There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
Answer:
The maximum area is therefore is 93750 ft²
Step-by-step explanation:
The given parameter are;
The a]length of fencing available = 1500 ft.
The perimeter of the figure = 9·x + 4·y
Therefore, 9·x + 4·y = 1500 ft.
The area of the figure = 6 × (x × y) = 3·x × 2·y
From the equation for the perimeter, we have;
9·x + 4·y = 1500
y = 1500/4 - 9/4·x = 375 - 9/4·x
y = 375 - 9/4·x
Substituting the value of y in the equation for the area gives;
Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²
Area = 2250·x - 27/2·x²
The maximum area is found by taking the derivative and equating to zero as follows;
d(2250·x - 27/2·x²)/dx = 0
2250 - 27·x = 0
x = 2250/27 = 250/3
x = 250/3
y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5
The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²
The maximum area is therefore = 93750 ft.²
What value of x is in the solution set of 9(2x + 1) < 9x – 18?
Answer:
-3 > x
Step-by-step explanation:
Multiply 2x and 1 by 9. You have 18x + 9 < 9x - 18.Add 18 to 9. You are adding because it is the opposite of subtraction, so it cancels out. You now have 18x + 27 < 9x.Subtract 18x from 9. There is no addition sign in front of the 18x, but it's basically implied. You now have 27 < -9x.Divide both sides by -9. When you divide by a negative, the inequality sign flips. You now have -3 > x.The maximum speed possible on a length of railroad track is directly proportional to the cube root of the amount of money spent ob maintaining the track. Suppose that a maximum speed of 25 km/hr is possible on a stretch for which 450,000 was spend on maintence, find the maximum speed if the amount spent on maintence is increased to $1,750,000 Pls help me show steps please
Answer:
[tex]39.29\ \text{km/h}[/tex]
Step-by-step explanation:
s = Speed of the train
m = Money spent on maintanence
[tex]s\propto m^{\dfrac{1}{3}}[/tex]
Let k be the constant of proportionality so
[tex]s=k (m)^{\dfrac{1}{3}}[/tex]
Now a case is given where 25 km/hr is possible on a stretch for which 450,000 is spent so
s = 25
m = 450000
[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow k=\dfrac{s}{m^{\dfrac{1}{3}}}\\\Rightarrow k=\dfrac{25}{450000^{\dfrac{1}{3}}}\\\Rightarrow k=0.326[/tex]
Now when m = 1750000
[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow s=0.326\times 1750000^{\dfrac{1}{3}}\\\Rightarrow s=39.29\ \text{km/h}[/tex]
The maximum speed of the train would be [tex]39.29\ \text{km/h}[/tex].
HALP MEEEE
Alice, Maggie, Luna, and Zeinab were making necklaces for the school fair. Alice made 52 necklaces that are each 8.2 inches long. Maggie made 46 necklaces that are each 7.8 inches long. Luna made 21 necklaces that were each 7.7 inches long. And Zeinab made 31 necklaces that were each 8.7 inches long. They all used beads that were each 2 centimeters long. how much beads would the girls use to fit all of the necklaces they made?
Alice:_______
Maggie:_______
Luna:_______
Zeinab:_______
Answer:
Alice: 2184
Maggie:1794
Luna:798 this one is weird cause it has a decimal but u cant have a fraction of a bead so i left it out
Zeinab:1333 same with this one
Step-by-step explanation:
The table list the profits of some of the worlds largest corporations in 2013. List the companies in order from greatest to least amount of profit
Answer:
C
Step-by-step explanation:
What is the slope of this graph?
O
5
3
o
3
O
-3
Answer:
where is the graph?
Step-by-step explanation:
______ terms are also expressions. (fill in the blank)
A. No
B. All
C. Some
Noa was paid a 25 percent commission for selling a used car.
Percents
Total
100%
If she was paid $1,631.24, what was the selling price of the car?
