A rectangular dog pen is constructed using a barn wall as one side and 60 meters of fencing for the other three sides. What is the maximum area of the dog pen?

Answers

Answer 1

Answer:

450 m²

Step-by-step explanation:

Let x = length of rectangle and y = width of the rectangle.

Therefore,

2x + y = 60...............(1)

Making y subject of the formula, we have:

y = 60 - 2x............... (2)

We know area of a rectangle is length * width i.e A = x*y

Let's substitute (60-2x) for y,

A = x * (60-2x)

= 60x - 2(x)²

= -2x² + 60x

[tex] \frac{dA}{dx} = -2x^2 + 60x = [/tex]

-4x + 60 = 0

-4x = -60

[tex] x = \frac{-60}{-4} = 15 [/tex]

Let's substitute 15 for x in equation 2, we have:

y = 60 - 2(15)

= 60 - 30

y = 30

Since x = 15 & y = 30, the area would be:

A = xy

A = 15 * 30

A = 450 m²

The maximum area of the dog pen is 450m²


Related Questions

Some Insight: This is a Unit Rate question. Please Answer soon as possible.

Answers

Answer: C

Step-by-step explanation:

Because it only shows a single price and we don’t know what that price is for.

plzzzzzzzzz help me im dewwwwwww plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz pros

Answers

Answer:

C

Step-by-step explanation:

[tex]x^2-2x-80=[/tex]

[tex](x-10)(x+8)[/tex]

You can confirm this by expanding this:

[tex](x-10)(x+8)=[/tex]

[tex]x^2-10x+8x-80=[/tex]

[tex]x^2-2x-80[/tex]

Therefore, the answer is choice C. Hope this helps!

Answer:

C

Step-by-step explanation:

x^2-2x-80

(x^2+8)+(-10x-80)

factor out the -10 for -10x-80

=x(x+8)-10(x+8)

(x+8)(x-10)

pls mark me brainliest

Karina is making accessories for the soccer team. She uses 628.86 inches of fabric on headbands for 45 players and 2 coaches. She also uses 384.30 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

Answers

Answer:

21.92 inches

Step-by-step explanation:

628.86 inches of fabric on headband for 45 players and 2 coaches

Total persons=45 players +2 coaches=47

Each person uses 628.86/47 inches of fabrics

=13.38 inches per person

384.30 inches for wristband for players only

Each player uses 384.30/45 inches of fabrics

=8.54 inches per person

Karina uses 13.38 inches of fabric for headband and 8.54 inches of wristband for each player

13.38+8.54

=21.92 inches of fabric for each player

Simplify the slope of AC.

Answers

Answer:

1

Step-by-step explanation:

The slope of a line can be found by dividing the rise over the run, or how much the line rises over a certain amount of sideways movement. In this case,  the line AC moves from (0,0) to (a,a), meaning that it rises and moves sideways the same amount. Since a/a=1, the slope of this line is 1. Hope this helps!

Answer:

1

Step-by-step explanation:

Point A is (0, 0) and Point C is (a, a).

The "rise" from A to C is a and the "run from A to C" is also 1.

Thus, the slope of line A is m = rise / run = 1 / 1 = 1.

how many days are in a year. ALSO ANSWER MY OTHER MATH QUESTION PLEASE!

Answers

Answer:

365 1/4 days

Also I haven't seen your other question

Answer:

365, 366 every 4 years. 366 on 2020, 2024, 2028, 2032, 2036, 2040 and so on

I really need help on this, please help out

Answers

Answer:

x+y= idk

Step-by-step explanation:

sorry i need the points

Answer:

15

Step-by-step explanation:

so you know that the hypotenuse for the triangle with "x"'s is 5 square root two, and because we know that the triangle is an isoceles triangle we know the other two side are equal and as a result x=5. Now for the next triangle it is 5 square root 2 on both sides and that is also an isoceles triangle and y is the hypotenuse so it 5 square root 2 times square root 2 which just becomes 2 so then it is 5 times 2 which is 10. So Y=10 and X=5 so X+Y=15.

