Mr. Jones' other friend Ms. O'Neill has "x" meters of fencing, what is the maximum area in square meters she can have?

Answers

Answer 1

Answer:

[tex]Max\ Area = \frac{x^2}{16}[/tex]

Step-by-step explanation:

Given

[tex]P = x[/tex] ---- the perimeter of fencing

Required

The maximum area

Let

[tex]L \to Length[/tex]

[tex]W \to Width[/tex]

So, we have:

[tex]P = 2(L + W)[/tex]

This gives:

[tex]2(L + W) = x[/tex]

Divide by 2

[tex]L + W = \frac{x}{2}[/tex]

Make L the subject

[tex]L = \frac{x}{2} - W[/tex]

The area (A) of the fence is:

[tex]A = L * W[/tex]

Substitute [tex]L = \frac{x}{2} - W[/tex]

[tex]A = (\frac{x}{2} - W) * W[/tex]

Open bracket

[tex]A = \frac{x}{2}W - W^2[/tex]

Differentiate with respect to W

[tex]A' = \frac{x}{2} - 2W[/tex]

Set to 0

[tex]\frac{x}{2} - 2W = 0[/tex]

Solve for 2W

[tex]2W = \frac{x}{2}[/tex]

Solve for W

[tex]W = \frac{x}{4}[/tex]

Recall that:

[tex]L = \frac{x}{2} - W[/tex]

[tex]L = \frac{x}{2} - \frac{x}{4}[/tex]

[tex]L = \frac{2x- x}{4}[/tex]

[tex]L = \frac{x}{4}[/tex]

So, the maximum area is:

[tex]A = L * W[/tex]

[tex]A = \frac{x}{4}*\frac{x}{4}[/tex]

[tex]Max\ Area = \frac{x^2}{16}[/tex]


Related Questions

Math help please urgent

Answers

Answer:

16 m^2

Step-by-step explanation:

Area of triangle = (Base * Height) / 2

Area of triangle = ( 8 * 4 ) / 2

Area of triangle = 16

37 + (-37) im looking for the answer

Answers

Answer:

0

Step-by-step explanation:

37 + (-37)

open the bracket

remember when u multiply the bracket - sign and + sign also gets multiplied and (-) * (+) is( -) . So

37 - 37

0

HELP PLEASE! for 20 points

Answers

Volume is base * height

Volume is hence 24 in * 6 in

Which gives you 144 in

Volume is 144in^3 (144 in cubed)

Will


Give BRIANLIST



Write the sentence as an equation use x to represent a number

“Six times the difference of 11 and a number is -72”

Answers

Answer:

6 × (11 - x) = -72 => x = 23

or

6 × (x - 11) = -72 => x = -1

Step-by-step explanation:

there are at least two possibilities, as the "difference between two numbers a and b can be excised as either a-b or b-a.

in any case, just following the sentence

Six times = 6 ×

difference of 11 and a number = 11 - x

is -72 = -72

so,

6 × (11 - x) = -72

and that is true for x = 23

but

the other direction is possible too

6 × (x - 11) = -72

and that is true for x = -1

Help! What is the answer?

Answers

Answer:

c ......................

Tell whether the triangle with the given side lengths is a right triangle. Y/N question

Answers

Answer: need a picture of the traingle but if it's at a 90 degree angle on any sides then yes

Step-by-step explanation:

What is the probability of an event that is certain?

Answers

Answer:

Nvm my answer is wrong

An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

se cumple que: A^2 + B = 486 y el M.C.D. de A y B es 9. ¿Cuál es el valor de B

Answers

Answer:

i dont know spanish

Step-by-step explanation:

The ratios a: B and B :c are equivalent to one another
Select all the statements that must be true

Answers

Answer:

Options (2) and (5)

Step-by-step explanation:

Given ratio is a : b and b : c

[tex]\frac{a}{b}=\frac{b}{c}[/tex]

[tex]\frac{b}{a}= \frac{c}{b}[/tex] [Option 2]

[tex]\frac{a}{b}=\frac{b}{c}[/tex]

b × b = a × c

b² = ac

If a = b,

b² = bc

b = c [Option 5]

Therefore, Options (2) and (5) are the correct options.

Help me please
The question is in the picture above..​

Answers

Can barely see it my guy

Please helpp I will mark brainliest!!<3

Answers

It’s, 4+x=12. Hope this helps☺️

Step-by-step explanation:

x+4=12

In this equation, x is a unknown value,

x plus four is twelve.

So, it also represents four more than x is twelve.

PLEASE HELP ME, THANK YOU!!

EXPLAIN YOUR ANSWER FOR BRAINLIEST


A prism with an volume of 148 cubic cm is dilated by a factor of 5.5.

The volume of the dilated prism is ___ cubic cm.

(this is just a word question)

Answers

Answer:

24623.5 cubic cm

Step-by-step explanation:

A prism with an volume of 148 cubic cm is dilated by a factor of 5.5.

