if you have 240 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
Answers
The largest area that can be enclosed by a fence of 240 m and a wall is 7200m²
It is given that the rectangular area will be fenced up against a long rectangular wall. Therefore, the fencing will be done on just three sides.
Let one side be x
Then the side opposite to it must be x cm as well
The sum of the three sides should be equal to 240 m
Hence the third side must be 240 - 2x m
Therefore the area of the region fenced must be
A = x(240 - 2x)
or, A = 240x - 2x²
Now we need to maximize the above equation
Taking the first derivative zero we get
A' = 0
or, 240 - 4x = 0
or, 60 - x = 0
or, x = 60
Now we will test whether the above output is maximum or not. The second derivative of A is
A'' = -4
Since A'' is a constant function,
Now, A''(60) = -4
Therefore, the maximum side will have lengths of 60 m and 120 m.
Hence the largest area that can be enclosed with the fence is
60 X 120 m²
= 7200 m²
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Related Questions
What is the slope of the line graphed below?
A. -2
B. 2
C. 2
D.-2/2
Answers
Answer:
if this is not corecct do not blame me
-2/2
Step-by-step explanation:
solve pls in a more easy way
[tex] \frac{1}{5 { \frac{2}{3} }^{} } [/tex]
Answers
Answer:
[tex]\cfrac{3}{17}[/tex]-------------------------
Given fraction [tex]\cfrac{1}{5\frac{2}{3} }[/tex]Simplify it in below steps[tex]1:5\cfrac{2}{3} =[/tex] Show the fraction as division[tex]1:\cfrac{5*3+2}{3} =[/tex] Make improper fraction[tex]1:\cfrac{17}{3} =[/tex] Simplify[tex]1*\cfrac{3}{17} =[/tex] Convert division into multiplication[tex]\cfrac{3}{17}[/tex] Solutionwhat is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called?
Answers
The process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called is called scoring a card.
In the given question we have to explain what is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called.
As we know that, a score a card is a statistical model generated using information about the portfolio's past performance. The main advantage of categorizing clients using a statistical scorecard is that it gives the client an accurate numerical forecast of their future behavior.
So, the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called is called scoring a card.
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The right question is:
What is the process for classifying or predicting the value of the target variable of a new observation for given values of predictor variables called?
Target value predictingPredicting a recordClassifying a variableScoring a recordGraph the points (1,
–
5), (
–
4.5,1), and (3.5,
–
2.5) on the coordinate plane.
Answers
The points (1, 5) , (4.5, 1) , (3.5, 2.5) are shown in graph plotted.
What is a Graph?In graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". In a graph the points are plotted using coordinates in the form of (x, y) or (x, y, z) or (r, Ф, z) or (r, θ, Φ) as per need on different types of coordinate graphs.
We have the following coordinates -
(1, 5) , (4.5, 1) , (3.5, 2.5)
The following points are plotted on the graph as shown in the image attached.
For any coordinate -
(x, y)
[x] is plotted along the [x] - axis
[y] is plotted along the [y] - axis
Therefore, the points (1, 5) , (4.5, 1) , (3.5, 2.5) are shown in graph plotted.
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Answer: (1, 5) , (4.5, 1) , (3.5, 2.5)
Step-by-step explanation:
Which of the following is NOT an example of a linear equation?
5x + 2zk = 2
2x + 3y = 12
2x = -3
Answers
All of the equations given are linear equations
5x + 2zk = 2 Linear equation
2x + 3y = 12 Linear equation
2x = -3 Linear equation
How to determine the function classified as linear equationInformation given in the question include
5x + 2zk = 2
2x + 3y = 12
2x = -3
What is linear function ?A linear function or equation consists of equations where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
m = sw + c
Examining the given equations all of them are of exponents of 1 that is raised to the power of 1. This is how to know linear equations
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Lilianna uses \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction calories per minute just by sitting. She uses 111 more calorie per minute by walking. Lilianna uses a total of 12\dfrac{1}{4}12
4
1
12, start fraction, 1, divided by, 4, end fraction calories walking to the park.
Lilianna uses the equation, d\left(\dfrac{3}{4}+1\right)=12\dfrac{1}{4}d(
4
3
+1)=12
4
1
d, left parenthesis, start fraction, 3, divided by, 4, end fraction, plus, 1, right parenthesis, equals, 12, start fraction, 1, divided by, 4, end fraction to represent the situation.
