Answer:
1. Express the width of the rectangle in terms of the length X.
width = 500 - X
2. Express the surface area of the rectangle in terms of X.
area = -X² + 500X
3. What value of X gives the maximum surface area?
maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250
X = 250 ft
4. What is the maximum surface area?
maximum surface area = X² = 250² = 62,500 ft²
Step-by-step explanation:
since the perimeter = 1,000
1,000 = 2X + 2W
500 = X + W
W = 500 - X
area = X · W = X · (500 - X) = 500X - X² or -X² + 500X
The area of a shape is the amount of space it occupies.
The width in terms of x is 500 - xThe surface area in terms of x is x(500 - x)The value of x that gives maximum surface area is 250 feetThe maximum area is 62500 square feetThe length is represented as x.
Let the width be y.
So, we have:
[tex]\mathbf{Perimeter =2(x + y)}[/tex]
This gives
[tex]\mathbf{2(x + y) = 1000}[/tex]
Divide both sides by 2
[tex]\mathbf{x + y = 500}[/tex]
Make y the subject
[tex]\mathbf{y = 500 -x}[/tex]
So, the width in terms of x is 500 - x
The surface area is calculated as:
[tex]\mathbf{A = xy}[/tex]
Substitute [tex]\mathbf{y = 500 -x}[/tex]
[tex]\mathbf{A = x(500 - x)}[/tex]
So, the surface area in terms of x is x(500 - x)
Expand [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 500x - x^2}[/tex]
Differentiate
[tex]\mathbf{A' = 500- 2x}[/tex]
Equate to 0
[tex]\mathbf{500- 2x = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = 500}[/tex]
Divide both sides by 2
[tex]\mathbf{x = 250}[/tex]
So, the value of x that gives maximum surface area is 250
Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]
[tex]\mathbf{A = 250 \times 250}[/tex]
[tex]\mathbf{A = 62500}[/tex]
Hence, the maximum area is 62500
Read more about areas at:
https://brainly.com/question/11906003
Answer This Question For Brainliest, Tip: It has to be right for brainliest
Answer:
B.
Step-by-step explanation:
Hope dis helps! :) I know for a fact its correct.
Answer:
The Correct answer for this question is B.
I hope this helps you answer this question.
:)
Given: BC = DA, LCBD = ZADB
Prove: ABCD = ADAB
Statements
Reasons
I need help:(
HELP PLEASE!! NUMBER 6!!
You will get the brainiest if you can tell me how you did it, so I can finish doing them myself lol. If It comes back right, I will give it you instantly. Thank you very much.
Answer:
hey it's not clear....
An 8-foot piece of twine costs $5.76. What is the price per inch?
Answer:
$0.06
Step-by-step explanation:
First, find how many inches are in 8 feet.
Since 1 foot is 12 inches, multiply 8 by 12:
8(12)
= 96
Then, to find the price per inch, divide the price by the number of inches:
5.76/96
= 0.06
So, the price per inch is $0.06
Answer:
$0.06
Step-by-step explanation:
There are 12 inches in a foot, and there are 8 feet all together, meaning there is 96 inches for $5.76.
Divided the cost y the number of inches to get the cost per inch,
5.76 divided by 96 = 0.06.
need a little help with this problem
Answer:
Step-by-step explanation:
Rate (slope) of miles per gallon of gas: m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
(0, 0)
(2, 50)
[tex]m_{carA}[/tex] = 25 mi/gal.
(0, 0)
(3, 60)
[tex]m_{carB}[/tex] = 20 mi/gal.
Car B use less gasoline.
Write the equation in slope-intercept form of a line that has a slope of 1/3 and passes through the point (-6,0).
A. y=1/3x
B. =1/3x-6
C. y=1/3x-2
D. y=1/3x+2
(Conditionals)
TRUE OR FALSE:
If a number is a perfect square, then it has only 3 factors.
Answer:
False
I hope this helps!
Combine like terms: 4 - 3m - 1 + 2m
Answer:
-m+3
Step-by-step explanation:
4 - 3m - 1 + 2m
4-1-m
-m+3
Please help!
Part A: Which quantity is the independent variable?
Part B: Which quantity is the dependent variable?
Part C: Which graph is scaled appropriately for this situation?
