Sai has a garden on the side of his house that will be enclosed with 196 ft. of fencing. The
rectangular plot will be fenced in on all sides except for the side against the house. What
dimensions will maximize the plot of land? What is the maximum area?
PLEASE DO THESE BELOW
-use written and verbal explanination that justifies each step
-Use at least one representation(ex number sentences, diagrams, charts, etc)
Answers
Answer:
49 and 98, with an area of 4802
Step-by-step explanation:
So, let X be one of the sides, and Y be the other
X*Y would be the area of the rectangle since width*length = area, and X is the width and Y is the length
2X+Y would be the perimeter, excluding the wall (since we don't need fencing for the side sticking to the wall)
To find the max area, we can plot our two equations
so, our two equations:
1. 2X+Y=196 (since perimeter)
2. X*Y=area, and we're trying to maximise it
We can re-arrange the first equation to get
3. Y=196-2X
plug our new equation (#3) into the second equation(#2)
to get:
X*(196-2X)=area=196X-[tex]2X^2[/tex]
And now that we have this equation, we can either:
Graph it to see the largest area (the highest point)
Or calculate the max area using calc
We have a quadratic function that goes up, then down as X increases, so we'll try to find the point where the function stops going up, and instead goes down as X increases (image is attached, not to scale). Recall that the first derivative basically tells is the slope of a function/equation at a given X, so when the function is at a slope of 0, we know that the area is at its max point.
Take the first derivative
(196X-2X^2)'=196-2(2X)=196-4X
196-4X is the equation of the slope, so when X = 49, then the slope is 0
This means that one of the side lengths should be 49
To find out which one, we can use trial and error: (there are 2 cases)
1. 49*((196-49)/2)=3601.5
or:
2. 49*(196-2*49)=4802
The second option is correct since the number, or the area is larger.
Side length 1: 49
Side length 2: (196-2*49), or 98
Note: there's definitely another way to do this problem
Related Questions
I’m wondering if somebody can help me with this-
Answers
Pls help again
100 Points
Answers
Answer:
p < 8
Step-by-step explanation:
Let p = number of pounds of candy Lena will buy
Given:
Candy = $5 per poundLena will spend less than $40Create an inequality using the given information:
⇒ 5p < 40
Solve the inequality:
⇒ 5p < 40
Divide both sides by 5
⇒ p < 8
The inequality to solve this would be 5p < 40
In the equation you are multiplying 5 by p, so you do the opposite and divide 5 and 40 by 5
5 divided by 5 cancels out, and 40 divided by 5 = 8. Take the leftover p and the < and make an inequality with 8. p < 8
math question on the sceen shot
Answers
Answer:
(8,9) it is corrrect I am sure of it because
if you put the dotson a grid they will
create a rectangle so that wht that answer is corr
What is the slope of the equation2y=6x-8
4
2
6
3
please help
Answers
Step-by-step explanation:
2y=6x-8
Divide the equation by 2
y=3x-8 => y=MX+c
m=3
slope is 3
out of these
two files and one is the question and the other is answers
Answers
Answer:
I believe it would be A.
Answer:
A
Step-by-step explanation:
because 65/90=x/100 is the formula for it.
PLEASE MARK ME AS BRAINLIST
Brett create a function of X with seven points each in a different location on the grid he graph sixth of the points as shown use the add point tool to show the location of a point that could be the seventh point of Brett function
Answers
Answer:
any point where x=3, 4, or 6.
Step-by-step explanation:
The thing that makes a function a function and not a relation is having only 1 y value per x value, which means if you draw a vertical line through a point, it should not intercept any other points. Basically, the main difference between a function and a relation is that a function can't have 2 points on top of each other.
Pick a point where x=3, 4, or 6. Those are the open spots on the grid with nothing above or below them. It doesn't matter which point you pick, as long as there is NOTHING directly above or below that point.
I hope you understood this solution. Happy mathing!
The solution is, any point where x=3, 4, or 6, is the location of a point that could be the seventh point of Brett function.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The thing that makes a function a function and not a relation is having only 1 y value per x value, which means if you draw a vertical line through a point, it should not intercept any other points.
Basically, the main difference between a function and a relation is that a function can't have 2 points on top of each other.
so, we have,
Pick a point where x=3, 4, or 6.
Those are the open spots on the grid with nothing above or below them. It doesn't matter which point you pick, as long as there is NOTHING directly above or below that point.
Hence, The solution is, any point where x=3, 4, or 6, is the location of a point that could be the seventh point of Brett function.
To learn more on function click:
brainly.com/question/21145944
#SPJ2
3. Which two integers are 7 units away from the number 5 on a number line?
A. -2 and 2
B. -2 and 7
C. -7 and 7
D. -2 and 12
Answers
Answer:
2B
3D
Step-by-step explanation:
2A is
a/b + -a/-b = a/b + a/b = 2a/b
this is NOT 0/0. you can't add numerator and denominator. when you have the same denominator, you can only add the numerator.
and don't forget : -×- and -/- are both + !
