = 1(x - 4)
y + 1 = x - 4
Add -1 to both sides.
y + 1 - 1 = x - 4 - 1
y = x - 5
Now, let's convert this to standard form.
Ax + By = C
Here,
y = x - 5
Add +5 to both sides.
y + 5 = x - 5 + 5
y + 5 = x
x - y = -5
Now the equation is in standard form.
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Select the correct answer from each drop-down menu.
You can measure the ____ between points A and B by using ____ as zero.
First blank
1-positive distance
2-negative distance
3-positive or negative distance
Second blank
1-only point b
2-only point A
3-either point
Answers
You can measure the 1-positive distance between points A and B by using 3-either point as zero.
What is the distance?Distance means a distance magnitude or a direction vector.
Distance between points A and B is a distance magnitude, which can never be negative because it is the amount of space between the two points. It does not take into account the direction of the displacement.
The distance between points A and B shows the size of the displacement. The distance will remain the same whether measured from point A or from point B.
Thus, measuring the points between A and B can start from any of the points, and the measured distance is always positive.
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Which equation has no solution?
6x - 9 = 9x- 6
6 - (2x + 3) = -4 (x + 1) + 7
6x + 8 = 3 (2x + 4)
-3 + 4x = 13
Answers
Answer: Option C. 6x+8=3(2x+4)
Step-by-step explanation:
Solution = S
No Solution = NS
( S ) A. 6x - 9 = 9x - 6
6x - 9 + 9 = 9x - 6 + 9
6x = 9x + 3
6x - 9x = 9x + 3 - 9x
-3x = 3
-3x/-3 = 3/-3
x = -1( S ) B. 6 - (2x+3) = -4 (x + 1 ) + 7
6 - (2x+3)
6 - 2x - 3
-2x + 3
-2x + 3 = -4x + 3
-2x + 3 - 3 = -4x + 3 - 3
-2x = -4x
-2x + 4x = -4x +4x
2x = 0
2x/2 = 0/2
x = 0( NS ) C. 6x + 8 = 3 (2x +4)
6x + 8 = 6x + 12
6x + 8 - 8 = 6x + 12 - 8
6x = 6x + 4
6x - 6x = 6x + 4 - 6x
0 = 4
The sides aren't equal; there is no solution( S ) D. -3 + 4x = 13
-3 + 4x + 3 = 13 + 3
4x = 16
4x/4 = 16/4
x = 4There are 20 kids at Jacob's halloween party. 1/2 of the kids are in superhero costumes. 1/4 of the kids are witches or wizards. The rest are pirates. How many pirates are at the party?
Answers
Answer:
Total number of kids = 20
1/2 are in super hero costumes
= 1/2×20
= 10
1/4 are witches or wizards
= 1/4 ×20
= 5
Pirates= 20 - (10 + 5)
= 20 - 15
= 5
Is f(x)=x^2 a polynomial function?
Explain your answer
Answers
Answer:
For example, f(x)=2 is a constant function and f(x)=2x + 1 is a linear function. It is important to notice that the graphs of constant functions and linear functions are always straight lines. We have already said that a quadratic function is a polynomial of degree 2
Step-by-step explanation:
Need help ASAP!!
At the beginning of a snowstorm, Hassan had 2 inches of snow on his lawn. The snow then began to fall at a constant rate of 2.5 inches per hour. Assuming no snow was melting, how much snow would Hassan have on his lawn 5 hours after the snow began to fall? How much snow would Hassan have on his lawn after t hours of snow falling?
Answers
Answer:
14.5 inches of snow, S=T(H)+B
Step-by-step explanation:
This question is a linear equation. First, we will extract the important numbers
amount of snow at beginning=2
snow falling per hour=2.5
trying to find how much snow has fallen after 5 hours.
First, lets put this into an equation, variables will go as follows
total amount of snow=S
hours=H
snow at beginning=B
Rate of snow fall=T
Now, we make an equation
S=T(H)+B
Now, substitute the variables out
S=2.5(5)+2
Then, solve
S=12.5+2
S=14.5
For the second question, just put the equation you made as the answer
A piano keyboard has a total of 88 key.Which best describes the relationship the black keys have with each other
Answers
The relationship that the black keys have with each other in piano keyboard has a total of 88 keys is that there are 9 blacks keys for every 22 keys.
How to illustrate the information?It should be noted that in a piano keyboard that has a total of 88 keys, the number of black keys that are in the piano is 36 black keys.
Therefore, the appropriate ratio between the black keys and total keys will be:
= 36 / 88
= 9 / 22
= 9:22
Therefore, the relationship is that there are 9 blacks keys for every 22 keys.
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rkdksksnsenvjdkdkdkdndbsbbnbbbbvggggggggggggggggggggggggvbbbbnnjjnnnnnnn
Answers
Answer: Improper Response
Step-by-step explanation: Please be more specific and I'll answer
(8-5)(5-3)^2 I need help please
Answers
Answer:
Step-by-step explanation:
So start with your parentheses, (8-5)(5-3). 8-5=3 and 5-3=2, and when two parentheses are next to each other they will be multiplied.
Example: 3(5-3)^2 ---> 3 x 2^2
Although this "^" means "to the power" so 2 to the power of 2 is 2 x 2=4
So putting it all together we get, (8-5)(5-3)^2 --> 3(5-3)^2 --> 3 x 2^2 [2x2=4] --> 3 x 4 = 12
Your final answer is 12!
If you are still confused please do tell me what is confusing you. :)
Jake is saving quarters he starts with 5 quarters in his container he adds 3 quarters each day how many quarters will he have for the first 6 days how many will he have on the 13th day
Answers
There are 23 quaters in the container in first 6 days and there are 44 quaters in the container on 13th day.
How to find the number of quaters on the container on frist 6 days and 13 th day?given that
on first day Jake was saved 5 quarters in the container.
Then he adds 3 quaters each day.
now find the how many quarters will he have for the first 6 days.
from the question
5 + (3 X 6) = 5 + 18 = 23
so, there are 23 quaters in the container in first 6 days.
now find how many quaters will he have on the 13th day.
from the question
5 + (3 X 13) = 5 + 39 = 44
so,there are 44 quaters in the container on 13th day.
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Hannah makes $8.75 per hour. She works 30 hours per week. Find:
a. Her weekly pay
b. Her monthly pay
c. Her yearly pay
can someone explain this?
Answers
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Hannah makes $8.75 per hour.
If she works 30 hours per week then
So, her weekly pay
=30*8.75
=262.5
Then her monthly pay
=4* 262.5
=1050
Then the yearly pay would be
=12* 1050
= 12600
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