Answer:
oooooooooooo
Step-by-step explanation:
mark me as a brainlist
Now that you’ve created your hypotheses, it’s time to prove them. First, look at the sum of two rational numbers. Let’s say they are two rational numbers, x and y. Because they’re rational, they can be written as a ratio of integers. Let x = and y = , where a, b, c, and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c, and d is shown. Statement Reason substitution Create common denominators. Simplify. Based on this sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
The question is missing parts. Here is the complete question.
Now that you've created your hypotheses, it's time to prove them. First look at the sum of two rational numbers. Let's say they are two rational numbers, x and y. Because they're rational, they can be written as a ratio of integers. Let [tex]x=\frac{a}{b}[/tex] and [tex]y=\frac{c}{d}[/tex], where a, b, c and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c and d is shown in the figure below.
Based on the sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
Answer: The sum of two rational numbers equals a rational number.
Step-by-step explanation: Rational number is defined as a number that can be made by dividing two integers.
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number, as demonstrated in the table below.
3x = 0.5.x2
o o
O x= -6 or x = 0
O
x= -4 or x = 3
o
x = -2 or x = 1.5
x = 0 or x = 6
Answer:
the answer is x=0 or x=6, hope this helps
Use the inequality below to find the value of r .
150 - 5 r ≥ 87.5
a. r ≥ 12.5
b. r ≤ 12.5
c. r ≥ -(12.5)
d. r ≤ -(12.5)
The density D of an object is the quotient of its mass m and its volume v
If a function f is increasing on (a,b) and decreasing (b,c), then what can be said about the local extremism of f on (a,c)?
Answer:
The point (b, f(b)) is a local maximum.
Quick 50 points brainliest
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Answer:
[tex]0\leq d\leq 7[/tex]
Step-by-step explanation:
[tex]11.79=11(1.01^d)\\1.01^d=\frac{11.79}{11} \\1.01^d=1.0718\\ln(1.01^d)=ln(1.0718)\\d ln(1.01)=ln(1.0718)\\d=\frac{ln(1.0718)}{ln(1.01)} \\d=\frac{0.069}{0.0099} \\d=6.9696[/tex]
By rounding up.
d=7
Hence, the domain is
[tex]0\leq d\leq 7[/tex]
Answer:
0<x<d
its so easy if you need help
Ava bought 1.7 lb of plums and 7.2 lb of peaches how many was her total. Plums:$0.23. per pound peaches:$1.22 per pound
Answer:
0.391+8.42=8.811
8.811 in dollars is 10.42 United States Dollars
Step-by-step explanation:
Your answer is 10.42 c:
F(x)=4x+5whsts the value of. F(-3). Is
Answer:
F(-3) = -7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
F(x) = 4x + 5
F(-3) is x = -3
Step 2: Evaluate
Substitute: F(-3) = 4(-3) + 5Multiply: F(-3) = -12 + 5Add: F(-3) = -7Can someone Please help with this problem,please help me ASAP !!!l
Answer:
I'd say B bcs it's the only thing that would fit with the shift on x axis and y axis
how would i slove for x??
Answer:
x=12
Step-by-step explanation:
First you need to find the 3rd angle.
180-118=x
x=62
Once you have that 3rd angle, set all the inside angles equal to 180
4x-6+5x+16+62=180 ---> set to 180
9x+72=180 -->combine like terms
9x=108 --> subtract 72 from both sides
x=12 -->divide both sides by 9
Type the following fractions in order from greatest to least:
5/4, 4/10, 5/12, ¼, 11/12
Write the decimals in the boxes from greatest to least:
0.5, 0.91, 0.04, 0.89, 0.51
Answer:
Just put the greatest number first and then the second greatest etc
Write 2 equivalent ratios for 24/30
Answer:
Two equivalent ratios are: 4:5 and 48/60.
Step-by-step explanation:
Well, you can divide on the first one, and multiply on the second one. Hope it helps!
Albert's mom bought
5 2/3
pounds of potatoes. There are 5 people in Albert's
family and they all eat the same amount of potatoes.
How many pounds of potatos will Albert eat?
A monthly budget with expenses is shown.