What does the variable ddd represent in the equation?
Answers
The variable d in the given equation represents the number of minutes that Lilianna spends walking to the park.
What does the variable d represent?Calories that Lilianna uses by sitting = 3/4
Calories that Lilianna uses by walking = calories used sitting + 1 : 1 + 3/4
Calories that Lilianna uses when she walks to the park = calories used per minute when walking x number of minutes spent walking.
Calories that Lilianna uses when she walks to the park = d(1 + 3/4)
12 1/4 = d(1 + 3/4)
d - 12 1/4 ÷ 1 3/4
d = 49 / 4 x 4/7
d = 7 minutes
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George invet $500 in hi friend' tartup company. Hi friend agree to give him 8% of the original invetment each year for the next 3 year. Write a linear function for thi ituation
Answers
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The linear equation for this situation is
3y = 500+40x
Geroge invest in his friend's startup = $500
let the number of year = y
His friend agree to give 8% of his investment = 500*8/100
=4000/100
= $40
total money given by his friend = x
so the total return of george would be sum of his investment and his interest of each year.
the number of year is 3, so
y = 3y
so the equation be:
3y = 500+40x
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graph the equation y=-2/3x+5
Answers
Step-by-step explanation: Graph the line using the slope and y-intercept, or two points.
Slope: 2, 3 and the y-intercept: (0,−5)
x | y
0 -5
3 -3
Dennis made an extra $245.00 for selling furniture. The extra $245.00 was 7% of the total value of the furniture he sold. What was the total value of the furniture Dennis sold?
Answers
Answer:
Option A
Step-by-step explanation:
Dennis made an extra $245.00 for selling furniture. The extra $245.00 was 7% of the total value of the furniture he sold. What was the total value of the furniture Dennis sold?
245 = 0.07x
divide both sides by 0.07:
245/0.07 = 0.07x/0.07
x = $3,500
Option A
Find the cost to the nearest cent. $72.95 jacket; 4% tax need help what the answer pls
Answers
+ Sales tax (4%): $ 2.92
Total price including tax: $ 75.87
i need omg omg dis is hard prob not
Answers
Answer: The denominator
Step-by-step explanation:
Remember what I said last time?
The numerator is the number on top
The denominator is the number on the bottom
And the fraction line is well, the line!
Try to remember that the numerator is on top and the denominator is on the bottom.
The way I remember is how both bottom and denom end with the same syllable!
Answer: Denominator.
Step-by-step explanation:
The denominator is the bottom, the fraction line separates the numerator (top number) and denominator (bottom number), and a integer is a whole number.
Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1 6 units 8 units 10 units 36 units
Answers
The line segment from minus 5 comma 5 to minus 3 comma -1 is 10 Units long.
Given,
The line segment from negative 5 comma 5 to 3 comma negative 1
How can I determine a line segment's length?
A line that is divided into two points on a line is referred to as a line segment.
The line segment from 3 comma negative 1 to negative 5 comma 5 is determined by applying the formula;
Square root of (x₂ - x₁)² +(y₂ - y₁)²
= [tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }[/tex]
= [tex]\sqrt{8^{2}+6^{2} }[/tex]
= √100
= 10 units
That is,
The line segment from minus 5 comma 5 to minus 3 comma -1 is 10 Units long.
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What is the solution to the system of equations y 2 3x 3 x 2?.
Answers
The solution of two equations y=(2/3)x + 3 and x=-2 is [tex](-2,5/3)[/tex]
Define an equation .
A mathematical statement that shows that two mathematical expressions are equal.
What is a Subsitution method ?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
The given two equations are y=[tex]\frac{2}{3}[/tex]x + 3 and x=-2
So on subsituting x=-2 in another given equation ,we get
y=[tex]\frac{2}{3}[/tex] (-2) +3
=[tex]\frac{-4}{3}[/tex] + 3
On taking LCM both sides ,we get
y=[tex]\frac{(-4+9)}{3}[/tex]
= [tex]\frac{5}{3}[/tex]
Hence ,the solution of the system of equations is (x,y) is ([tex]-2,\frac{5}{3}[/tex])
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Correct question:
What is the solution of two equations y=(2/3)x + 3 and x=-2 ?