$4,078.10
$6,524.96
$8,156.20
$40,781.00
Answer:
$6,524.96
Step-by-step explanation:
His quarter commission times four is the awnser
Answer:
BHOPE THIS HELPSFind the area of a square with side length x when x is equal to the given value. Are the area of a square and the length of its side directly proportional? Justify your answer. x=10 in.
Step-by-step explanation:
The formula for calculating the area of a square is expressed as;
A = x² where;
x is the length of one side of the square
Given
x = 10in
A = 10²
A = 10 * 10
A = 100in²
Area of the square with side length 10in is 100in²
From the equation A = x², we can see that as the value of x increases, the value of the area also increases and vice versa. This means that the area of the square is directky proportional to its length. Hence we can say YES, the area of a square and the length of its side directly proportional
Answer:
100 sq in
Step-by-step explanation:
No, not proportional
Penelope is raising money for a school trip by selling bags of chips and fruit snacks. The price of each bag of chips is $1.75 and the price of each fruit snack is $1.50. Yesterday Penelope made $42.50 and sold 15 more bags of chips than fruit snacks. Determine the number of bags of chips sold and the number of fruit snacks sold.
Answer:
bag of chips - 20 ; number of fruit snacks - 5 .
Step-by-step explanation:
Find the product: a) (5 – 2h) (3 + h) b)4p ^2 q ^2 (p ^2 – q ^2)
Answer:
A.) -8h
Step-by-step explanation:
a.) . (5 – 2h) (3 + h)
a.) (5 – 2h) (3 + h)
(5+3) (h-2h)
8(-h)
-8h
solve 5x + 20=75
What is x
Answer:
x = 11
Step-by-step explanation:
this answer can be solved by simple operations
5x + 20 = 75
5x = 55 (subtracted the 20 from 75)
x = 11 (divided the 5 by 55)
hope this helps !!
- emily
Emie read that the movie made 25,992,412.50 in its third week he also read that the average ticket price for this week was 8.35how many people saw the movie this week
Given :
Collection in third week, C = $25,992,412.50 .
Average ticket price, T = $8.35 .
To Find :
Number of people who saw movie in week.
Solution :
Let, number of people are x.
[tex]\text{Number of people }=\dfrac{\text{Total amount }}{\text{Average price}}\\\\= \dfrac{25,992,412.50 }{8.35}\\\\[/tex]
≈ 3112864
Therefore, around 3112864 people saw the movie this week.
Hence, this is the required solution.
Your school band is performing a concert. Tickets cost $3 for students and $5 for adults. A total of 125 people attended the concert for a total ticket sales of $475. Write and solve a system of equations to find the number of students and adults that attended the concert. Make sure to write your answer in a complete sentence.
Given :
Tickets cost $3 for students and $5 for adults.
A total of 125 people attended the concert for a total ticket sales of $475.
To Find :
The number of students and adults that attended the concert.
Solution :
Let, number of students and adults that attended the concert is x and y.
Mathematical equation of given conditions :
x + y = 125 ....1)
3x + 5y = 425 ....2)
Putting value of x from 1 to equation 2 is :
3( 125 - y ) + 5y = 425
375 - 3y + 5y = 425
2y = 50
y = 25
x = 125 - 25
x = 100
Therefore, number of students and adults that attended the concert is 100 ans 25 respectively.
Hence, this is the required solution.
I have something to say- Brainly your users are very rude like im failing bEcAuSe YoU pEoPlE! but like yu history people r like saving my life-
Sincerely - Miha~
Answer:
thank you. someone had to say it
Step-by-step explanation:
Answer:
Omg ik what you mean i feel you
Step-by-step explanation:
using the same application you used in part f, reflect the line segment across the x-axis. then, rotate it 90° clockwise. Finally. translate it down 2 units. what is the relationship between the original line segment and the transformed segment ? if you transform a line segment with a seweurnce of reflections, to stations, or translations, is it still a line segment ?
Answer:
non
Step-by-step explanation:
Help!
What is one and sixty-seven hundredths added to fifteen and nine tenths?