2B
you do not multiply anything. you ADD (but again NOT the denominators) !
and +×- or +/- = - !
overall this this adding a negative number to the same positive number. the result : always 0
2C
cannot be added like that. first you would have to bring both to a common denominator. but then you ADD !
2D
very similar to 2C.
3
5 + 7 = 12
5 - 6 = -2
these are the 2 integers 7 units away from 5.
can u devide in graphs?
Answers
Answer:
yes I can devine in graphs
know the answer for this???
Answers
x = 5 makes 2x≤ 10 true but not 2x < 10 because "≤" means less than or equal to, which means 2x would be the same as 10, so 10 ÷ 2 = 5, x = 5.
Answer:
Step-by-step explanation:
2x ≤ 10, when x = 5
2(5) ≤ 10
10 ≤ 10 (10 is less than OR equal to 10)
2x < 10, when x = 5
2(5) < 10
10 < 10 (10 is less than 10) - that is false
x = 5 does not makes 2x < 10 true because 10 can't be less than 10.
Hope this helps!
Select all the events that are possible, but unlikely.
•opening a 300 oage book to exactly page 143.
• a second grade classroom contains some books.
•you will roll a 7 on a standard 6 sided number cube.
•everyone in your school will get to school on time on the next school day.
•a triange has 3 sides.
Answers
Answer:
opening a 300 page book to exactly page 143.
everyone in your school will get to school on time on the next school day.
Step-by-step explanation:
"Opening a 300 page book to exactly page 143" and "everyone in school will get to school on time next day" are the possible but unlikely events.
Unlikely event:
If something which probably will not happen and actually happens.
Certain event:A certain event is an event that is sure to happen. E is a certain event if and only if P(E) = 1.
According to the given question
Opening a 300 page book to exactly page 143 is a random event and very unlikely to happen.A second grade classroom contains some books it is an event with high probability.Getting a 7 on a standard 6 sided number cube , it is an impossible event.Everyone in school will get to school on time on the next day is also a random event and very unlikely to happen.A triangle has 3 sides , it is a certain event.Hence, first and fourth are possible but unlikely events.
Learn more about unlikely events:
https://brainly.com/question/23050068
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a town credits the introduction of a drunl driving law for reducing fatal automobile accidents by over 50% the year it first took effect. the bar graph here shows the number of fatal automobile accidents in that town from 2000 to 2008 what year did the law first take effect
A. 2001
B. 2002
C. 2003
D. 2005
Answers
Answer: 2001
Step-by-step explanation:
Dropped from 35 to about 17.5.
After 5 years, $40,000 deposited in a savings account with simple interest had earned $26,000 in interest. What was the interest rate?
Answers
Step-by-step explanation: Je n'ai pas calculé les intérêts depuis un moment, donc je peux me tromper. Si j'ai raison, envisagez de me donner le plus intelligent.
Bonne journée! :)
Help please!! What can you tell about the mean of each distribution?
Answers
Answer:
I think it's c I have looked it through and now I think it's c
please help as soon as possible.
Answers
Answer:
Question 3
In 15 minutes, the tortoise walked 400 meters
1 hour ---> 60 minutes
60 minutes is 4 x 15 minutes
4 x 15 // 400 x 4
1 hour // 1600 meters = 1.6 kilometers
the tortoise can walk 1.6 Kilometers per hour
Question 4
2 quart bottle for 2.56$
1 quart = 32 fluid ounces
2 quart = 64 fluid ounces
2.56/64 = 0.04$ per fluid ounce
Demarcus has to wrap a gift for his friend's birthday party. The gift is in a rectangular box with the dimensions shown below. He's trying to figure out how much gift wrap he needs to cover the entire box. Should he calculate the total surface area or the lateral surface area? Pick the right measurement and then calculate it for him.
In your answer, specify whether he should use total surface area or lateral surface area. Calculate the one you choose, give that measurement of the box, and then explain how you calculated it.
Answers
Answer:
Surface Area = 2lw + 2lh + 2hw = 2(lw+lh + hw) = 2(12x8 + 12x4 + 4x8) = 2(96+48+32) = 2(176) = 352 square inches
Step-by-step explanation:
The surface area of the is mathematically given as
A= 1048in^2
What is the Surface Area?Question Parameter(s):
Generally, the equation for the Surface area is mathematically given as
A = 2(lw + wh +lh)
Therefore
A = 2(20(8) + 8(13) +20(13))
A = 2(160+104+260)
A= 1048in^2
In conclusion, the Surface area is
A= 1048in^2
Read more about Measurement
https://brainly.com/question/17972372
Look at the screenshot
Answers
Answer:
The answer is d and b hope this helps!
for b, the relationship is 1/4 and for d it's 7/1
NEED HELP FAST!!!! NEED ANSWER IN 6 MIN!!!!!!!!!!!!!!
Answers
Answer:
28
Step-by-step explanation:
First find the area of the small rectangle, 16 then subtract that from the big rectangle, 44.
