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

what is the larger fraction 5/6 or 8/10​

Answers

Answer:

5/6

Step-by-step explanation:

5/6=0.84, 8/10= 0.8

5/6 is the larger than 8/10

Quadrilateral MNOP is similar to quadrilateral SRUT.
Which proportion can be used to find the value of x?​

Answers

Answer:

8/12 = x/14

Not sure if this is a proportion but this is how I would solve it.

Can someone help me?It's urgent and thank you!

Answers

Answer:

575.71

Step-by-step explanation:

Year 1: 960 x .88 (100%-12%)=844.80

Year 2: 844.80 x .88 =743.424

Year 3: 743.424x.88=654.21

Year 4: 654.21 x .88=575.71

The length of the triangle for the pool table is the twice the sum of 5 and a number. If the rack is equilateral, what is the perimeter, in inches, of the triangle?​

Answers

Answer:  

30 + 6x inches

Step-by-step explanation:  

Let the required number be x

If the length of the triangle for the pool table is twice the sum of 5 and a number

L = 2(5+x)

L = 10+2x

Since the triangle is quadrilateral, this means that all sides are equal

Perimeter = 3L

Perimeter = 3(10+2x)

Perimeter = 30+6x

Hence the perimeter, in inches, of the triangle is 30 + 6x inches

74 + -28 =[find the difference and put the sign of big number]

Answers

Answer:

It should be 74+(-28) as 2 signs can bit be put together.

74+(-28)

=74-28 (sign only changes when there is (minus) before it

=48

We are not putting a minius (-) as 74 is digger that 28 and it has plus (+) before it.

I HOPE IT HELPS

HAVE A GREAT DAY

[tex]#Liliflim✌[/tex]

Which equation represents a line that passes through (2, -1/2) and has a slope of
3?

Answers

Answer:

it should be d or c

Step-by-step explanation:

The answer is c
Step by step: y= 3x -19/3
Point-slope form- y+1/3 =3•(x-2)

Really stuck, please help

Answers

Answer:

Step-by-step explanation:

what do you know about the angles of a triangle? They make 180° right?

since you know that, now you can find  angle  Y  , by using the triangle on the left,   and you can find X by using the triangle on the right,  then,  when you know  X & Y , use both of those to find  Z  :)   got it?

Answer:

we know that a triangle's angles MUST add up to 180 degrees.

We can look at the triangle with the angles of 55, 80, and y. As the angles must add to 180, 55+80+y must be 180. Therefore, we find that y is equal to 45.

We can look at the triangle with the angles of 100, 60, and x. As the angles must add to 180, 100+60+x must be 180. Therefore, we find that x is equal to 20.

We then look at the triangle formed from x, y, and z. As the angles must add to 180, x+y+z must be 180. x is 20, y is 45, so 20+45+z = 180. Thus, z is 115.

So:

y = 45

x = 20

z = 115.

The junior senator can do a labyrinth in 50 minutes. The senior senator can do a labyrinth in 30 minutes. Working together, how many minutes would it take them to work their way through 12 labyrinths?

Answers

Answer:

[tex]225\:\text{minutes}[/tex]

Step-by-step explanation:

To navigate through this problem, start by finding how much each senator can complete in a fixed amount of time. I'll choose 10 as it's the greatest common factor of 30 and 50.

In 10 minutes, the junior senator can complete [tex]\frac{10}{50}=\frac{1}{5}[/tex] of the labyrinth.

In 10 minutes, the senior senator can complete [tex]\frac{10}{30}=\frac{1}{3}[/tex] of the labyrinth.

Therefore, working together, they can complete [tex]\frac{1}{5}+\frac{1}{3}=\frac{8}{15}[/tex] of the labyrinth in 10 minutes. Thus, it will take them [tex]\frac{15}{8}\cdot 10 \text{ minutes}=18.75\:\text{minutes}[/tex] to complete one labyrinth.

The amount of time it take them to complete 12 labyrinths is then [tex]18.75\cdot 12 =\boxed{225\:\text{minutes}}[/tex]


Use SOH CAH TOA to find the missing side.

