A rectangle has a perimeter of 100 inches, and

one side has length x. Express the area of the

rectangle as a function of x.


Use the function in part a to find the dimensions of the rectangle with permitter 100 inches and the largest possible area

Answers

Answer 1

Answer:

a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²

Step-by-step explanation:

a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have

P = 2(L + W)

100 = 2(L + x)

dividing both sides by 2, we have

100/2 = L + x

50 = L + x

making L subject of the formula, we have

L = 50 - x

Now, the are of a rectangle A = LW. Substituting the values of L and W, we have

A = LW

A = (50 - x)x

A = 50x - x²

b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.

So, dA/dx = d(50x - x²)/dx

dA/dx = d50x/dx - dx²/dx

dA/dx = 50 - 2x

dA/dx = 0 ⇒ 50 - 2x = 0

50 = 2x

dividing both sides by 2, we have

x = 50/2

x = 25

To find it this gives maximum value for A, we differentiate A twice.

d²A/dx² = d(50 - 2x)/dx

d²A/dx² = d50/dx - d2x/dx

d²A/dx² = -2

Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.

Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in

So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²

The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²


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HELP ME OUT IM DUMB

Answers

Answer:

around 15.3

Step-by-step explanation:

3^2 + 15^2=c^2

Answer:

Step-by-step explanation:

Formula:

a^2 + b^2 + c^2

3^2 + 15^2 + c^2 = To find hypotenuse

3 • 3 + 15 • 15 = -c^2

9 + 225 = -c^2

234 = c^2

square root of 234 = 15.2970585408

c = 15.2970585408

The roof is 15.2970585408

Solve the system using a method of your choice

Answers

Answer:

(4, 1)

Step-by-step explanation:

Method elimination would be good for this system

2x - y = 7 ........ (1)

x + y = 5 ......... (2)

(1) + (2)

3x = 12 ⇒ x = 4

4 + y = 5 ⇒ y = 1

(4, 1)

X= 4.25
Y= 0.75

4.25 +0.75 = 5
4.25 - 0.75 = 3.5

If an oxygen atom gains 2 electrons what is it's overall charge?

(Remember: electrons have a negative charge)

Answers

Answer:

I think it would be -2 if it has a negative charge

Step-by-step explanation:

Tara plans to put wallpaper on the walls of her room. She will not put the wallpaper across the doorway, which is 3 feet wide and 7 feet tall. Tara decides to get the same wallpaper for both rooms. Write the expression for the total amount of wallpaper she needs.

Answers

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Step-by-step explanation:

hope this helps

Find the value of X and Y in this triangle.

Answers

Step-by-step explanation:

if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)

if leg b is unknown, then. b = √(c² - a²)

for hypotenuse c missing, the formula is. c = √(a² + b²)

Answer:

[tex] \sin(60) = \frac{45}{x} \\ [/tex]

[tex] x = \frac{45}{ \sin(60) } [/tex]

x=5 1.96

Step-by-step explanation:

[tex] \tan(30) = \frac{y}{45} [/tex]

[tex]y = 45 \tan(30) [/tex]

y=25.98


In RST, if m than seven times x, find x and the measure of each angle.

Answers

Answer:

RST

Step-by-step explanation:

Which graph represents a function?

Answers

this one bc there’s one point vertically and there’s no more than one point when you draw a vertical line down

A grocery store clerk can scan 1 product every
1/2
of a second. At what rate can she scan products?

Answers

She can scan 2 products per second

scientific notation for 1.0 ×10^6​

Answers

Answer:

1000000

Step-by-step explanation:

I'm not sure what you meant by "scientific notation". So uhh, I only solved the 1.0 times 10^6,

10^6=10×10×10×10×10×10

10^6=1000000

(Fun fact. If you ever see a power of 10, you don't actually need to solve it. Look at the power, and add the same amount of 0's. For example 10^2. Power sign is 2. 2 trailing 0's.)

For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy?
Help please!!!! thank you sm!!

Answers

Answer:

64 cups

Step-by-step explanation:

64 cups! A half gallon equals 8 cups. 8 cups x 8 half gallons = 64 :)

A person invests 5500 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14700 dollars?

Answers

Answer:

It’s 17.6

Step-by-step explanation:

Question is attached!​

Answers

Answer:

what are the answer

Step-by-step explanation:

The correct answer is X= 3!

What is the square root function?

Answers

Answer:

f(x) = [tex]\sqrt{x}[/tex]

Step-by-step explanation:

hope this helped :-)

2y + 14x - 7x + 9y ​

Answers

Answer:

1, - 2

Step-by-step explanation:

Answer:

7x + 11y

Explanation:

1. Subtract 7x from 14x. 2y + 7x + 9y

2. Add 2y and 9y together. 11y + 7x

A student has some $1 bills and $5 bills in his wallet. He has a total of 13 bills that are worth $45. How many of each type of bill does he have?