Answer:
28 sq. units
Step-by-step explanation:
Area (shaded) = Area (big rectangle) - Area (small rectangle)Area = 4 x 11 - 2 x 8Area = 44 - 16Area = 28 sq. unitsASAP What percentage of total expenses is spent on housing? (round to nearest whole percent)
Answers
show work on how to do the question
Answers
Answer:
8.4
Step-by-step explanation:
subtract 18-9.6 to get the answer of 8.4
What is 6 5/7 rounded around the nearest whole number
Answers
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
5/7 is 0.714....
7 is greater that 5 so u round up to 7
Please Help me out!
1.) Hexagon: x = _______
Set up a proportion to solve for y.
y = _______
2.) Set up a proportion to solve for z.
z = __________
Answers
Answer:
1. x = 82 y = 402. z = 80A clock is dropped and stops working. What is the probability that the second hand is stopped between the 12 and 1? Show how you solved the problem.
Answers
Answer:
The distance between any 2 consecutive numbers on a clock is 1/12 of the circumference
Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 inches. The length of the frame is 20.3 inches.
Write an equation to find the width of the frame, x.
Enter the correct equation in the box.
What is the equation
Answers
Answer
x=15.8
Step-by-step explanation:
20.3*2=40.6
72.2-40.6=31.6
31.6/2=15.8
(15.8*2)+(20.3*2)=72.2
20.3*2+x*2=72.2
x=15.8
Hope this helps.
One-step inequalities
5 star equations for correct answers
byeee :3
Answers
Hi!
[tex]\\ \sf\longrightarrow \dfrac{x}{7}\geqslant -6[/tex]
[tex]\\ \sf\longrightarrow x\geqslant -6(7)[/tex]
[tex]\\ \sf\longrightarrow x\geqslant -42[/tex]
Solution set in interval notation
[tex]\\ \sf\longrightarrow x\in[-42,\infty)[/tex]
Kevin and Tiana are making soup. The recipe calls for a pound of onions. They have one onion that weighs ½ pound and another that weighs ⅖ pound. Kevin says they only have 3/7 pound of onions, so they definitely don’t have enough. Why is Kevin wrong?
PLSSSS HELP!
Answers
Molly is painting a model house and needs to know how much paint she will need. She knows the surface area of the prism is 216 square inches and the surface area of the pyramid is 84 square inches.
1. Which surface is shared by the two solids? What are the dimensions of this surface?
2. There is another surface that Molly does not need to paint, because it won’t show when she displays the model house. Describe that surface, and explain why it doesn't need to be painted.
3. To find the area Molly needs to paint, she should add the surface areas of both solids and subtract:
twice the area of the triangle
twice the area of the square
three times the area of the square
the area of the square
4. Find the area Molly needs to paint. Show your work, and be sure to include units with your answer.
Oh and here's an image to help you out
Answers
Answer:
1. a square which is 6 × 6in
2. the inside of the prism or cube as it is not seen from the outside
3. the area of the square - 6 × 6 = 36in
4. 6 x 6 = 36 / one face of prism
× 5 = 180
4 × 6/2 = 12 / one face of pyramid
x 5 = 60
60 + 180 = 240
Please help!! It has to be *TWO* angles
{An angle measures 150° less than the measure of its supplementary angle. What is the measure of each angle?}
Answers
Answer:
165° & 15°
Step-by-step explanation:
Let the first angle be 'a'
second angle be (a-150°)
a+(a-150°) = 180°
2a=180°+150°
2a=330°
a=330/2
a=165°
first angle is 165°
second angle is 165-150=15°
Hector is using wood to build a dog house. Each wall is 4/7 of a yard tall and 3/5 of a yard wide. Know that the area of each wall is the base times the height, how many square yards of wood will he need to build 4 walls of equal size?
a
1 2/3
b
1 13/35
c
12/35
d
1 4/12
Q2
Which of the following is equivalent to 4/10 x 3/8?
a
4 ÷ (10 x 3) ÷ 8
b
(4 + 3) x (10 + 8)
c
(4 x 3) ÷ (10 x 8)
d
(4 - 3) ÷ (10 - 8)
Answers
Answer:
a
Step-by-step explanation:
b
Please answer the question down below
Answers
[tex]x + 62 = 90[/tex]
[tex]x = 90 - 62[/tex]
[tex]x = 28[/tex]
Answer:
28
Step-by-step explanation:
angle AOC is a right angle that equals 90 degreeds
90-62=28
Estimate the difference 7 3/4-2/25 Show your work.
Answers
Answer: 7 3/4 - 2/25 = 767/100 = 7 67/100 = 7.67
Step-by-step explanation:
Conversion a mixed number 7 3/4
to a improper fraction: 7 3/4 = 7 3/4 = 7 · 4 + 3/4= 28 + 3/4 = 31/4
To find a new numerator:
a) Multiply the whole number 7 by the denominator 4. Whole number 7 equally 7 * 4/4 = 28/4
b) Add the answer from previous step 28 to the numerator 3. New numerator is 28 + 3 = 31
c) Write a previous answer (new numerator 31) over the denominator 4.
Seven and three quarters is thirty-one quarters
Subtract: 31/4 - 2/25= 31 · 25/4 · 25 - 2 · 4/25 · 4 = 775/100 - 8/100 = 775 - 8/
100 = 767/100