MONTHLY BUDGET
for a family of three
in San Antonio, Texas
Rent
$870
Food
$550
PR Child care
$375
Transportation
$480
Utilities
$400
Insurance
$235
Savings
$400
Taxes
$290
Monthly total
Which equation can be used to determine y, the minimum amount of money a family must earn to meet the requirements of this budget for one year?
y = 3600 x 12
y = 3600 + 7
y = 3600 x 4
y = 360052
Answer:
[tex]y = 3600 * 12[/tex]
Step-by-step explanation:
Given: Breakdown of Monthly Budget
Required
Determine the equation that shows minimum earnings in a year
First, we need to get the sum of the given list of budgets:
[tex]Budget = 870 + 550 + 375 + 480 + 400+235+400 + 290[/tex]
[tex]Budget = 3600[/tex]
The are 12months in a a year; So, the yearly budget (y) is:
[tex]Yearly\ Budget = Monthly\ Budget * Duration[/tex]
[tex]Yearly\ Budget = 3600* 12[/tex]
i.e.
[tex]y = 3600 * 12[/tex]
×5=30
×5=300
×5=3,000
×5=30,000
×5=300,000
×5=3,000,000
×5=30,000,000
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From up to down :
[tex]6[/tex]
_________________________________
[tex]60[/tex]
_________________________________
[tex]600[/tex]
_________________________________
[tex]6,000[/tex]
_________________________________
[tex]60,000[/tex]
_________________________________
[tex]600,000[/tex]
_________________________________
[tex]6,000,000[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
1. 6
2. 60
3. 600
4. 6,000
5. 60,000
6. 600,000
7. 6,000,000
Step-by-step explanation:
Solve for n: 0.22n = 6.6.
Answer:
30
Step-by-step explanation:
Solve for n: 0.22n = 6.6.
6.6/0.22 (because for example 3/3 and n/n= 1 so 0.22/0.22 = 1 so we have to divide 6.6 since it is part of the equation and we have to do it on both sides.)=30
A color printer prints 19 pages in 8 minutes.
How many minutes does it take per page?
Answer:
I believe the answer is two
Step-by-step explanation:
19 divided by eight equasl two
Please help and don’t answer with random letters I actually need the answer
Multiply x ^ (3/4) * x ^ (1/5)
1) x ^ (4/9)
2) x ^ (3/20)
3) x ^ (11/20)
4) x ^ (19/20)
Answer:
the answer is 4) i think
Step-by-step explanation:
i'm not sure but what i know, if the base is the same number, u can just add the power. for example, the bases is the same number which is x, so u can just solve the power which 3/4 + 1/5 then u get answer.
p/s: sorry for my english
A restaurant bill is $75. You want to leave about a 20% tip. Which is a 20% tip?
A candy store sells caramels for $9/pound and chocolate for $12/pound. How much more is the cost of 2 pounds of caramel than 1.5 pounds of chocolate? *Show your work*
Answer:
The caramel is $0 more than the chocolate. In other words, they cost the same.
Step-by-step explanation:
Since we have 2 pounds of caramel and caramel costs $9/pound, the cost of 2 pounds of caramel can be found by this equation:
2lbs · $9 = $18
Since we have 1.5 pounds of chocolate and chocolate costs $12/pound, the cost of 1.5 pounds of chocolate can be found by this equation:
1.5lbs · $12 = $18
To find how much bigger the cost of caramel is than that of chocolate, we will subtract the total cost of the chocolate from the total cost of the caramel.
$18 - $18 = $0
Error Analysis A contractor purchases 4 dozen pairs of padded work gloves for $54.24. She
incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct
unit price? What is the error?
The correct unit price is $
per pair.
Answer:
the unit rate for each pair is $1.13
Step-by-step explanation:
Okay this is how you would do this problem correctly:
we know that 4 dozen pairs of gloves cost $54.24 however we want to know what the cost is for one pair so we have to make a equation by dividing total cost by the number of glove pairs.
$54.24/4 dozen
the reason we are putting 4 dozen instead of just dividing $54.24 by 4 is because we want to know the unit price for each pair of gloves so it would actually look like this:
$54.24/4(12)
Dozen = 12
so we multiply 12 by 4 to get 48 pairs of gloves, we then divide $54.24 by 48 to find our unit rate of pricing for each pair:
$54.24/48 = 1.13
so now we place a dollar sign in front of 1.13 to get your answer:
for every pair bought it costs $1.13
So how did the Analysis A contractor get the wrong answer? well when she had bought the 4 dozen gloves she divided $54.24 by 4, which in this case would make it seem as though the gloves came in a 12 pack of gloves. However she was buying the gloves individually so she would have to multiply 4 by 12 before dividing the total number of gloves from $54.24.