a school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions should they use to build the largest possible athletic complex. Include appropriate units with your answer.
Answers
The area of a shape is the amount of space it occupies.
The dimensions to build the largest possible athletic complex is 100 by 50 feet
Assume the length of the fence is y.
So, we have:
[tex]\mathbf{Area = xy}[/tex]
[tex]\mathbf{Perimeter = 2y + 4x}[/tex]
Substitute 400 for perimeter
[tex]\mathbf{2y + 4x = 400}[/tex]
Divide through by 2
[tex]\mathbf{y + 2x = 200}[/tex]
Make y the subject
[tex]\mathbf{y = 200 -2x}[/tex]
Substitute [tex]\mathbf{y = 200 -2x}[/tex] in [tex]\mathbf{Area = xy}[/tex]
[tex]\mathbf{Area =x(200 - 2x)}[/tex]
[tex]\mathbf{Area =200x - 2x^2}[/tex]
Differentiate
[tex]\mathbf{A' =200 - 4x}[/tex]
Set to 0
[tex]\mathbf{200 - 4x = 0}[/tex]
Collect like terms
[tex]\mathbf{4x = 200}[/tex]
Divide both sides by 4
[tex]\mathbf{x = 50}[/tex]
Recall that: [tex]\mathbf{y = 200 -2x}[/tex]
So, we have:
[tex]\mathbf{y = 200 - 2 \times 50}[/tex]
[tex]\mathbf{y = 200 - 100}[/tex]
[tex]\mathbf{y = 100}[/tex]
Hence, the dimensions to build the largest possible athletic complex is 100 by 50 feet
Read more about areas and perimeters at:
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Related Questions
Help please :) will give brainliest if the answer is right
Answers
Answer:
(A) D.
(B) Cosh(-x)= e^-x+e^x
2
and the last box on the bottom would be 2
Step-by-step explanation:
5−1/4x=15−14/x helppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
x=-41.354157 or x=1.354157
Answer:
x = -2(10 + √114) , x = 2(-10 + √114)
Step-by-step explanation:
5 − 1/4x = 15 − 14/x
-5 -5
----------------------------
-1/4x = 10 - 14/x
*4x *4x
-----------------------------
-x^2 = -56 + 40x
-----------------------------
x = -2(10 + √114) , x = 2(-10 + √114)
The grocery store is having a sale on frozen vegetables. 3 bags are being sold for $10.35. At this rate, what is the cost of 7 bags?
Answers
Answer:
24.15
Step-by-step explanation:
10.35 x 2 = 20.7 But you still need 1 bag 1/3 of 10.35 = 3.45 Add all of them up = 24.15
Grandpa has a barrel of apples. 2/5 of the apple are rotten. 24 of the apples are good. How many apples are there in total?
Answers
Answer:
40 Apples
Step-by-step explanation:
3/5 of the apples are good so divide 24 by 3 which is 8, then multiply 8 by 2 which is 16, add 24 and 16 together to get 40. Let me know if I'm wrong.
Given: ΔABC ≅ ΔMNP. What is the corresponding angle to ∠A A. ∠B B. ∠N C. ∠M D. ∠P
Answers
Answer:
C. ∠M
Step-by-step explanation:
Answer:
C. < M
Step-by-step explanation:
Congruent triangle notations are written in order of their corresponding parts.
For ΔABC ≅ ΔMNP we have angle A corresponding to angle M
Δ A B C ≅
↓ ↓ ↓
Δ M N P
5) Add using Place-Value diagrams: 215 six + 43 six
Answers
As I understand, we want to perform the given sum by adding the correspondent place values.
Using this method, we will see that the value of the sum is 258.
First, we define the place values as the value that each "position" has, where the reference is the decimal point.
The first place at the left of the decimal points is the units digit.
The second is the tens digit, and so on.
With this, we can rewrite te twi given numbers as:
215 = 2*100 + 1*10 + 5*143 = 4*10 + 3*1Then the sum can be done as:
215 + 43
(2*100 + 1*10 + 5*1) + ( 4*10 + 3*1)
2*100 + (1 + 4)*10 + (5 + 3)*1
2*100 + 5*10 + 8*1 = 258
Then we have:
215 + 43 = 258
If you want to learn more, you can read:
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OMG I NEED HELP BADLY RN
In which quadrant does the point (3 , 19) lie?