This is calculated as:

Let the volume of the dilated prism = x

Hence:

x/148 = (5.5)³

Cross Multiply

x = 148 cm³ × 5.5³

x = 24623.5 cm³

The volume of the dilated prism is 24623.5 cubic cm.

Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes

Answers

Answer: [tex]7.81\ km[/tex]

Step-by-step explanation:

Given

Runner A runs towards North at speed of 10 km/h

Runner B runs towards East at speed of 12 km/h

After half hour, they covered a distance of

[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]

[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]

They are running in perpendicular direction to each other

So, the distance between them is  given by

[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]

What is the product?

(x − 3)(2x2 − 5x + 1)

Answers

Answer:

5x2+20x−15

Step-by-step explanation:

Dana enters a race where she has to cycle and run. She cycles a distance of 25km and then runs for 20km. Her average running speed is half of her average cycling speed. If dana completes the race in 5 hours, what is her average cycling speed !

Answers

Step-by-step explanation:

Let running speed = x.

So, cycling speed = 2x.

Total distance traveled = 20 + 25 = 45km

Time taken running = 20/x

Time taken cycling = 25/2c

Total time taken = 5 hours

So, 5 = 20/x + 25/2x

Solving this equation for x gives:

10x = 65. Thus x = 6.5

Since cycling speed = 2x, cycling speed = (6.5)(2)

So cycling speed is 13 km/h.

Hope it helps.

у=-3x+3
y = -9x + 15

Answers

Answer:

(2, - 3 )

Step-by-step explanation:

Given the 2 equations

y = - 3x + 3 → (2)

y = - 9x + 15 → (2)

Substitute y = - 3x + 3 into (2)

- 3x + 3 = - 9x + 15 ( add 9x to both sides )

6x + 3 = 15 ( subtract 3 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (1)

y = - 3(2) + 3 = - 6 + 3 = - 3

solution is (2, - 3 )

please help with number 53!!!!
pretty please

Answers

Answer:

The sequence would be arithmetic. This is because an arithmetic sequence has a common number multiplying, adding, subtracting etc. The common rule for this set of numbers was x5. 9x5=45, 45x5=225 etc. We simply used this method with negative numbers, but the rule was still multiplying.

Happy learning!

--Applepi101 :)

Answer:

Arithmetic

Step-by-step explanation:

It has a constant difference between each number whilst Geometric usually has the same difference between each number

(5x-3)=(3x+27) I dont understand

Answers

Answer:

x = 15

Step-by-step explanation:

(5x-3)=(3x+27)

Subtract 3x from each side

(5x-3x-3)=(3x-3x+27)

2x-3 = 27

Add 3 to each side

2x-3+3 = 27+3

2x= 30

Divide by 2

2x/2 = 30/2

x = 15

Please help thanks this is due today!

Answers

D. [tex] ({ - 8})^{2} - 9 + ( - 7)[/tex] ✅

Step-by-step explanation:

[tex] {( - 32 \div4 })^{2} - 9 + ( - 7) \\ \\ = ({ - 8})^{2} - 9 +(- 7 )\\ \\=64-9-7\\\\ = 64 - 16 \\ \\ = 48[/tex]

Note:-

[tex]\sf\red{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\sf\red{(+\:x\:-)\:=\:-}[/tex]

[tex]\sf\red{(-\:x\:-)\:=\:+}[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Please help thank you!

Answers

Answer:

24.

(-24 ÷

[tex] {6}^{2} [/tex]

16+8= 24

I NEED HELP WITH C , help i dont understand

Answers

Answer:

SAS

Step-by-step explanation:

SAS (Side-Angle-Side) is a proof of congruence for two triangles. Since C stipulates that [tex]\angle ENM=\angle ZNM[/tex], the two triangles would share two sides and the angle between them, thus being congruent from SAS.

G
A right rectangular prism has a height of 15 meters, a length of 4 meters, and a width of 3 meters. Which expressions
show how to calculate the volume? Check all that apply.

Answers

Answer:

180m^3

Step-by-step explanation:

Given data

Height = 15m

Lenght= 4m

Width=3m

We know that the volume of a rectangular prism is expressed as

Volume= L*W*H

Substitute

Volume= 4*3*15

Volume= 180m^3

Pls I need this before midnight (USA)

Answers

Answer:

I can’t post an image, but I’ll explain below

Step-by-step explanation:

Start at a point where the line crosses through a coordinate exactly, like (0,1), and find a second one. Draw a line from the first to the right until it’s over the second point, then go down to the second point. It should look like half of a rectangle. Just follow the lines of the graph :)

I hope this helps just point it on the line

Consider the systems of equations:

y=4/5 x−3

y=4/5 x+1

Without graphing, determine and explain how many solutions you would expect this system of equations to have.

Answers

Answer:

no solutions; the lines are parallel

Step-by-step explanation:

The eqautions are in slope intercept form.