Answers

sin(43) × hypotenuse of 19 gives you oppo

= 13

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

A rectangular park is 260 m by 480 m. Danny usually trains by running 5 circuits around the edge of
the park. After heavy rain, two adjacent sides are too muddy to run along, so he runs a triangular path
along the other two sides and the diagonal. Danny does 5 circuits of this path for training. Show that
Danny runs about 970 metres less than his usual training session

Answers

Answer:

971 m to nearest metre

Step-by-step explanation:

training distance = 5*2*(260 + 480) m  

Diagonal distance = √(2602 + 4802) m

Heavy rain training distance = 5*(260 + 480 + √(2602 + 4802)) m

Difference between these:

 

5 × 2  × ( 260 + 480 ) - 5 ×( 260 + 480  + √ 260 ^ 2 + 480 ^ 2 )

   = 970 . 5311872087638744

 

difference = 971 m to nearest metre

Hope this answer helps you :)

Have a great day

Mark brainliest

2- La longueur d'un rectangle mesure 2 cm de plus que le triple de sa largeur. Si le périmètre de ce rectangle est supérieur à 12 cm, mais d'au maximum 48 cm, dans quel intervalle se situe la largeur de ce rectangle?​

Answers

Answer:

5 < L < 18,5

5 < L < 18,52 < W < 5,5

Step-by-step explanation:

longeur = length = L

largeur = width = W

L = 3W +2

12 < 2L+2W < 48

———————————————

12 < 2*(3W+2)+2W < 48

12 < 6W+4 +2W < 48

12 < 8W+4 < 48

8 < 8W < 44

2 < W < 5,5

———————————————

12 < 2L+2W < 48

L = 3W +2

L - 2 = 3W

L/3 -2/3 = W

12 < 2L +2*(L/3 -2/3) < 48

12 < 2L + ⅔L -4/3 < 48

12 < 2⅔L -4/3 < 48

13⅓ < 2⅔L < 49⅓

5 < L < 18,5

hope it helps.

brainly exists in French too. brainly.fr or switch country in app

x/6 + 12 = 6
Please help me

Answers

Answer:

[tex]x=-36[/tex]

Step-by-step explanation:

[tex]\frac{x}{6} +12=6[/tex]

[tex]\frac{-36}{6} +12=6[/tex]

[tex]-6+12=6[/tex]

Hence, x = -36

Answer:

X = -36

Step-by-step explanation:

x/6 + 12 = 6

-12         = -12

x/6 = -6

(6) = (6)

 x = -36

The volume of a cuboid, whose length and height are equal is 108 m3. If the breadth is 12 m, find the cuboid's length and surface area.

Answers

Answer:

Surface area = 162 m^2

Step-by-step explanation:

Below is the given values:

Length of cuboid = Height of cuboid

The volume of the cuboid = 108 m^3

The breadth of the cuboid = 12 m

Now use the volume formula:

Volume = area of one surface × height

Volume = (L x B) * H

(L x 12) * H = 108       (L = H)

L x 12 x L = 108

L^2 = 108/12

L = 3 m

Thus length and height is = 3m

Surface area = 2 (L x B + b x h + L x h)

Surface area = 2 (3 x 12 + 12 x 3 + 3x 3)

Surface area = 162 m^2

Find (-3/7) / (-1 1/14).

45/98

2/5

2 1/2

-2/5

Answers

Answer:

option B .   [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

[tex](-\frac{3}{7}) \div (-\frac{15}{14}) = (-\frac{3}{7}) \times (-\frac{14}{15}) = \frac{3 \times 14}{7 \times 15} = \frac{2}{5}[/tex]

Answer:

2/5

Step-by-step explanation:

(-3/7) / (-1 1/14) = 0.4

0.4 = 4/10

simplified = 2/5

I hope this helps uwu.

URGENT: Graph y = cosx for -3\pi/2 <= x <= -pi/2

What is the largest value in the range?


A. -1

B. 0

C. 1/2

D. 1

Answers

I’m pretty sure it’s d

A parabola is defined by the equation x2 = 3/4 y. In which direction will the parabola open?