The solution of two equations y=(2/3)x + 3 and x=-2 is [tex](-2, \frac{5}{3})[/tex]
Define an equation .A mathematical statement that shows that two mathematical expressions are equal.
What is a Subsitution method ?The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
The given two equations are y = [tex]\frac{2}{3}[/tex]x + 3 and x=-2
So on substituting x=-2 in another given equation ,we get
y = [tex]\frac{2}{3} \times (-2) + 3[/tex]
= [tex]\frac{-4}{3} + 3[/tex]
On taking LCM both sides ,we get
y = [tex]\frac{(-4 + 9)}{3}[/tex]
= 5/3
Hence ,the solution of the system of equations is (x, y) is [tex](-2, \frac{5}{3})[/tex]
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Correct question: What is the solution of two equations y=(2/3)x + 3 and x=-2 ?
pls answer will mark brainliest
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
a. -x^2+19x+8
b. -x^2+26x+8
c. 8x^2+10x+8
d. 8x^2+26x+8
Answers
Answer:
x^2+12x-8
Step-by-step explanation:
(x-8)(x+1) = x^2-7x-8
x^2+9x-7x+10x-8
simplify:
x^2+12x-8
Answer: -x^2+26x-8
Step-by-step explanation:
1. Multiply
9x-(x-8)(x+1)+10x
9x-x^2-x+8x-8+10x
2. Combine Like Terms
-x^2+26x-8
Answer: -x^2+26x-8
Age of mother i 4 time the age of her daughter after 8 year the um of their age will be 66 year. Find the age of her daughter and her mother
Answers
The age of mother and daughter are 10 and 40 years old, respectively.
Given that,
Mother is 4 times her age. Her daughter's age plus her daughter's age after 8 years equals 66 years.
It can be written into equation as :
Let Mother's age be x
Let daughter's age be y
By using algebra,
x =4y --------> (1)
(x+8) + (y+8) = 66
x+ y = 66-16
x + y = 50--> (2)
Now substitute x = 4y in (2) we get
x + y = 50
4y + y = 50
5y= 50
y = 10 years which means x = 4y = 40 years
Therefore, the age of daughter and her mother is 10 and 40 years respectively.
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How do I do this?? Please help!!
Answers
Answer:
Step-by-step explanation:
You need to find the slope of each line to determine if they are parallel. Beginning with AB, you do the formula for slope and get a value of -1/3. Next, you do CD and find it also has a slope of -1/3. Because both of these lines have equal slopes it makes them parallel because they will both be traveling at the same rate and will never get closer or further from each other.
*In order for lines to be perpendicular they need to have inverse slopes
Ex. a slope of 1/2 is perpendicular to a slope of -2
Pleaseeeee helpppppp, i've been trying to solve this for 7 days!!!!
Answers
Solution of the given expression (9/4) -2(4x +4/3) +(5/2)x is equivalent to the following one:
-(5/12) - (11/2)x -(5/12) - 8x +(5/2)x (9/4) -2(4x) -2(4/3) + (5/2)xAs given in the question,
Given expression is equal to :
(9/4) -2(4x +4/3) +(5/2)x
Solution of the given expression (9/4) -2(4x +4/3) +(5/2)x is equivalent to the following one:
(9/4) -2(4x +4/3) +(5/2)x
= (9/4) - 2(4x) - 2(4/3) + (5/2)x
Simplify the like terms of the given expression we get,
= (9/4) -(8/3) - 8x + (5/2)x
= (27-32)/12 -8x +(5/2)x
= -(5/12) -8x + (5/2)x
= -(5/12) +((-16+5)/2)x
= -(5/12) -(11/2)x
Therefore, solution of the given expression (9/4) -2(4x +4/3) +(5/2)x is equivalent to the following one:
-(5/12) - (11/2)x -(5/12) - 8x +(5/2)x (9/4) -2(4x) -2(4/3) + (5/2)xLearn more about equivalent here
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On the seventh grade trip to Washington DC for every 8 students there were 3 chaparones twelve chaperones were needed how many students went on the trip
Answers
Answer:
32
Step-by-step explanation:
i hope this helped
Solve the equation. Check your solution. 4(3/8x + 3) - x =8(1/4x - 3) + 6
Answers
i broke it down to the lowest so it should be x=20
Mario's current credit card balance is $2,109.65 with a minimum payment of $68.00. Over the next month, he plans to spend $471.00. If the APR is 31.99%, what will Mario's new balance be, including interest?