A.
Quadrant I
B.
Quadrant II
C.
Quadrant IV
D.
Quadrant III
Answers
Answer:
Quadrant I
Step-by-step explanation:
There are four quadrants that go like this.
Quadrant I = Top Right
Quadrant II = Top Left
Qudrant III = Bottom Left
Quadrant IV = Bottom Right
As long as you can graph an equation you just need to remember the quadrants.
A package of 3 pairs of insulated gloves costs $16.47. What is the unit price of the pairs of gloves?
Answers
Answer:
$5.49 per pair of gloves
Step-by-step explanation:
16.47/3=5.49
Answer:
do 16.47 divided by 3 and thats ur answer
Step-by-step explanation:
the answer is $5.49 for 1 pair of gloves
If a sum invested gains 10% each year how long will it be before it has doubled its
value?
Answers
Using an exponential equation, it is found that it will be 7.3 years before the value is doubled.
The equation for an increasing exponential function is given by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial amount.r is the growth rate, as a decimal.In this problem:
Gains 10% each year, thus [tex]r = 0.1[/tex].The doubling time is t for which [tex]A(t) = 2A(0)[/tex], then:
[tex]A(t) = A(0)(1.1)^t[/tex]
[tex]2A(0) = A(0)(1.1)^t[/tex]
[tex](1.1)^t = 2[/tex]
[tex]\log{(1.1)^t} = \log{2}[/tex]
[tex]t\log{1.1} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.1}}[/tex]
[tex]t = 7.3[/tex]
It will be 7.3 years before the value is doubled.
A similar problem is given at https://brainly.com/question/23008760
Estimate and then solve 3397÷59
Answers
3397 round down to 3300
59 round up to 60
3300 / 60 = 55
Solved :
3397/59 = 57.5762712
How do you get the right answer?
Answers
Change 3/2 3.14 to degree measure
A. 180 degrees
B. 90 degrees
C. 270 degrees
D. 360 degrees
Answers
Answer:
option b
hope ut is help full
Help me please (I have to write something to send a question)
Answers
Answer:
1. This helps me to know if the answer of an opposite integer will be positive or negative by simply subtracting their absolute values then put the sign of the largest absolute value between the two.
2. By identifying first the largest absolute value of the two integers that are being add up. Without, calculations, i will know the sign of the sum.
3. the picture attached is the answer
Step-by-step explanation:
hope it will help you
Which of the following are perfect squares? 2, 4, 6, 16, 20,25, x², x³, x¹⁵, x²⁰, x²⁵
Answers
Answer:
4, 16, 25, [tex]x^{2}[/tex], [tex]x^{20}\\[/tex].
Step-by-step explanation:
Answer:
16, 4, 25, x², x ²⁰
. . . . . . . .
A rectangular picture frame has a length that is 6 cm greater than the width. The total perimeter is 36
cm. What are the dimensions for the frame? Write an equation, solve and then fully answer the
question.
Answers
Answer:
Step-by-step explanation:
width= x
length= x+6
perimter = 2x+ 2(x+6)
36= 2x+ 2x+ 12
36= 4x + 12
36-12= 4x
4x= 24
x= 6
therefore width= 6cm
length= 6+6 = 12
The points (-6, 4) and (-4, r) lie on a line with slope 3. Find the missing coordinate r.
Answers
[tex]\\ \sf\longmapsto m=3[/tex]
(-6,4)(-4,r)[tex]\\ \sf\longmapsto \dfrac{r-4}{-4+6}=3[/tex]
[tex]\\ \sf\longmapsto \dfrac{r-4}{2}=3[/tex]
[tex]\\ \sf\longmapsto r-4=6[/tex]
[tex]\\ \sf\longmapsto r=6+4[/tex]
[tex]\\ \sf\longmapsto r=10[/tex]
Could use some help here plz.
Answers
Simplify the ratio (divide both sides by a greatest common factor [5])
75:1
The factory bottles 75 bottles of juice every one minute.
A sea lion jumped out of the water to a height of 3 feet above sea level. The number line shows the location of the sea lion at the top of its jump. From this location, the sea lion dove down 9 feet. Describe how to use the number line to find the new location of the sea lion.
Answers
Answer: on the number line it would go from 0 and with a positive line go to 3 and when it’s dive down it would with a negative line go 9 spaces towards the negative side of the number line and the answer would be -6 I think that kind of exsplains it step by step there but let me know if you information :) please leave a thanks and five stars I need some for my own quiz! Thank you!