Please help. I’ve been here for hours and no one wants to help. I’ll give brainliest answer :(

Answers

1. D

2. J

3. L

4. A

5. B

6. K

7. C

8. I

9. F

10. G

Radius = Center to Perimeter of Circle

Minor Arc = Arc that goes around less than 1/2 of circle

Major Arc = Arc that goes around more than 1/2 of circle

Chord = The straight line segment between 2 points on a circle

Secant = A line that passes through 2 points on a circle

Semicircle = 1/2 Circle

Tangent = Line that touches 1 point on a circle's perimeter

Central Angle = Angle with a vertex at the center of a circle

Inscribed Angle = Angle whose 3 points (vertex & 2 other points) are on the outside of the circle

Right Angle = Angle with 90 degree measure

Find the area of the semicircle? Helpppp

Answers

Answer:

14.135

Step-by-step explanation:

6 divided by 2 (half) = 3, π·32≈28.27433 dived by 2 (half) equals 14.135

Answer:

14.13 units ^2

Step-by-step explanation:

A= 3.14 (3)^2 (area of a circle)

A= 28.26 / 2 (divide to find half of the circle)

A=14.13 units ^2

You roll a fair 6-sided die. what is the probability rolling greater than 4

Answers

Answer:

1/3

Step-by-step explanation:

There are 6 possible outcomes when you roll this die: 1,2,3,4,5 and 6. Of these, only 5 and 6 are greater than 4, which is 2 successful outcomes. Probability is successful outcomes/total outcomes = 2/6 = 1/3. Hope this helps!

A given line has the equation 10x+2y=−2 .

What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?

Answers

Answer:

Step-by-step explanation:

2y = -10x - 2

y = -5x - 1

y - 12 = -5(x - 0)

y - 12 = -5x + 0

y = -5x + 12

what is t if 5/7t = 15

Answers

Answer:

21

Step-by-step explanation:

15/ 5/7 = 21

30 points! Fraction Equasion

Answers

Answer: -3.3

Step-by-step explanation:

Answer:

-3.3

Step-by-step explanation:

-2.3 - (4.5 - 3 1/2)

Change the fraction to a decimal)

-2.3 - (4.5 - 3.5)

Parentheses first

-2.3 - (1)

Subtract

-3.3

Plz help! Question on picture :)

Answers

Answer:

125 students participated

Step-by-step explanation:

66% + 30% = 96%

100% - 96% = 4%

4% = 5 students

100% ÷ 4% = 25

25 × 5 = 125

125 students participated

Answer:

125 students

Step-by-step explanation:

30+66=96

100-96=4

5 students make up 4%.

100/4=25

25x5=125 students

The high for Monday was 0 degrees Fahrenheit and the low was -4 degrees Fahrenheit. What is the difference between the high and low temperature?

Answers

One is in the negatives. The difference is 5

Determine the vertex of the function f(x) = 3x2 – 6x + 13.

1. Identify the values of a and b.

a =
and b =

2. Find the x-coordinate of the vertex.

negative StartFraction b Over 2 a EndFraction =

3. Find the y-coordinate by evaluating the function at the x-value found in the previous step.

The vertex is

.

Answers

Answer:

1.)

A=3

B=-6

2.)

1

3.)

(1,10)

Answer:

1.  Identify the values of a and b.            

a =  

✔ 3

and b =

✔ –6

2.   Find the x-coordinate of the vertex.

negative StartFraction b Over 2 a EndFraction  =

✔ 1

3.  Find the y-coordinate by evaluating the function at the x-value found in the previous step.

The vertex is

✔ (1, 10)

When we plot all the points that satisfy an equation or inequality we __ it.