At a farming supply store 7 pounds of seed cost $153.37. If a farmer needed 4 pounds of seeds, how much would it cost him?
Solve the equation for y , (REDUCE IF POSSIBLE, AND WRITE YOUR ANSWER IN THIS FORM; y=mx+b).
−6x+y=18
Answer:
y=6x+18
Step-by-step explanation:
add the -6x to the other side to get y alone
Answer:
-6x + y = 18 reduced is -2x + y = 2
Step-by-step explanation:
it is called the Hamber Pickering Formula according to STUIPDPEDIA LOL!
Carlos biked StartFraction 139 over 8 EndFraction miles on Saturday and StartFraction 135 over 7 EndFraction miles on Sunday. On which day did he ride further and by how much? Carlos rode further on Saturday by 1 and StartFraction 51 over 56 EndFraction miles. Carlos rode further on Saturday by 3 and StartFraction 5 over 56 EndFraction miles. Carlos rode further on Sunday by 3 and StartFraction 51 over 56 EndFraction miles. Carlos rode further on Sunday by 1 and StartFraction 51 over 56 EndFraction miles. Mark this and return
Answer:
Carlos rode further than on Saturday by 107/56 miles.
Step-by-step explanation:
i did the quiz lol
Answer:
Its D
Step-by-step explanation:
I took the test and got it right.
A cleaning mixture requires 5 cups of water for every 2 cups of solution which ratio of cups of water to cups of solution will make the same cleaning mixture?
a. 15:6
b. 8 :20
c. 60;18
d. 20:14
Answer:
a.15.6
Step-by-step explanation:
simplify all the ratios to their simplest forms.
15/3:6/3
5:2
What is the definition of scale factor
Answer:
The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Example: Here, XYUV=123=4 . So, the scale factor is 4 .
Step-by-step explanation:
:D
write an equation for the line above
Answer:
y= -3x/5
Step-by-step explanation:
y=mx+b where m is the slope and b is the y-intercept
m= rise/run = -3/5 (go from one point to the other on the graph)
y-intercept is (0,0)
Nadia charges $5.50 an hour for babysitting. She babysits 19.50 hours the first week of the month and 19 hours the second week of the month. Suppose Nadia raises her rate by $0.55 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month? Complete the explanation and give your answer. Nadia's new hourly rate is $ . She would need to work hours in the next two weeks to make the same amount she made in the first two weeks.
Answer:
Step-by-step explanation:
ind her earnings for the first two weeks of the month at the $5.50 an hour rate.
5.50 × (18 + 20.50) = 5.50 × 38.5
= 211.75
She earned $211.75 the first two weeks of the month.
Find her new hourly rate, if she raises her rate by $0.55.
5.50 + 0.55 = 6.05
Her new hourly rate is $6.05.
Find how many hours she would need to work at $6.05 an hour in order to earn $211.75.
211.75 ÷ 6.05 = 35
She would need to work 35 hours.
Find the slope of each line.
Work out the area of the shape drawn below.
Give your answer correct to 2 decimal places.
Answer:
39.27
Step-by-step explanation:
Formula: PIEr^2/2
so 5 square which is 25.
then 25 times pie which is then divided by 2
39.27
Help plz:))) I’ll mark u brainliest
Jordie's curtain company is making curtains for a local hotel. He wants each curtain to be 36 inches long. At the fabric store, fabric is sold by the foot. If Jordie's curtain company wants to make 67 curtains, how many feet of fabric will he need?
Answer: 201 feet
Step-by-step explanation:
It should be noted that 1 foot = 12 inches. Therefore, 36 inches = 36/12 = 3 feets.
Each cotton uses 3 feets in length. Therefore, 67 curtains will use:
= 67 × 3 feets
= 201 feets
How do you solve this problem?
9=-y it is equations and inequalities
PLEASE HELP
What figure models 6 divided by 3/2?
(6 divided by 3/2 equals 4)
NEEDS HELP NOW!
BRAINLIEST!