Step-by-step explanation:
Write an explanation to a friend about how you
would estimate 17 1/5 / 3 4/5.
Answers
Answer:
67/5
Step-by-step explanation:
17 1/5
17x5= 85 + 1= 86/5
3 4/5
3x5=15+4= 19/5
86/5 - 19/5=
86-19= 67/5
hope this helps!
If you have 1/4 of a pie left and you give away 5/8 how much pie do you have left
Answers
Answer:
You cannot give away more than you have. You have no pie left.
Step-by-step explanation:
1/4 - 5/8
Multiply 1/4 by 2 to get a common denominator in order to subtract.
2/8 - 5/8
= -3/8
You can't have -3/8 of a pie.
Therefore, you have no pie left.
3. They each have a brother who
weighs 40 units. Whose brother
weighs 40 pounds, and whose
weighs 40 kilograms? Explain your
reasoning
Answers
Lin's brother weighs 40 pounds, and Elena's brother weighs 40 kilograms, because kilograms are heavier than pounds and Elena's brother is bigger.
Find the x-intercept and y-intercept of the line and then graph the equation
-4x+2y=-4
Answers
Answer:
x-intercept is 1 and y-intersect is -2
Step-by-step explanation:
To find the x-intercept let y = 0 and to find the y-intercept let x = 0 and solve each equation.
-4x + 2y = -4 Let x = 0 and solve for y
-4(0) +2y = -4
0 + 2y = -4
2y = -4
y = -4/2 ; y = -2 y- intercept is -2
Let y = o and solve
-4x + 2y = -4
-4x + 2(0) = -4
-4x + 0 = -4
-4x = -4
x = -4/-4 ; x = 1 x-intercept is 1
What is the product of 14.5×100
Answers
Answer:
1450
Step-by-step explanation:
Any number times 10 goes up one value.
ones become tens, and tens become hundreds etc..
87x10=870
And a number times 100 goes up two values.
23.5x100= 2350
hope this helped ;)
Step-by-step explanation:
you don't have a calculator ? with that you would have gotten the answer immediately.
so you had to write the question in here, need to wait for an answer, ...
but actually, this is very easy to solve even without a calculator, as this is how our decimal numbers work : based on powers of 10.
multiplying by 100 moves the decimal point 2 positions to the right (and fill up with zeros where necessary) :
14.5 × 100 = 1450
a multiplication by 10 moves the decimal point 1 position to the right.
a multiplication with 1000 3 positions to the right. and so on.
a division by 100 moves the decimal point 2 positions to the left (and fill up with zeros where necessary). and so on.
The slope is negative in the graph as you move from left to right the line of the graph is going
Answers
Answer:
Down
Step-by-step explanation:
The line slants downward from left to right if the slope is negative.
I mark brainliest!! fill the table using the function rule, y=-10x+3
Answers
13
3
-7
-47
Pls help I’ll brainlest
Answers
The cat is not hungry, or doesn't like the can of tuna food, which is why they refused to eat it when it was given to them.
Try to give the cat the food again and see their reaction, if that fails, try to give the cat other foods and note the reaction to determine if the cat just doesn't like the tuna in a can or just wasn't hungry at the moment.
whats 10x2= n nnn nnnnnnn
Answers
Answer:
20
Step-by-step explanation:
10 x 1 = 10. 10 x 2 = 20.
Answer:
20
Step-by-step explanation:
10 x 1 = 10
Then, 10 x 2 = 20
Is triangle RWS triangle QWT
Answers
Answer:
Try it as a RWS triangle
the flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the of the third angle of the triangle is 40° more than three times the measure of either of the other two angles, find the measure of each the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
Answers
The two equal angles are each 36°.
The third angle is 108°.
A drilling machine can drill 12 holes in 6 minutes. If the machine drills holes at a constant speed, it can drill
holes in 25 minutes. HELPPP
Answers
Answer:
The machine can drill 50 holes in 25 minutes!
Explanation:
6 by 4 is 24, which in this context will be 24 minutes. Therefore, multiply 12 by 4 to get the sum of 48. Then, to find the remaining 1 minute, divide 12 by 6 to get 2 which is the amount of holes per minute. Add 2 to 48 and that is your answer!