Answers

when we plot all the points that satisfy an equation or inequality we GRAPH it

A plane is descending into an airport. When its altitude is 3 1/2 miles, it is 250 miles from the airport. When its altitude is 1 mile, it is 75 miles from the airport. At 2 1/2 miles, it is 175 miles from the airport. Problem 6 a. If the pilot follows the same pattern, what will the plane's altitude be at 25 miles from the airport? *

Answers

Answer: 1/2 miles

Step-by-step explanation:

Given the following:

Altitude (miles) - - - - - - - - - - distance (miles)

3 1/2 - - - - - - - - - - - - - - - - - - - 250

2 1/2 - - - - - - - - - - - - - - - - - - - - 175

Calculate the plane's altitude at 25miles from the airport

7/2 = 250

5/2 = 175

(7/2 - 5/2) miles = (250 - 175)miles

1 mile = 75 miles

From the above, the plane craft 's altitude reduces by 1 mile for every 75 miles moved

Therefore, at a distance of 25 mile from the airport,

Distance moved = (250 - 25)miles = 225miles

225miles / 75 miles = 3

Therefore, the altitude will reduce by 3 miles from the initial altitude at 250 miles

Therefore,

( 3 1/2 - 3) miles = 1/2 miles

Therefore, the plane craft will have an altitude of 1/2

how many grams each of a 10% salt solution and a 5% salt solution must be mixed in order to obtain 400g of an 8% solution?

Answers

I dont want to give you the exact equation so u wont be copying- here is an example.

let x=grams of salt that you already have

let y=grams of salt that need to be added

let z=total amount of salt in the solution after adding salt

We know that salt makes up 25% of the 400g solution, and that 25% can also be written as .25. Thus, we can write an equation to determine x's value:

x=.25*400g

x=100g

Therefore, there are 100 grams of salt already in the solution.

Now that we've determined x's value, we'll bring z into the equation. There are two ways to calculate z. z is equivalent to the sum of x and y. Remember, x is equal to 100 grams. So, z's equation is as follows:

z=100g+y

The other way to calculate z is as a percentage of the final solution. As the question states, we want the final solution to have a salt content of 40% (which we can write as .40). The final amount of solution can be written as below:

400g+y=total amount of solution after adding salt.

This is because we are adding y (the amount of salt needed to bring the salt content to 40 percent)to the amount of solution which we already have.

Therefore, the second way to express z is below:

z=.40*(400g+y)

After we have two equations for z, we can set them equal to each other as follows:

100g+y=.40*(400g+y)

We then can distribute the .40 over the parenthesis.

100g+y=160g+.40y

And then we can subtract 100 grams from both sides of the equation.

y=60g+.40y

Next, we subtract .40 y from both sides of the equation to get y on one side.

.6y=60g

Finally, we can divide both sides by .6 to isolate y.

y=100g

Therefore, you must add 100g of salt to the solution to make it 40 percent salt.

DID I DO IT RIGHTT?? pls tell me

Carlos bought 80 feet of wire for ​$17.60. He needs 30 more feet. If the unit price is the​ same, how much will he pay for the extra 30 feet of wire​?

Answers

Answer:

Carlos bought 80 feet of wire for ​$17.60.

Then the price for 1 feet of wire is 17.6/80 = 0.22

=> 30 feet of wire would cost: 30 x 0.22 = 6.6

Hope this helps!

:)

True or False: Sine is the ratio of opposite side to adjacent side in a right triangle? *

Answers

Answer:

The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan.

Which transformation of ABC produces the Congruent image DEF?
Please someone answer ASAP

Answers

Answer:

Rotate 90° counterclockwise about the origin, then translate 9 units right and 1 unit down.

Step-by-step explanation:

If you use some kind of see through paper like parchment, and trace Triangle ABC and rotate it around the origin 90° counterclockwise, translate 9 units right and 1 down, it should overlap Triangle DEF

The correct sequence of transformations is -

Rotation 90° counterclockwise.Translate 9 units right.Translate 1 unit down.

What are triangles?