Answers

I’m pretty sure it’s positive so a upward one that looks like :u

Shante is calculating the amount of time it takes a rocket to get to the moon. The moon is around 239,000 miles from Earth. How many hours would it take a rocket that can travel at 200 miles per minute to travel to the moon? Round to the nearest hour.

Answers

Answer:

20 hours

Step-by-step explanation:

Mathematically we know that;

time = distance/ speed

distance = 239,000 miles

Time = 200 miles per minute

time = 239,000/200 = 1195 minutes

Let us convert this to hours by dividing by 60 (since 60 minutes equal an hour

So we have 1195/60 = 19.91

This is approximately 20 hours

Answer:

D

Step-by-step explanation:

20 hours

Simplify the expression. (–8.6)0

1
–1
–8.6
0

Answers

Answer:

(-8.6)0

= 0

explanation:

help......................​

Answers

Answer:

17.

[tex] 7 \times {10}^{ - 6} [/tex]

18. 8 sides (and 8 corners)

19. the chance is 50% or 0.5, and yes, both colors have the same chance.

20. on a coordinate grid make a point at x=1 and y=5. and then simply draw a line through that point.

Step-by-step explanation:

17. the defining digit is 7. and it is at the the 6th position after the decimal point. that is how you write this.

18. the more corners or sides a polygon has, the closer it gets to a circle. that means that the outside angles always add up to 360 degrees.

so, with the inside angles being 135 degrees, the outside angles are 180-135 = 45 degrees.

his many such outside angles can we add together until we reach 360 degrees ?

360/45 = 8 (just imagine : 2×45 = 90, and 90×4 = 360)

so, this polygon has 8 corners and therefore 8 sides.

19. 12 balls are in the bag. the chance for a single ball to be pulled is therefore 1/12.

but there are 6 red balls. we don't care which specific ball we pull, as long as it's red. so, we have 6/12 chances to achieve that.

and yes, for exactly the same reason, black balls have the same chance.

Can someone help me with this. Will mark brainliest. Thank you.

Answers

Answers:

circlecenterradiuschorddiametersecant

=======================================

Explanations:

Consider a campfire and people surrounding it to warm up. The fire itself is the center of the circle, and the people around it are points on the circle's edge. Assume that each person is the same distance away from the fire. Refer to the diagram below.We always refer to the circle name by the center point. Think of it being like at the center of the universe, or you could think how the sun is at the center of the solar system. While technically the planets orbit in ellipses and not perfect circles, this idea still could be useful to help remember the naming convention. If we go back to the example in part 1, the radius is the distance from the campfire to any given person. The radius is half the diameter. This is not to be confused with the spelling "cord" which refers to wiring used in electronics, or in fabric fibers. If we connected any two campers with a segment, then we formed a chord. Refer back to part 1 above. Any diameter is a chord, but not the other way around.The diameter is a special type of chord that goes through the center. Note the endpoints of the diameter are on the circle's edge. A secant line is basically a chord but we've extended both endpoints off infinitely in both directions. A secant cuts the circle at 2 different points. In contrast, a tangent line touches the circle at exactly one point only.

28. Barrett's mom has a flower vase that is shaped like a perfect cylinder.
The vase has a height of 9 inches, and its radius is 4 inches. What is the
total volume of water that the flower vase can hold?

Answers

Answer:

Vase volume is 452.16 in³

Step-by-step explanation:

The question asks for the volume of a cylinder of radius r and height h.  The relevant formula is V = (pi)(r)^2*h

With h = 9 in and r = 4 in, that max volume (of water) is

V = (3.14)(4 in)^2*(9 in) = 452.`16 in³

The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario. Which graph represents this wage increase for x < 12? ​

Answers

你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關 $$

The solution is Option C.

