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)
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
The diameter of a circle is 14 in.
What is the radius of the circle?
A. 7 in
B. 21 in
C. 28 in
D. I don't know.
I believe the answer is 7
Step-by-step explanation:
The radius is like half of the diameter and 14/2=7
Hope this helps
Make a bell curve for the data: (99, 60, 82, 78, 93, 71, 68, 86, 80, 95, 72, 64)
Answer:
Make a bell curve for the points 99, 60, 82, 78, 93, 71, 68, 86, 80, 95, 72, 64 · The variables x and y have a proportional relationship, and y=7 when x=2.
Step-by-step explanation:
This is the graph of a polygon. What is the approximate perimeter of the polygon?
A:18.3 units
B:20.5 units
C:24.3 units
D:28.5 units
NO LINKS OR IMPROPER ANSWERS
Rebecca had these results when she drew 10 tiles from the bag. The bag has a total of 20 tiles. Her classmates got similar results. What is a good predication for the number of green and red tiles out of 20?
Answer:
10/20
Step-by-step explanation:
if she has 20 in total and there's only two colours I would assume it's an even chance,
For example a coin has two sides, = even chance of getting each side.
Good luck hope this helped
The population of a city was 60,000 in 2015 and 63,000 in 2016. The percent increase in the population from 2015 to 2016 was the same as it was from 2016 to 2017. What was the population of the city in 2017?
Answer:
The population will be 66150.
Step-by-step explanation:
3000 / 60000 = 0.05 (5% Increase)
60000 X 1.05 = 66150
Answer: Kentwood, Michigan had a population of 49,000 in the year 2013. The infrastructure of the city allows for a carrying capacity of 60,000 people. rmax ...
and the link mite help
Step-by-step explanation:Hope it helps you.
A rectangular prism has a length of 4 in., a width of 2 in., and a height of 212 in.
The prism is filled with cubes that have edge lengths of 12 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism, ___ cubes are needed.
Answer:
V = 1696 in3
Step-by-step explanation:
your asking how many cubes are needed to fill the rectangle which just means your asking for the volume, if you multiply L*W*H you'll get the answer
hope that helps
i need help on this how do i do this
You hang two strands of decorative lights.
a strand of red and blue decorative lights a strand of yellow and green decorative lights
Strand 1: changes color every 18 seconds Strand 2: changes color every 27 seconds
Both strands just changed color. After how many seconds will the strands change color at the same time again?
The strands will change color at the same time again after
seconds.
Answer:
The stands will change color at the same time after 54 seconds.
Step-by-step explanation:
Find the Lcm number of both number (18 and 27)
The answer will be 54
Pls Help..............
Answer:
12
Step-by-step explanation:
V = l*w*h
V = 4*1.5*2
V = 12
Hope this helps :)
What is 3/5 divided by (-4/9)?
Answer:
-1.35. As a fraction, it'd be -1 7/20
Step-by-step explanation:
solve for angle 1 i got an answer but i dont know if it’s right
Answer:
73
Step-by-step explanation:
72 - 35 = 107
180 - 107 = 73
107 + 73 = 180
i need helppppp can u explain this
Answer:
1. 2^5
2. 5^2
3. 3^4
4. 4^3
5. 6^3
6. 3^6
Please give brainliest!!
Answer:
1. 2^5
2. 5^2
3. 3^4
4. 4^3
5. 6^3
6. 3^6
Step-by-step explanation:
A square scarf has a side length of 3/4 yard on each side.
What is the area of the scarf?
Enter your answer in the boxes as a fraction in simplest form.
Answer:
[tex]\frac{9}{16}\ yd.^2[/tex]
Step-by-step explanation:
Area of a square: [tex]a^2[/tex] = [tex]a*a[/tex]
[tex]A = a^2\\\\A = \frac{3}{4}* \frac{3}{4}\\\\A = \frac{9}{16}[/tex]
Therefore, the answer of the scarf is [tex]\frac{9}{16}\ yd.^2[/tex]
Hope this helps!
Question belowwwwwww............................
Answer:
I think it's 4 ft.
Step-by-step explanation:
Answer:
i think it c
Step-by-step explanation:
PLEASE HELP ME WITH MY MATH
Oh my gosh,
I need an answer for that as well..
Answer:
EYYRHEHF
Step-by-step explanation:
I HAVE NO IDEA PLEASE I NEED POINTS AND WANT TO BE BRAINLIEST I NEEEED ITTT !!!!11
Solve rational Equation
Please Show Full Steps Please!
Answer:
x=1
Step-by-step
Step 1:
Simplify x/x2
Dividing exponential expressions :
1.1 x1 divided by x2 = x(1 - 2) = x(-1) = 1/x1 = 1/
Equation at the end of step 1:
2 1 1
(((—+1)-—)-1)-((2•—)-1) = 0
x x x
STEP 2:Rewriting the whole as an Equivalent Fraction:
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
1 1 • x
1 = — = —————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2 - (x) 2 - x
——— = ———
x x
Equation at the end of step 2:
2 1 (2-x)
(((—+1)-—)-1)-————— = 0
x x x
STEP 3:
Simplify 1/x
Equation at the end of step 3:
2 1 (2 - x)
(((— + 1) - —) - 1) - ——————— = 0
x x x
STEP4:
Simplify: 2/x
Equation at the end of step 4:
2 1 (2 - x)
(((— + 1) - —) - 1) - ——————— = 0
x x x
STEP 5:
Rewriting the whole as an Equivalent Fraction :
5.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x as the denominator :
1 1 • x
1 = — = —————
1 x
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
2 + x x + 2
————— = —————
x x
Equation at the end of step 5:
(x + 2) 1 (2 - x)
((——————— - —) - 1) - ——————— = 0
x x x
STEP 6:Adding fractions which have a common denominator :
Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(x+2) - (1) x + 1
——————————— = —————
x x
Equation at the end of step 6:
(x + 1) (2 - x)
(——————— - 1) - ——————— = 0
x x
STEP 7:
Rewriting the whole as an Equivalent Fraction :
7.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
1 1 • x
1 = — = —————
1 x
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
(x+1) - (x) 1
——————————— = —
x x
Equation at the end of step 7:
1 (2 - x)
— - ——————— = 0
x x
STEP 8:
Adding fractions which have a common denominator :
8.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 - ((2-x)) x - 1
——————————— = —————
x x
Equation at the end of step 8:
x - 1
————— = 0
x
STEP 9:
When a fraction equals zero :
9.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
x-1
——— • x = 0 • x
x
Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
x-1 = 0
.2 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
One solution was found :
x = 1
Look at the number 3,939.39 below, as well as the position of each digit in the number.