A triangle is a polygon with three edges and three vertices.

Given is a transformation of ΔABC to the Congruent image ΔDEF.

Congruent triangles have both the same shape and the same size.

The statement that correctly matches the transformation is -

Rotation 90° counterclockwise.Translate 9 units right.Translate 1 unit down.

Therefore, the correct sequence of transformations is -

Rotation 90° counterclockwise.Translate 9 units right.Translate 1 unit down.

To solve more questions on congruent triangles, visit the link below -

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Five people buy individual insurance policies. According to the research, the probability of each of these people not filing a claim for at least 5 years is . The probability that all 5 have not filed a claim after 5 years is , and the probability that exactly 3 will have filed a claim after 5 years is . Reset Next

Answers

The complete question is;

Five people buy individual insurance policies. According to the research, the probability of each of these people not filing a claim for at least 5 years is 2/3.

The probability that all 5 have not filed a claim after 5 years is A: 0.132 B: 0.868 C: 1 , and the probability that exactly 3 will have filed a claim after 5 years is A: 0.016 B: 0.033 C: 0.067

Answer:

1) P(all 5 file no claim after 5 years) = 0.132

2) P(exactly 3 file claim after 5 years) = 0.033

Step-by-step explanation:

1) we are told that the probability of each of these people not filing a claim for at least 5 years is 2/3.

Thus, for all 5 of them,

The probability will be;

P(all 5 file no claim after 5 years) = (2/3)^5 = 0.1317 ≈ 0.132

2) since probability of each not filing a claim for last 5 years = 2/3

Then probability of each filing a claim after 5 years = 1 - 2/3 = 1/3

So, P(exactly 3 file claim after 5 years) = (1/3)^3 ≈ 0.037.

The closest answer is 0.033.

Answer: not have filed a claim: 0.132

Will have filed a claim 0.165

Step-by-step explanation: I got this right on Edmentum

All measurements listed are in kilometers. What is the horizontal distance from the plane's starting position to its finishing position? Round your answer to the nearest tenth of a kilometer.

Answers

Complete question:

An airplane takes off, levels off, and lands according to the diagram shown below.

All measurements listed are in kilometers. What is the horizontal distance from the plane's starting position to its finishing position? Round your answer to the nearest tenth of a kilometer.

Answer: 13.3km

Step-by-step explanation:

Kindly see attached picture for detailed explanation.

The question is missing data. The full question is here.

An airplane takes off, levels off and lands according to the diagram shown below. All measurements listed are in kilometers. What is the horizontal distance from the plane's starting position to its finishing position? Round your answer to the nearest tenth of a kilometer.

Answer: d = 13.3 km

Step-by-step explanation: The image show 2 right triangels and 1 square. To determine x and y, use Pythagorean Theorem.

To find x:

hypothenuse² = side² + side²

5² = 3² + x²

x² = 25 - 9

x = [tex]\sqrt{16}[/tex]

x = 4

To find y:

7² = 3² + y²

y² = 49 - 9

y = [tex]\sqrt{40}[/tex]

y = 6.32

Now, to determine the total horizontal distance, sum up all the parts:

d = x+y+3

d = 4 + 6.3245 + 3

d = 13.3

The horizontal distance from start to finish position is 13.3 km

PLEASE HELP ASAP 10 POINTS AND ITS MULTIPLE CHOICE

Which equation represents the line that is parallel to the following?
Y=-3x-4

A. Y=3x+4
B. Y=3x+1
C. Y=-1/3x-4/3
D. Y=1/3x-4

Answers

Answer:

A. Y=3x+4

Step-by-step explanation:

Use properties of operations to write two expressions that are equivalent
to 3/4n + (8 + 1/3z).