The graph which represents the inequality equation is

f ( x ) = { 0.50 , if x < 3

             1       , if 3 ≤ x < 6

             1.50  , if 6 ≤ x < 9

             2.00 , if 9 ≤ x < 12 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of years be = x

Let the increment in wages be = y

Now , the equation will be

For the employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour

So , the inequality equation is x < 3 , f ( x ) = 0.50

Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00

So , the inequality equation is 3 ≤ x < 6 , f ( x ) = 1

Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour

So , the inequality equation is 6 ≤ x < 9 , f ( x ) = 1.50

Employees of at least nine years, but less than twelve years receive an increase of $2.00

So , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2

Therefore , the graph which represents the solution is Option C.

Hence , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2

To learn more about inequality equations click :

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Bob works as a carpenter and needs to buy some tools for
work. A framing hammer costs $22. A 4-foot level costs
$18. A carpenter's square costs $7. What are Bob's total
expenses for these tools?

Answers

answer: 47. reason: 22 + 18 + 7 = 47

Pythagoras


1.if the radius of the smaller circle is 3, find it’s area


2. Find the area of the yellow ring


3. Find the area of the white ring

Answers

Answer:

1. [tex]Area = 28.26[/tex]

2 and 3: See explanation

Step-by-step explanation:

Solving (1)

[tex]r = 3[/tex] --- radius

The area is:

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14* 3^2[/tex]

[tex]Area = 28.26[/tex]

There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.

However, the following formula will be used to calculate the required areas.

[tex]Area = \pi r^2[/tex] --- same process as (1)

What is the solution to the system of equations ?
Y=2/3 x + 3
X= - 2

Answers

Answer:

x = -2, y = 5/3

Step-by-step explanation:

we have the value of x already (-2).

x=-2

Plug it into the first equation y = 2/3x+3

y = 2/3(-2)+3

y = -4/3+3

y = -4/3+9/3

y = 5/3

x = -2, y = 5/3

A hot air balloon holds 4,328 cubic meters of helium. The density of helium is 0.1785 kilograms per cubic meter. How many kilograms of helium does the balloon contain, rounded to the nearest tenth of a kilogram? (5 points)

Question 7 options:

1)

3,747.9 kg

2)

3,875.3 kg

3)

772.5 kg

4)

4,383.2 kg

Answers

Answer: 3) 772.5 kg

Step-by-step explanation: That's what I got and I'm 100% sure that's the answer

Answer:

The answer 772.5

Step-by-step explanation:

You would use the density formula to figure out the mass.

Density = mass/volume

We have the density of helium (0.1785) and the volume of how much the hot air balloon can hold (4,328).

0.1785 = x / 4,318

0.1785 * 4,318 = x

772.548 = x

Then rounded to the nearest tenth would be 772.5, the third option.

There were 60 7th grade students last year in CHAMPS. This year, there are 48 7th grade students. What is the percent decrease from last year to this year?

Answers

20%

Hope this helps! :)

______________

write 36m÷9m in standard form

Answers

4x^2. This is the simplified answer

The expression (36m ÷ 9m) is equivalent to 4.

What is division in mathematics? What is a mathematical function, equation and expression?division : Division is the process of splitting a number or an amount into equal parts.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is the following division as follows -

(36m ÷ 9m)

We have the following expression -

36m ÷ 9m

So, we can write -

(36m/9m)

36/9

4

Therefore, the expression (36m ÷ 9m) is equivalent to 4.

To solve more questions on functions, expressions and polynomials, visit the link below -

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A system of equations consisting of a circle and a line is graphed. Which statements about the number of possible solutions are correct? Check all that apply.
A circle and a line always intersect, so the system can have an infinite number of solutions.
A circle and a line can intersect at one point, so the system can have one solution.
A circle and a line can intersect at three points, so the system can have three solutions.
A circle and a line can intersect twice, so the system can have two solutions.
A circle and a line do not have to intersect, so the system can have no solution.

Answers

Answer:

the solution is where the two objects intersect ...

1) A line can completely miss the circle (no solutions is possible)

2) a line can "kiss" the circle at one point (one solution)

3) note that a line can not "bend"... it can touch one side of the circle pass

through the center and touch the circle in a second spot (going out) .. two solutions...

those are the three possibility that are in the question that was posted...

three check comments are true

Step-by-step explanation:

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