9
9
Number 3
Position A
3 93
C D
DE
B
F
Fill in each blank below with the correct value. Drag and drop the correct numbers into the blanks.
• The 9 in position B has a value that is
times the value of the 9 in position D
• The 3 in position E has a value that is
times the value of the 3 in position C.
2
HE
11
1
-
3
:: 9
.: 10
100
:: 100
please look at comments i will put an image so you can see
Answer:
1) 100
2) 100
Please mark BRAINLIEST
Determine which is the better buy.
9 straps for $10.25 or 30 straps for $66.00
Answer:
9 straps for $10.25
Step-by-step explanation:
Price rate
9 straps for $10.25 = 10.25/9 = $1.14 per strap30 straps for $66 = 66/30 = $2.20 per strapBetter buy
9 straps for $10.25Less cost per strapbetter buyAnswer:
9 straps
Step-by-step explanation:
If you're selling 30 straps for $66 then you get a 2.2 per each
But 9 straps for $10.25 will get 1.139
So, the value that's smaller which is 9 straps for $1.139 is a better buy
HElp me?
Please? Yikes?
Answer:
A
Step-by-step explanation:
if one box has a surface area of 240 inches what is the surface area of 5 boxes??
#answernowuwuplease
Answer:1200
1 box=240
so if you take 240 x5 you get 1200
Step-by-step explanation:
I need help if anyone could help me solve these problems that would be very helpful!
(I'll give brainliest if you can solve all of them!)
Please lmk which ones you've solved so I know which question it is. thanks!
Answer:Q9 is 12.2. Q10 is C. Q11 is C. Q12 Is 2.8. The level 3-4 thing the hight is 24.
Step-by-step explanation: a^2+b^2=c^2 pythagoras theorem or whatever. Hope this helped.
PRACTICE PROBLEM
Find the area of the parallelogram
_____ Square units
KHAN ACADEMY
Answer:
18
Step-by-step explanation:
parellelogram area is b(vh), 6 x 3 = 18
If It's CORRECT I will give BRAINLIEST!!!!!
Answer:
Im pretty sure its C... Step-by-step explanation: what im seeing here is 10 with the small numbers in front so it looks like scientific notation, Maria has 1 million because 1 x a number = that number, 10 multiplied by itself 6 times equals 1 million, 10 x10 = 100 x 10 = 1000 x 10 = 10,000 x 10 = 100,000 x 10 = 1,000,000. so from this we know what Larry's 10 to the power of 5 is, we need to know what 100,000 x whatever equals. If im doing this right, Larry's number is 1 million 2 hundred thousand which is greater than 1 million. (sorry if the explanation is wanky and sorry if it was wrong, im new to brainly.)
Michael has 26 shirts to fold. Let N be the number of shirts he would have left to fold after folding F them. Write an equation relating N to F . Then use this equation to find the number of shirts he would have left to fold after folding 23 of them.
Answer:
N = 3 F = 26
Step-by-step explanation:
If there's 26 in total and Michael has folded 3 of them N would be 3. F will be the total after folding 'N' amount left of the clothes!
This diagram shows a park's walking path in the shaded area.
The outside circumference of the walking path is 62.8 meters and the inside circumference of the walking path is 31.4 meters.
What is the area of this walking path?
Use 3.14 for π.
Enter your answer as a decimal in the box.
Answer:
197.192
Step-by-step explanation:
62.8x3.14=197.192
Two cubes with edge lengths of 3 centimeters and 2 centimeters are placed on top of each other is shown. What is the surface area of the resulting figure?
Answer:
I believe the answer is B
Answer:
70 cm2
Step-by-step explanation:
Use the number line to answer the question.
Answer:
2.23
Step-by-step explanation:
The reason why this is your answer is that this number is between 2 2/10 and 2 3/10. That means that turned into decimals, this number will be somewhere between 2.2-2.3
Now, we can see that this is 3 units away from 2 2/10 on the number line, which tells us that the decimal is 2.23
So hence, your answer is 2.23
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If you see someone without a smile, give them one of yours!
Thanks!
Have a great day!
:D
Hi everone can you help i will be sending more qusetions each one is 10 points thank you
Answer:
144 cubic inches
Step-by-step explanation:
volume = l x w x h. This = 8 x 6 x 3.
Hope this helps :)
hi everone can you help i will be sending more qusetions each one is 10 points thank you
Answer: 326
The blank space equals 326, 326 times 15 is 4890 as you’d start by multiplying 326 times 10 then multiply 326 times five then add the two sums and get your answer.
We can use inverse operations to find this question by dividing 4890 by 15. We can check our answer by multiplying 326 by 15.
Answer:
326
Step-by-step explanation:
We can use inverse operations to find this question by dividing 4890 by 15. We can check our answer by multiplying 326 by 15.
Hope this helps :)