Answers

Answer:

(9z+96nz+4n)/12nz

Step-by-step explanation:

3/4n + 8+ 1/3z. distributive property

The required equivalent expression is [9z + 96nz + 4n] / 12nz and the property used is distributive property.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
= 3/4n + (8 + 1/3z)

Using the distributive property for the association,
= 3/4n + 8 / 1 + 1/3z
=  [9z + 96nz + 4n] / 12nz

Thus, the required equivalent expression is [9z + 96nz + 4n] / 12nz, and the property used is the distributive property.

Learn more about simplification here:

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What type of number is -4\pi−4πminus, 4, pi?
Choose all answers that apply:

(Choice A)
Whole number

(Choice B)
Integer

(Choice C)
Rational

(Choice D)
Irrational

Answers

Answer:

Choice C Rational

Step-by-step explanation:

Answer:

d irrational

Step-by-step explanation:

i did it

13 POINTS!!!

In ΔABC, c = 4.2 inches, ∠C=24° and ∠A=115°. Find the area of ΔABC, to the nearest 10th of an square inch.

Answers

Answer:

12.9 [tex]in^{2}[/tex]

Step-by-step explanation:

So to find the area of this triangle, you will need to use the equation

Area = [tex]\frac{1}{2}[/tex]c*b*sin(A) = [tex]\frac{1}{2}[/tex]a*b*sin(C)

Here, we have ∠A, ∠C, and side c

We can use the fact that [tex]\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex] so solve for the other variables we do not have.

First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,

∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°

Now that we have all three angles, we can solve for the sides

Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.

Since [tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex], solving for b would give us [tex]b=\frac{csin(B)}{sin(C)}[/tex]. Then plugging in our values we get [tex]\frac{4.2sin(41)}{sin(24)}[/tex]= 6.77 = b

Now we can solve for the remaining side, a, using the same method.

Since [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex], solving for a would give us [tex]a=\frac{bsin(A)}{sin(B)}[/tex]. Then plugging on our values we get [tex]\frac{6.77sin(115)}{sin(41)}[/tex]= 9.36 = a

Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒

Area =[tex]\frac{1}{2}[/tex]c*b*sin(A)= [tex]\frac{1}{2}[/tex](4.2)(6.77)sin(115) = 12.9[tex]in^{2}[/tex] or [tex]\frac{1}{2}[/tex]a*b*sin(C) = [tex]\frac{1}{2}[/tex](9.36)(6.77)sin(24) = 12.9[tex]in^{2}[/tex]

Help me please I think you have to find the area

Answers

Answer:

I got B) ; 54m2

Step-by-step explanation:

the above diagram is a trapezium.

the area is gotten by; 1/2 (a+b)h

a = shortest side.

b = the longer side that is directly opposite to (a).

h = height.

1/2(3 + 9)9

1/2 by 12 by 9

to get 54

please help me, someone!

Answers

Answer:

76.275

Step-by-step explanation:

First - the entire circles area is 78.54. [tex]\pi r^{2}[/tex] with r being 5

6 triangles of that size could fit in that circle.

A=3[tex]\sqrt{3}[/tex]/(2) * a2

The area of that would equal 64.95

78.54-64.95 = 13.59

then divide that number by 6

which is 2.265.

Take that number from the original 78.54

78.54-2.265 = 76.275

Describe in your own words what a hyperbola is.

Answers

Answer:

A conic section that can be thought of as an inside-out ellipse

Step-by-step explanation:

Hyperbola is a two-branched open curve-conic section.

What is a hyperbola?

Hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.

For the given situation,

We need to describe about a hyperbola.

A hyperbola is two curves that are like infinite bows. It is a two-branched open curve, a  conic section produced by the intersection of a circular cone and a plane that cuts both nappes of the cone.

The standard equation of hyperbola is

                     [tex][\frac{x^{2} }{a^{2} }-\frac{y^{2} }{b^{2} }]=1[/tex]

where,[tex]b^2 = a^2 (e^2 -1)[/tex]

a,b are the points on the plane and e is the eccentricity.

Hence we can conclude that hyperbola is a two-branched open curve-conic section.

Learn more about hyperbola here

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