A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1500 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions
Step-by-step explanation:
Let x be the length and y be the width of the rectangular plot.
The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,
x+2y = 1500
x = 1500 - 2y ....(1)
We know that the area of a rectangular plot is given by :
A = xy ....(2)
Put the value of x from equation (1) in (2)
[tex]A=(1500-2y)y\\\\A=1500y-2y^2[/tex] .....(3)
For largest area, differentiate above area equation wrt y.
[tex]\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375[/tex]
Put the value of y in equation (1).
x = 1500-2(375)
= 750 m
Put the value of y in equation (3).
[tex]A =1500(375)-2(375)^2\\A=281250\ m^2[/tex]
Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.
The difference between two numbers is 8. Twice the number is 4 more than the larger number. What is the smaller number?
Answer:
If the two numbers are x and y, then:
x + y = 8
18 - 2x = 4y - 2.
When we subtract y from both sides in our first equation we get:
x = 8 - y, so:
18 - 2(8 - y) = 4y - 2
18 - 16 + 2y = 4y - 2
2 + 2y = 4y - 2
2y = 4
y = 2
Since x + y = 8, and y = 2, x = 6, and since 6 > 2, the larger number is 6.
a painter painted 3/5 of a portrait in 20 minutes. If she continues working at the same rate, how many portraits will she paint in one hour?
Answer:
one and four fifths 1 4/5-
Step-by-step explanation:
Enter the simplified form of the complex fraction in the box.
Assume no denominator equals zero.
Answer: this is the answer
x^2+11x+6/(x+2)(x+5)
Step-by-step explanation:
Answer:
Here is the complete answer key with all correct and incorrect choices shown including this question. Good luck future users.
The formula for temperature conversion is F=1.8C+32. If the Fahrenhei
temperature (F) is 86, What is the Celsius (C) temperature?
Answer:
30
Step-by-step explanation:
(86-32)/1.8 =30
HELP ME ON THIS. 10 POINTS
Answer:
This is sooo easy
Step-by-step explanation:
The answer is B
because It does not go through the Origin
every time they ask if something is proportional
ALWAYS check if its a straight line or if it go through the origin
hope I helped sorry If you get it wrong
plz help me out if you can
Answer:
D $26
Step-by-step explanation:
evaluate - 31 - 8 + 31
Answer:
-8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
-31 - 8 + 31
Step 2: Evaluate
Subtract: -39 + 31Add: -8(b) At Smith's Bike Rentals, it costs $26 to rent a bike for 6 hours.
How many hours of bike use does a customer get per dollar?
Can someone help me so stressed
29 points
Thanks
Answer:a square
Step-by-step explanation:a square
In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°. Find the length of j, to the nearest centimeter.
Given:
In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°.
To find:
The length of j, to the nearest centimeter.
Solution:
According to Law of sine,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
In ΔHIJ, using law of sine, we get
[tex]\dfrac{j}{\sin J}=\dfrac{h}{\sin H}[/tex]
[tex]\dfrac{j}{\sin (20^\circ)}=\dfrac{40}{\sin (93^\circ)}}[/tex]
[tex]j=\dfrac{40\times \sin (20^\circ)}{\sin (93^\circ)}}[/tex]
On further simplification, we get
[tex]j=\dfrac{40\times 0.34202}{0.99863}[/tex]
[tex]j=\dfrac{13.6808}{0.99863}[/tex]
[tex]j=13.69958[/tex]
Approximate the value to the nearest centimeter.
[tex]j\approx 14[/tex]
Therefore, the length of j is 14 cm.
Triangle DEFDEFD, E, F is similar to triangle PQRPQRP, Q, R. Solve for k.
Alaina is making a birdseed mix with 2 1/3 lb sunflower seeds, 5/6 lb cracked corn, and 1/6 lb peanuts. How much cracked corn does Alaina need to make 5 lb of birdseed mix? Show your work.