$2,512.65
$2,897.25
$2,579.63
$2,784.32
Answers
Mario's new credit balance including interest is $2579.63
Given,
Mario's current credit balance = $2,109.65
Minimum payment amount = $68.00
The amount Mario plans to spend over the next month = $471.00
APR = 31.99%
We have to find the new balance including interest.
Monthly interest rate on credit card = APR/12 = (31.99%/12)
The credit balance before interest = (current balance) + (expense for next month) - (minimum payment)
= 2109.65 + 471 - 68
= $2512.65
The credit balance after interest = 2512.65 × (1 + 0.3199/12) = $2579.63
That is,
Mario's new credit balance including interest is $2579.63
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Julian sells 4 pieces of artwork for $72, and each piece is sold at the same rate.
How much does one piece of Julian's artwork cost?
Answers
Answer:
The answer is $18
Step-by-step explanation:
To solve this all you would do is divide $72 by 4 to get $18
875²-125² factorise the following fully
Answers
Answer:
750000
Step-by-step explanation:
When Ashley left her house in the morning, her cell phone battery was partially charged. Let B represent the charge remaining in Ashley's battery, as a percentage, t hours since Ashley left her house. A graph of B is shown below. Write an equation for B then state the y-intercept of the graph and determine its interpretation in the context of the problem.
B = _____
The y-intercept of the function is ___ which represents
(A) the number of hours until Ashley's phone dies.
(B) the charge of the battery when Ashley left her house
(C) the percentage charge that Ashley's phone loses each hour
(D) the charge of the battery when Ashley woke up.
Answers
The y-intercept of the function is 50% which represents; (B) the charge of the battery when Ashley left her house
What is the y-intercept of the Linear Graph?The general format for the equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
Now, the y-intercept is defined as the point where the graph line crosses the y-axis or the point at which x is zero.
The slope is defined as the ratio of change of the vertical axis with the horizontal axis.
From the given linear graph, we can see that;
The line intersects the y-axis at y = 50. Thus;
y-intercept = 50
Now, the y-axis represent the percentage charge remaining on the phone battery while the x-axis shows that number of hours since Ashley left her house. Thus;
When the number of hours is zero, the percentage charge remaining on the phone battery is 50%
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A tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year. Organize the weekly earnings for each year in a table.
Answers
The weekly earning for each year is $135, $520, $2040, $8080
What is expression?Numbers, symbols and operators grouped together that show the value of something.
Given that, a tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year
The weekly earnings for 1st year are,
q = $10, p = $25, x = 5, (px+q) = $135
The weekly earnings for 2nd year are,
q = $20, p = $50, x = 10, (px+q) = $520
The weekly earnings for 3rd year are,
q = $40, p = $100, x = 20, (px+q) = $2040
The weekly earnings for 4th year are,
q = $80, p = $200, x = 40, (px+q) = $8080
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In 2011, it rained 1. 651 x 10 to the 3rd power centimeter in New Orlean. In 2012 it rained another 8. 1 x 10 to the 2nd power centimeter. How many centimeter of rain did New Orlean exprience total?
Which mathematical operation i ued for the problem
Answers
New Orlean experience total rain is 2461 centimeters.
Given:
In 2011, it rained 1. 651 x 10 to the 3rd power centimeter in New Orlean. In 2012 it rained another 8. 1 x 10 to the 2nd power centimeter.
Total rain = rain in 2011 + rain in 2012
= 1.651*[tex]10^{3}[/tex] + 8.1*[tex]10^{2}[/tex]
= 1.651*1000+8.1*100
= 1651 + 810
= 2461 centimeters.
Therefore New Orlean experience total rain is 2461 centimeters.
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A diver i 5 feet ea level. He decend an additional 3 feet. What integer repreent the dive' location now?
Answers
If a diver descends 5 feet below sea level and descends an additional 3 feet, then the integer representation of the diver's location is -8 feet
The number of feet that diver descends below sea level = -5 feet
Which is represented by negative number because which is below sea level, The sea level considered as the reference level that is represented as zero.