The slope of both lines is 4/5; therefor the lines are parallel

The y-intercept of one line is -3 and the other is 1

That means the parallelines never meet.

There are no solutions

There are no solutions for the system of equations y=4/5 x−3

and y=4/5 x+1

What is slope intercept form of line?

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The system of equations,

y=4/5 x−3

y=4/5 x+1

The equations are in slope intercept form.

As we observe the equations, the slopes of two equations is 4/5.

The slope of both lines is 4/5

Therefor the lines are parallel

The y-intercept of one line is -3 and the other is 1

That means the parallel lines never meet. There are no solutions

Hence there are no solutions for the system of equations y=4/5 x−3

and y=4/5 x+1

To learn more on slope intercept form click:

https://brainly.com/question/9682526

#SPJ2

A line that includes the point (2, 9) has a slope of 8. What is its equation in slope-intercept
form?

Answers

Answer:

y-8x+7=0

Step-by-step explanation:

slope(m)=8

using slope intercept form of equation of staright line we get

y=mx+b

y=8*x+b

y-8x=b ................  eq(i)

since the line include the point (2,9) it satisfies the euation,

here x=2 and y=9

equation: y-8x=b

9-8*2=b

9-16=-b

-7=b

substituting the value of b in eq(i) we get

y-8x=-7

y-8x+7=0   is a required equation of the line.

A full waterbed mattress is 6 ft by 2 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 lb /ft3. Find the weight of the water in the mattress to the nearest pound.

Answers

Answer:

749 lbs

Step-by-step explanation:

weight of the water in the mattress = volume of the mattress x weight of water

volume of the mattress = volume of a cuboid = length x width x height

6 x 2 x 1 = 12 ft³

weight of the water in the mattress = 12 x 62.4 = 748.8 lbs

749 lbs to the nearest pound

Fifty-five petcent of people in a survey said that they do exercise on a fairly regular basis. If 12,000 people were sureveyed, how many of them exercised on a fairly regular basis? A. 5,000 B. 5,500 C. 6000 D. 6,600​

Answers

Your answer might be “D. 6600”
Hope it helps : )

Which data set could be represented by the box plot shown below?

Answers

Answer:

The answer is C

Step-by-step explanation:

the lowest point of the box plot is at 1  and the highest is at 19, so by that it can't be A.

The box plot shows 12 being the median so that automatically leaves C but just to make sure the first half would be 6 and half of the last part would be 16 if that makes sense.

Match them BRAINLIEST IF CORRECT ​

Answers

Answer:

1/2 for the red card

1/52 for queen of hearts

1/4 for clubs

3/13

Step-by-step explanation:

the red card is 1/2 because the only other color is black

there is only one queen of hearts

it is one of four possible symbols

because that is the only one left

What are the coordinates of the point 1/6 of the way from a to b?

Answers

Answer:

B. (2, 6)

Step-by-step explanation:

Xp = 1 + (1/6 × (7-1)) = 1 + (1/6×6) = 1+1 = 2

Yp = 8 + (1/6 × (-4-8)) = 8+(1/6×(-12))

= 8+(-2) = 6

the coordinate => (2, 6)

Other Questions
For which rational expression is 2 an excluded value of x?a.(x-3)/x^2-4b.(x-3)/x^2+4c.(x-4)/x^2-3d.(x+4)/x^2-3 5x + 1/2 y^2 What is the value of the expression above when x = 3 and y = 2? You must show all work and calculations to receive full credit. (2-i)(2+i) please lmk the answer to this question. Need help with this ASAP DUE SOON PLEASE AND SHOW WORK 50 Pts!!!!!!! What is the straight line distance between the points? What ideas were changing in the scientific community at the time of Darwin's travels? How might those new ideas influenced Darwin? Which equation should be used to find the volume of the figure?A rectangular pyramid with a base of 10 centimeters by 6 centimeters and a height of 12 centimeters.V = one-third (10) (6) (12)V = one-half (10) (6) (12)V = one-third (10) (6) (13)V = one-half (10) (6) (13)Mark this and return question- pls help me find the ans Any help please?? I've been stuck on this answer for too long its embarrassing. What is the answer to this question will mark brainlist A lamp post 15 feet high casts a shadowthat is 12 feet long. At the same time astop sign 10 feet high casts a shadow howmany feet long? what is the value of x (with screenshot) The narrator of fever helps readers imagine the fear of living through the yellow fever outbreak by describing Which is a complete sentence? A bag contains 5 red marbles, 7 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue? What is m+n? Please solve! I really need help!! kathy runs a 26.2-mi;e marathon at an average pace of 6.2 minutes per mile how long will it take her to finish the marathon round your answer to the nearest minute g 1. Write a mechanism for the Grignard reaction of benzophenone with phenylmagnesium bromide. Be as complete as possible and show electron flow for all steps. justification of scissors The [OH-] of a solution is 7.89 10^-12 M. What is the pH of the solution? it acidic or basic? *