A rectangular area is to be fenced in with 600 feet of chicken wire. find the maximum area that can be enclosed.

Answers

Answer 1

600 ft is the perimeter of the area.
the area of the area is max when it's a square
the length of the square is 600/4 = 150
so the max area that can be enclosed is:
150×150 = 22500 ft square

Answer 2

The maximum area that can be enclosed is 22500 feet²

A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.

Let x represent the length and y represent the width. Hence:

perimeter = 2(length + width)

600 = 2(x + y)

300 = x + y

y = 300 - x

The area of a rectangle (A) = length * width

A = x * (300 - x)

A = 300x - x²

The maximum area is at dA/dx = 0, hence:

dA/dx = 300 - 2x

300 - 2x = 0

2x = 300

x = 150 feet

y = 300 - x = 300 - 150 = 150 feet

The maximum area = x * y = 150 * 150 = 22500 feet²

The maximum area that can be enclosed is 22500 feet²

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Related Questions

What is the slope of the line on the graph below?

A. -1/2
B. 1/2
C. 1
D. 2

Answers

Answer: choice D) the slope is 2

---------------------------------------------------------------------
---------------------------------------------------------------------

Work Shown:

Pick any two points on the line. I'm going to pick (0,1) and (1,3)

Label these two points as (x1,y1) and (x2,y2).
So,
(x1,y1) = (0,1) meaning that x1 = 0 and y1 = 1
(x2,y2) = (1,3) meaning that x2 = 1 and y2 = 3

Now use the slope formula
m = (y2 - y1)/(x2 - x1)
m = (3-1)/(1-0)
m = 2/1
m = 2

Going from (0,1) to (1,3) we move 2 units up and 1 unit to the right.
The "2 units up" is the "rise"
The "1 unit to the right" is the "run"

Slope = rise/run = (change in y)/(change in x)

Answer:

d on edge

Step-by-step explanation:

Can someone help me with this one real quick ? Thanks a lot! Please explain and show your work :)

Answers

a. Given.
You were given the proof.

b. Corresponding angles are congruent.
Since angles 1 and 2 are corresponding, then if one is 130, then the other one is also 130.

c. Vertical angles are congruent.
Angles 2 and 3 are vertical, meaning they'll also be congruent.

d. Transitive Property of Equality.
If angles 2 and 3 are vertical, then if 2 is 130, then 3 is also 130.

The cost of painting a circular traffic sign is $3.50 per square foot. How much, to the nearest dollar, will it cost to paint the sign if its diameter measures 36 INCHES.

Answers

area of a circle = pi x r^2

using 3.14 for pi

radius = 36/2 =18

area = 3.14 x 18^2 = 1017.36 square inches

1 sq ft = 144"

1017.36/144 = 7.065 sq ft

7.065*3.50 = $24.73 to the nearest dollar = $25

you invest 2,600 in an account that pays an interest rate of 8.5% compounded continuously. Calculate the balance of your account after 5 years

Answers

The formula is
A=p e^rt
A future value?
P present value 2600
R interest rate 0.085
T time 5years
E constant
A=2,600×e^(0.085×5)
A=3,976.94

Which of the relations given by the following sets of ordered pairs is a function?
Select one:
a. {
(2,4),(2,6),(2,8),(2,10),(2,12)
(2,4),(2,6),(2,8),(2,10),(2,12)
}
b. {
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
}
c. {
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
}
d. {
(8,1),(−4,1),(3,5),(0,4),(−1,2)
(8,1),(−4,1),(3,5),(0,4),(−1,2)
}

Answers

A function will not have any repeating x values...it can have repeating y values, just not the x ones. SO look at all the x values in ur answer choices...which answer choice has all x values different ?

ur answer would be D....because ur x values (8,-4,3,0,-1) are all different

Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.

A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.

The relations given by the following sets of ordered pairs is a function is,

d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}

Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.