Answers

Answer:

8 $5 bills and 5 $1 bills

Step-by-step explanation:

5x8=40, which would be $40

1x5=5, which would be $5

$40+$5=$45

hope this helps! :)

Answer:

it's not possible. I've tried every way, r these the right amounts?

i need help i will mark brainliest!! look at the pictures

Answers

Answer:

yes

Step-by-step explanation:

the picture is not clear

I’ll mark brainliest please help!

Answers

Answer:

4x + 2 = 30

Step-by-step explanation:

To find the perimeter of a triangle, add up the length of all three sides of the triangle.

Here, the sides of the triangle are "x+6", "x+6", and "2x-10". When you add up all three sides of the triangle, it should be equal to the perimeter, 30. So:

(x+6) + (x+6) + (2x-10) = 30

We can simplify this equation:

(2 * (x+6)) + (2x-10) = 30

2x + 12 + 2x - 10 = 30

4x + 2 = 30

Answer D: 4x + 2 = 30

Question 2
The cell membrane controls what enters and exits the cell to maintain
A.energy
B. Photosynthesis
C.respiration
D.homeostasis

Answers

Answer D is correct

Lines m and n are drawn in the coordinate plane. The equation of line m is y=-3x+8 and line n goes through point (-4,-11). When a transversal of the two lines is constructed the alternate interior angles formed by the transversal are congruent. What is the equation of line n?

Answers

Answer:

The equation of line n is;

y = -3x - 23

Step-by-step explanation:

Here, we want to find the equation of line n

For the alternate interior angles to be congruent after drawing the transversal, then both lines must be parallel

If the two lines are parallel, then their slopes are equal

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The equation of line m is y = -3x + 8

if we compare this with the standard form which is y = mx + c

Then the slope of line m is -3 and since they are parallel lines, the slope of line n is -3 too

So now, we need to get the equation of line n

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What we have already is;

y = -3x + c

we need to get the y-intercept to write the complete equation

To get the y-intercept we simply substitute for (-4,-11)

Thus, we have

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y = -3x - 23

The formula for the volume of a cylinder is V = gran.
Solve V = 872) for h, the height of the cylinder.
O A. =
nar
B. n =
O c. h =
Vr2
O D. h=
372

Answers

Answer:

B . n

Step-by-step explanation:

Noah pays $7.65 for a cappuccino on days he's running late to work. One week, he was late on Monday, Wednesday, and Friday. How much did he spend (in $) on cappuccinos that week? $

Answers

Answer:

Amount Noah spent on cappuccino for that week = $22.95

Step-by-step explanation:

Noah pays $7.65 for a cappuccino on days he's running late to work

Cost of cappuccino per day = $7.65

One week, he was late on Monday, Wednesday, and Friday.

That is 3 days in a week

How much did he spend (in $) on cappuccinos that week? $

Amount Noah spent on cappuccino = cost of cappuccino per day × 3 days

= $7.65 × 3

= $22.95

Amount spent on cappuccino for that week = $22.95

Devin paid $30 to be a member of the Fox Lake Gym. When he takes the boxing
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Answers

Answer:

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Answers

Answer:

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Answers

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Step-by-step explanation:

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Click below for question!
THANKS FOR ALL YOUR HELP GUYS!

Answers

Answer:

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Step-by-step explanation:

Subtract the 2nd y from the first (2-9)

Subtract the 2nd x from the first (11-6)

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Answers

Answer:

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 4.1     7776 = 25•35

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The answer is 7776^2
_____
343^2

Pls mark brainleist

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Answers

Answer:

calfdmf mjd fmjs  wsmc wsjmc jesd jms

Step-by-step explanation:

I have no idea how to do this, any clues?​

Answers

Answer:

(2x-5)+(x+25)+x

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Step-by-step explanation:

Simplify the expression.

You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
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cannonballs, as shown in the illustration. On an idle afternoon you decide to
calculate the number of cannonballs in the stack. What is the number of
cannonballs?

Answers

Answer: The correct answer would be 164(c)

Step-by-step explanation:

You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish

Army in Sevilla in the year 1842. Outside your barracks window is a stack of

cannonballs, as shown in the illustration. On an idle afternoon you decide to

calculate the number of cannonballs in the stack. What is the number of

cannonballs?

650 is the number of cannonballs.  It typically fires a projectile propelled by an explosive chemical.

What is cannonballs?

A cannon constitutes a large-caliber gun that belongs to the artillery category. It typically fires a projectile propelled by an explosive chemical. Prior to the development of smokeless powder in the late 19th century, gunpowder (sometimes known as "black powder") served as the main propellant.

Depending on their intended purpose on the battlefield, different types of gun combine and balance these characteristics to differing degrees. Cannons differ in gauge, effective range, mobility, rate of fire, angle of fire, and firepower. A large artillery weapon is a cannon.

By utilizing the formula of a square pyramid,

n(n+1)(2n+1)/6

12(12+1)(2(12)+1)/6

12(13)(25)/6

2*13*25

=650

Therefore, 650 is the number of cannonballs.

To know more about cannonballs, here:

https://brainly.com/question/14330897

#SPJ7

Find the surface area of the prism

Answers

Answer:

the answer is 29

Step-by-step explanation:

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