Answer:
2 1/3+5/6+1/6= 3 1/2
Step-by-step explanation:
Change your denominator to 6 and add then reduce if possible
For each incorrect answer on a test, the teacher changes the total points possible by −4 points. The total number of points possible on a test is 64. If a student has 9 incorrect answers, what will be that student’s score?
Answer:
-4×9=-36
then 64-36=28
Pete has 4 packs of gum balls. Each pack has 5 gum balls. If Pete gives the same number of gum balls to 6 friends, how many gum balls will each friend get?
2
3
4
5
Answer:
I would say 3
Step-by-step explanation:
Order of Operations with and without variables
Answer:
9
Step-by-step explanation:
3 (2²) - 2(2) + 1 =
3 (4) - 4 + 1 =
12 - 4 + 1 =
8 + 1 = 9
Three different divers kept track of the number of treasure boxes they've found this year.
Diver Dives Treasure boxes found
Scuba Sam 111111 333333
Wet Suit Willy 181818 818181
Deep Diving Dan 262626 104104104
Which diver found the most treasures per dive?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Scuba Sam
(Choice B)
B
Wet Suit Willy
(Choice C)
C
Deep Diving Dan
Answer:
ITS B
Step-by-step explanation:
find the number of each kind of atom
2MgO
Perform the operation. (-9x^2-2x)-(-9x^2-3x)
Answer:
(-9x^2-2x)-(-9x^2-3x)
Step-by-step explanation:
-9x^2 + 9x^2 - 2x + 3x
= 0x^2 + 1x
= 1x
Mark me as brainliest
Hope this helps!!!
What is the following product ? Assume y >= 0 3sqrt(10) * (y ^ 2 * sqrt(4) + sqrt(8y))
Answer:a
Step-by-step explanation:
Answer:
A on Edgen
Step-by-step explanation:
Correct
why do do we need it
Answer:
why do we need what?
Step-by-step explanation:
Because
Because
Because.
IS THIS CORRECT OR NAH
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
I will give Brainliest!! Please answer the question by simplifying!! Thanks so much and stay safe!!
1/3(9x +45) - x = 6x +4
1/3(9x+45)-x=6x+4
we can move the numbers on the right and the x's on the left
9x/3+45/3-x=6x+4
3x-x-6x=4-15
-4x=-11
x=11/4
Answer:
x = 11/4
Step-by-step explanation:
thats the answer...........................
PLZZZZ Hurry I’m in a rush
Answer:
y=10
Step-by-step explanation:
2y+3+9y-7+7y+4=180
18y=180
y=10
The two-way table shows the ages of the players on different sOCcer teams.
Team D
3
Total
21
23
14
58
Team C
Team A
4
Team B
8 Years Old
9 Years Old
10 Years Old
Total
4
3
13
3
5
16
4
15
14
Which statement is true?
O The probability that a randomly selected player on TeamA is 8 years old is
O The probability that a randomly selected 8-year-old player is on Team C is
O The probabilíty that a randomly selected player on Team C is 10 years old is
O The probability that a randomly selected 10-year-old player is on Team B is 13
58
What is the value of x in the equation 2 (6 x + 4) minus 6 + 2 x = 3 (4 x + 3) + 1?
1
3
4
6
Answer:
x=4
Step-by-step explanation:
I did the edge quiz pretty sure I got it correct
Answer:
x=4
Step-by-step explanation:
4x2
4x + 10 and 2x2 + 5x – 8.
Answer:
14x , -4+5x
I hope this helps
have a fantastic day
what is two cubed and then divided by 4?
Answer:
2
Step-by-step explanation:
2 cubed is 8, then divided by 4 is 2
Jacob is 4 feet 5 inches tall. How tall is Jacob in inches?
O 48 inches
09 inches
020 inches
0 53 inches
Answer:
He is 53 inches in height
Step-by-step explanation:
4 × 12 inches = 48 + 5 = 53