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Which is the best approximation for the value of √102?
A.10
B.11
C.50
D.51

Answers

10, because when you use a scientific calculator you get 10.09950494
which would be round to 10 because after the decimal the number is 0 below 5 so 10 stays as 10

We know that √100 = 10,
so √102 is approximately 10

Write an equation for each translation of y=lxl

7 units up

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ % left side templates \begin{array}{llll} f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}\\\\ --------------------\\\\[/tex]

[tex]\bf % template detailing \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]

with that template in mind.. .let's see

[tex]\bf y=|x|\implies \begin{array}{lllcll} y=&1|&1x&+0|+&0\\ &\uparrow&\uparrow &\uparrow &\uparrow \\ &A&B&C&D \end{array}[/tex]

7 units up, meaning D = 7

Evaluate the limit lim h → 0 (−5 + h)2 − 25 h

Answers

Easily substitute with h=0 is the limit function:

(-5 + 0)^2 -25(0) = 25 -0 = 25

The standard form of the equation of a parabola is x=y^2+6y+1. What is the vertex form of the equation?
A. X=(y+3)^2-8
B. X=(y+3)^2-5
C. X=(y+6)^2-35

Answers

A. x = (y+3)^2-8 is the correct answer.
What you want to do is get the quadratic (y^2+6y+1) into it's root factor form, in other words, the quantity of (y+what) squared will equal y^2+6y+1. Well it's not a perfect square so we'll have to play around with it a little.
In the format ay^2 + by + c, completing the square first requires finding out what value would do that: c = (b/2)^2 = (6/2)^2 = 3^2 = 9
So we need y^2+6y+1 to have the last number (c) to equal 9 to have (y+b/2)^2, or (y+3)^2
How do we get 9 down to the 1 that we have for c?? 9-1=8, so just subtract 8.
That means that y^2+6y+1 is the same as (y^2+6y+9)-8, and y^2+6y+9 = (y+3)^2, so now we have: y^2+6y+1 = (y+3)^2-8, which is answer [A]

Find the equation of the line specified.
The slope is 3, and it passes through ( -4, -7).

a.
y = 6x + 5
c.
y = 3x - 7
b.
y = 3x + 5
d.
y = 3x - 19

Please select the best answer from the choices provided

A
B
C
D

Answers

If slope is 3 then A answer is wrong for sure, and if the graph passes (-4; -7) point it means that when we put -4 instead of x we should get -7, if you try this method you will get the following answer:

B. y = 3x + 5

Answer:

Step-by-step explanation:

Edge 2021

Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find f of x over g of x.

Answers

The correct answer is
2x^3-6x^2-x

It is given in the question that

[tex]f(x) = 16x^5 -48x^4-8x^3 \ and \ g(x) = 8x^2[/tex]

And we have to find the value of

[tex]\frac{f(x)}{g(x)}[/tex]

Substituting the values of two functions, we will get

[tex]=\frac{16x^5 -48x^4 -8x^3}{8x^2}[/tex]

8x^3 is common in the numerator, and on taking it out, we will get

[tex]= \frac{8x^3(2x^2 -6x-1)}{8x^2} = x(2x^2 -6x-1)[/tex]

And that's the required answer .

Given the point (5, 6) and the slope of 5, find y when x = 21.

Answers

y=mx+b

6=5(5)+b
6=25+b
-19=b

y=5x-19

y=5(21)-19
y=105-19
y=86

Final answer: y=86

Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 107°, a = 10 cm, c = 22 cm

Answers

Answer:

105.19 cm²

Step-by-step explanation:

The applicable area formula is ...

area = (1/2)ac·sin(B) = (1/2)(10)(22)sin(107°) ≈ 105.19 cm²

Simplify 5(6x - (6 - 7y + 7x) + 6y)

-80x + 87y - 91
-5x + 65y - 30
-82x + 73y - 54
-60x + 9y - 17
None of the above

Answers

5(6x - (6 - 7y + 7x) + 6y)

= 5(6x - 6 + 7y - 7x + 6y)

= 5(-x + 13y -6)

= -5x +65y -30

Hence, the answer is B.

How can x2 = x2 + 2x + 9 be set up as a system of equations?

Answers

Final answer:

To set up x^2 = x^2 + 2x + 9 as a system of equations, we would have x^2 = x^2 + 2x + 9 and x = -4.5.

Explanation:

To set up x2 = x2 + 2x + 9 as a system of equations, we can separate it into two separate equations:

Equation 1: x2 = x2 + 2x + 9

Equation 2: 0 = 2x + 9

By rearranging Equation 2, we can rewrite it as:

x = -4.5

Therefore, the system of equations for x2 = x2 + 2x + 9 is: x2 = x2 + 2x + 9 and x = -4.5.

A stick 42 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two pieces ?

Answers

Total length of stick = 42 inches.

Let the shorter piece be x inches.

Thus, the longer piece is 2x.

2x + x = 42

3x = 42

x = 14

Therefore, the length of the two pieces are 14 inches and 28 inches.

The answer is 14 inches and 28 inches:

Total length of stick = 42 inches.

Let the shorter piece be x inches.