Then the diver descends an additional 3 feet
Then the diver's location = The number of feet that diver descends below sea level - 3 feet
Substitute the values in the equation
= -5 - 3
= - 8 feet
Hence, if a diver descends 5 feet below sea level and descends an additional 3 feet, then the integer representation of the diver's location is -8 feet
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Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
The equation of the line in fully simplified slope-intercept form is [tex]y=-0.4x-4[/tex]
Step-by-step explanation:
The equation of the line in fully simplified slope-intercept form can be calculated as follows ?
The first step is to calculate the slope [tex]m[/tex] of the given line using the slope formula as follows
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Take two coordinates on the given line
[tex](-5,-2)~ \text{and} ~(5,-6)[/tex]
Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]-2[/tex] for [tex]y_{1}[/tex], [tex]5[/tex] for [tex]x_{2}[/tex], [tex]-5[/tex] for [tex]x_{1}[/tex] in the slope formula
[tex]m=\frac{-6-(-2)}{5-(-5)}[/tex]
Take out the brackets in the numerator and the denominator at the right side of the equation
[tex]m=\frac{-6+2}{5+5}[/tex]
Simplify the numerator and the denominator at the right side of the equation
[tex]m=\frac{-4}{10}[/tex]
Convert the value of [tex]m[/tex] into decimal
[tex]m=-0.4[/tex]
The second step is to find the slope-intercept form of the given line by the point-slope form formula as follows
[tex]y-y_{1}=m\cdot (x-x_{1})[/tex]
Take any coordinates on the given line, take [tex](-5,-2)[/tex]
Substitute [tex]-2[/tex] for [tex]y_{1}[/tex], [tex]-5[/tex] for [tex]x_{1}[/tex], [tex]-0.4[/tex] for [tex]m[/tex]
[tex]y-(-2)=-0.4\cdot (x-(-5))[/tex]
Take out the inner bracket on the right side of the equation
[tex]y-(-2)=-0.4\cdot (x+5)[/tex]
Take out the bracket on the left side of the equation
[tex]y+2=-0.4\cdot (x+5)[/tex]
Expand the right side of the equation
[tex]y+2=-0.4x -2[/tex]
Substract [tex]2[/tex] from both sides of the equation
[tex]y+2-2=-0.4x -2-2[/tex]
Simplify the equation
[tex]y=-0.4x -4[/tex]
Hence the equation of the line in fully simplified slope-intercept form is [tex]y=-0.4x-4[/tex]
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Could somone help me with this question please
Answers
the correct answer is A because 3x1=3
A bag has 12 different-colored marbles: 4 green, 5 blue, 1 yellow, and 2 orange. You draw a marble from the bag. If you get an orange marble or yellow marble, you win a prize.
Answer these questions:
a. What is the theoretical probability of winning the game? Show your work..
b. What is the most likely outcome? Use probabilities to support your answer, and show your work.
c. What is the least likely outcome? Use probabilities to support your answer, and show your work.
d. Is it more likely that players will win or lose playing the game? Explain why.
Answers
Answer:
Step-by-step explanation:
4+5+1+2=12
1+2=3
4+5=9
12 - all marbles
4 - green marbles
5 - blue marbles
1 - yellow marble
2 - orange marbles
3 - yellow and orange marbles
9 - green or bule marbles
a. [tex]\frac{3}{12}[/tex] win only when draw 1 yellow or 1 of 2 orange.
b. [tex]\frac{5}{12}[/tex] the mostly likly outcom is for blue marbles, (more than other colour in bag)
c. [tex]\frac{1}{12}[/tex] the least likly outcom is for yellow marble, (less than other colour in bag)
d. [tex]\frac{9}{12}[/tex] propability of lose
[tex]\frac{9}{12} > \frac{3}{12}[/tex] player will lose more likly than win.
Rainforests represent 6% of the land on earth, and contain half of all living things. Find the ratio of rainforests to other habitats.
Answers
The ratio of the rainforests to other habitats= 3/47
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Rainforests = 6%Other habitats = 100% - 6% = 94%The ratio would there fore be:6%/94%In fraction:6% = 6/100 = 3/5094% = 94/100 = 47/50= 3/47hence,The ratio of the rainforests to other habitats= 3/47
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