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

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.

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.

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.

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

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

Answers

Can barely see it my guy

Help! What is the answer?

Answers

Answer:

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

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.

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.

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)

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.

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

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

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]

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 product?

(x − 3)(2x2 − 5x + 1)

Answers

Answer:

5x2+20x−15

Step-by-step explanation:

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 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.

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

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

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)

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

Please help thank you!

Answers

Answer:

24.

(-24 ÷

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

16+8= 24

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:

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 )

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.

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

(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

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

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 : )

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

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