Thus, the longer piece is 2x.

2x + x = 42

3x = 42

x = 14

Therefore, the length of the two pieces are 14 inches and 28 inches.

Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the formula A= Pe^rt, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.

Answers

This is substitution, it's very simple once you get the hang of it!

okay, what you want to do is plug in the numbers you already have, to get the number you don't have(r).

First, you plug in the numbers.

1. P= $2000
A=$2543
t= 4(years)
r=?

2543=2000^r(4)

Secondly, you want to solve the equation.

Answer:

Rate of interest = 6%

Step-by-step explanation:

Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account.

Use the formula,

[tex]A=Pe^{rt}[/tex]

[tex]P\rightarrow \$2000[/tex]

[tex]r\rightarrow ?[/tex]

[tex]A\rightarrow \$2543[/tex]

[tex]t\rightarrow 4\text{ years}[/tex]

Substitute the value into formula and solve r

[tex]2543=2000e^{4r}[/tex]

[tex]e^{4r}=1.2715[/tex]

Apply ln both sides

[tex]4r\ln(e)=\ln(1.2715)[/tex]

[tex]r=0.06[/tex]

Rate of interest = 6%

Hence, The rate of interest is 6%

What is the slope of the line shown below?

Answers

Answer:

correct option is B) 2

Step-by-step explanation:

Slope of line is calculated by formula :-

Suppose two points on line are [tex](x_1, y_1) and (x_2 ,y_2)[/tex] then slope 'm' is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

We can see two points on line of graph are :- (-1, -4) and (2,2)

then slope will be calculated as,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

since [tex]x_1 = -1, x_2 =2, y_1=-4\;and\; y_2=2[/tex]

now, put in formula

[tex]m=\frac{2-(-4)}{2-(-1)}[/tex]

[tex]m=\frac{2+4}{2+1}[/tex]

[tex]m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

Hence, slope is 2 of the provided graph.

Therefore, correct option is B) 2

if two triangles share a common side what else must be true for the SAS triangle congruence theorem to apply

Answers

They must share the same angle postion

The conditions to be added are:

The two triangles have congruent angles between the sides that are not the common side.

The two triangles have congruent lengths for the sides adjacent to the congruent angles.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The SAS (Side-Angle-Side) triangle congruence theorem states that if two triangles have two sides and the included angle of one triangle is congruent to two sides and the included angle of the other triangle, then the two triangles are congruent.

Therefore, in addition to sharing a common side, the two triangles must have congruent angles between the sides that are not the common side. Specifically, the angle opposite the common side must be congruent in both triangles.

To summarize, for the SAS triangle congruence theorem to apply, the following conditions must be met:

The two triangles share a common side.

The two triangles have congruent angles between the sides that are not the common side.

The two triangles have congruent lengths for the sides adjacent to the congruent angles (the "included" side).

Thus,

The conditions to be added are:

The two triangles have congruent angles between the sides that are not the common side.

The two triangles have congruent lengths for the sides adjacent to the congruent angles.

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Suppose you toss a coin 100 times and get 76 heads and 24 tails. based on these results, what is the probability that the next flip results in a head?

Answers

If it is a fair coin, the probability of the next flip resulting in "heads" is 50-50 or .5

The probability that the next flip results in a head is 50% or 0.5.

We have,

Total number of coins tossed = 100

Number of heads outcome = 76

Number of tails outcome = 24

Now,

The probability of getting heads in the tossing of coins 100 times.

= 76/100

= 0.76

= 76%

Now,

Generally for an unbiased coin.

The probability of getting a head in tossing a coin is 50%.

So,

Based on the results of the first 100 coin tosses, even if the probability of getting a head is 76% the probability that the next flip results in a head is still 50%.

Thus,

The probability that the next flip results in a head is 50% or 0.5.

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Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−1, 7) and (2, 3). incorrect: your answer is incorrect.

Answers

eh this is probably correct ?

what is the greatest integer that satisfies the inequality 3x-4≤8 ?
A.4
B.5
C.6
D.7

Answers

3x - 4 ≤ 8
3x ≤ 12
x ≤ 4

answer

A.4

To figure this out, we need to solve for the inequality. A quick way is to plug in an answer choice for x.
For example, answer choice "A.)";
3(4) -4 <_ 8
We plugged in 4 for x.
Let's see if A.) is correct.
3(4) -4 <_ 8
12 - 4 <_ 8
8 <_ 8

This is the GREATEST possible integer, as the question asks for what the highest possible number would match the inequality.

Your correct answer choice is "A.)"

I hope this helps!

HELPPPPPP make sure your right !:)

Answers

To find your constant of variation, you just need to figure out what you multiply the x by in order to get f(x). In other words, what do you multiply the 3 by to get 6? What do you multiply the 7 by to get 14? Another way to think of it is to divide f(x) by the x to get your constant.

a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?

Answers

Let [tex]g_n[/tex] represent the number of feet that the balloon rises in the [tex] n^{th} [/tex] minute.

so

[tex]g_1=40[/tex] ft , means that in the 1st minute, the balloon rose 40 feet

[tex]g_2=60[/tex] ft, means : in the 2nd minute the balloon rose 60 feet

[tex]g_3=80[/tex]

we notice that each minute, the balloon rises a multiple of 20, feet:

[tex]g_1=40=2*20[/tex]

[tex]g_2=60=3*20[/tex]

[tex]g_3=80=4*20[/tex]

so it is clear that [tex]g_n=(n+1)*20[/tex]

during the 15th minute the balloon rises [tex]g_1_5=16*20=320[/tex](feet)

Answer: 320

An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.

A: 42 sq. units
B: 21√2 sq. units
C: 21 sq. units

Answers

Draw this trapezoid, let it be ABCD, where AB is the smaller base (=4) and
DC, the larger one (=10)
From A & B draw the altitude AA' & BB'. You notice that ABA'B' is a rectangle and A'B' = 4,. You conclude that DA' = B'C = 3 .
Now let's calculate the altitude AA'.
The right triangle ADA' is also an isosceles right triangle:
( angle DA'A=90, angle ADA' = 45 and angle DAA' =45) , then
DA' = AA' (altitude) = 3 units. Now we can calculate the area of the trapezoid:
Area = (B+b).H/2

Area = (4+10)x3/2 = 14x3/2 = 42/2 = 21 sq.unit

Answer:

21 sq. units

Step-by-step explanation:

what is the vaule of 3.85+0.004+0.117 ?

Answers

3.85+0.004+0.117=3.971

(04.02 LC)

The graph represents function 1 and the equation represents function 2:

Function 2
y = 3x + 1

How much more is the rate of change of function 2 than the rate of change of function 1?
1
2
3
4

Answers

The graph is the horizontal line:

y=3 it has a slope of zero.

Function 2 is

y=3x+1, it is in slope-intercept form, y=mx+b where m is the slope and b is the y=intercept so in this case it has a slope of 3.

So the difference in slopes is 3-0=3

Final answer:

The rate of change of function 2 is 3 times greater than the rate of change of function 1.

Explanation:

The rate of change of a function measures how much the output of the function changes when the input changes by 1 unit. In function 1, since the graph is a straight line, the rate of change is constant. We can find the rate of change of function 1 by finding the slope of the line, which represents the rate of change. In function 2, the equation is y = 3x + 1, so the rate of change is 3. Therefore, the rate of change of function 2 is 3 times greater than the rate of change of function 1.

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There are 26.2 in a marathon .Write the number of miles using a fraction.

Answers

Partitioning the value 26.2

26.2 = 20+6+0.2

The decimal value 0.2 is read two tenth = 2/10

Writing 26.2 as mixed numbers

[tex]26.2=26 \frac{2}{10} [/tex]

If we want to write this as an improper fraction, multiply 26 by 10 then add the 2 to get the numerator

[tex]26.2 = 26 \frac{2}{10}= \frac{262}{10}= \frac{131}{5} [/tex]

What is the value of
x/3y, when x = 18 and y = 3?

Answers

assuming ya meant [tex]\frac{x}{3y}[/tex]

x=18 and y=3

[tex]\frac{18}{(3)(3)}=\frac{18}{9}=2[/tex]

this has been asked at least 3 times so far today

18/3*3 = 18/9 = 2

answer is 2

Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.

Answers

6.0 has only one digit, the least. Now 8.78 has two, but can't be written as 8,7, one needs to round it to one digit:

8.8 in this cas, so

8.79 + 6.0 = 8.8 + 6.0 = 14.8

14.8 is the answer

Answer:

The sum of the numbers is [tex]8.79+6.0=14.79[/tex]

Step-by-step explanation:

To find : Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.

Solution :

Writing the sum of the numbers according to significant digits by writing in their place value,

8 . 7 9

+6 . 0 0

----------

14 . 7 9

Therefore, The sum of the numbers is [tex]8.79+6.0=14.79[/tex]

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