A homeowner has $360 to spend on building a fence around a rectangular garden. Three sides of the fence will be constructed with wire fencing at a cost of $2 per foot. The fourth side is to be constructed with wood fencing at a cost of $6 per foot. Find the dimensions of the rectangle that will maximize the area of the rectangle.

Answers

Answer 1

Answer:

The width is 22.5 feet and the length 45 feet.

Step-by-step explanation:

Let l represent the length of the rectangle and  w represent the width of the rectangle. The cost of the fence (C) is:

C = 2l + 2w + 2l + 6w

C = 4l + 8w

360 = 4l + 8w

360 = 4(l + 2w)

90 = l + 2w

l = 90 - 2w

Area (A) of rectangle = length * width

A = l * w

Put l = 90 - 2w

A = (90 - 2w)w

A = 90w - 2w²

The maximum area is at A' = 0, hence:

Differentiating gives:

A' = 90 - 4w

Put A' = 0

0 = 90 - 4w

4w = 90

w = 22.5 feet

l = 90 - 2w = 90 - 2(22.5) = 45 feet

Hence the width is 22.5 feet and the length 45 feet.


Related Questions

Solve x2 – 8x + 15 < 0.

Select the critical points for the inequality shown.

Answers

Answer:

x=3,5

Explanation:

x2−8x+15=0

Try to express the terms of the equation in square form.

Adding 16 both sides of the equation,

(x2−2⋅x⋅4+42)+15=16

or,(x−4)2+15−16=0

or,(x−4)2−1=0

or,(x−4)2−12=0

This is the a2−b2=(a+b)(a−b)form.

(x−4+1)(x−4−1)=0

or,(x−3)(x−5)=0

Now, equate both the terms to zero since both of them when multiplied, give zero.

Either,

x−3=0

∴x=3

Or,

x−5=0

∴x=5

Ans:x=3,5 Hope this helpsXD...!!

Answer:

3<x<5

Step-by-step explanation:

an Univariate quadratic polynomial can be divided into the product of two first order equations

In this example, x2 - 8x + 15 =  (x-3) * (x-5) <0

as a result. the answer is 3< x <5

This equation was solved incorrectly.
6x – 2(4x – 6) = 16
6x + 8x – 12 = 16
14x – 12 = 16
Step 1:
Step 2:
Step 3:
Step 4:
14x = 28
x=2
Which step contains the first error? Explain the error.

Answers

what was i correct was the 2nd step since when multiplying -2x-6 it would be a positive 12 not a negative :)

2.1-?=1 1/2

Please answer this I don’t want to fail

Answers

.6. This is right, brainliest?
2.1-(-3.4)=11/2 . . . . . . .

Mr. Grove cut down in tree in his yard. He gave 1/3 of the tree to his neighbor and 1/6 of the tree to his brother. Mr. Grove kept the remaining portion. How much tree did he keep?
A. 1/3
B. 2/3
C. 1/2
D. 5/6

Answers

Answer:

1/2 or C

Step-by-step explanation:

1/3 = 2/6. 2/6 + 1/6 = 3/6. that leaves 1/2 left over

you have a bill of $56.40. find a 15% tip?​

Answers

Answer:

$8.46

Step-by-step explanation:

15%=0.15

56.40(0.15)

8.46

The correct answer would be $8.46

What is the value of 6a + 2b if a = 1 and b = 2?

Answers

Answer:

3a + 2b ; a=1, b =-2

3

(

1

)

+

2

(

2

)

(substitute the values of the variables)

From here on, it's just a matter of condensing down the numbers. Very straightforward, and easy points on tests and quizzes. You can do this in your head if you want, or you can just do it on your calculator (which is probably the best way to go as it's faster and more accurate).

3

+

(

4

)

(simplify)

3

4

=

1

So here, what we've proven is that in our given equation, if

a

=

1

and

b

=

2

, then it would yield us a product of

1

.

Once again, these types of evaluation problems are very straightforward, and are usually always easy points on tests and quizzes if you have an inkling of an idea of what the concept is about. Again, if you have a calculator with all the appropriate functions, that makes it even easier.

Try another:

6

a

2

b

+

8

with a = 1 and b = 3

6

(

1

)

2

(

3

)

+

8

6 - 3 + 8

= 11

Just as a sidenote here, make sure you're aware of the difference between

(

6

x

)

2

and

6

x

2

. The former refers to both the 6 and the

x

being squared, whereas the latter shows only the

x

being squared. Just be careful not to mix the two.

Try one more:

2

c

5

3

b

+

4

with b = 2 and c = 4

2

(

4

)

5

3

(

2

)

+

4

=

8

5

6

+

4

=

3

10

(or 0.3)

Speaking from experience, when you work with rational (fraction) polynomials on paper, it often tends to take up a bit of space and get messy. Therefore, I'd suggest you tried solving one equation at a time if you have the same issue.

Also, sometimes you may come across values that you don't want to type again in your calculator (like non-recurring decimals). For these, use the store function on your calculator to get maximum accuracy. With TI-84 and 83s, you can save values as letters (X, Y, etc.). Hence, you can just write out your equation using these, and hence significantly reduce the risk of typing the number wrong, while saving yourself some time.

Step-by-step explanation:

Answer:

The answer is 10

Step-by-step explanation:

6a + 2b

6(1)+2(2)

6+4

=10

If the ordered pair (a, b) satisfies the inequality. y > x-4, three of these statements are
true. Which statement is NOT true?

Answers

Number one jjnhhhnnbbb=20

Please help me with all, I will mark brainliest as long as u tell me how u got those answers

Answers

2 3 6 is a function because they can past through the line and 1 4 5 is not function because they can past through the straight line

You can run 10 miles in 80 minutes. How far can you run in 2.5 hours?

Answers

Answer:

18.75 miles

Step-by-step explanation:

1 hour = 60 minutes

2.5 Hours = 150 minutes

10 miles _____> 80 minutes

x_______> 150 minutes

x= ( 150 * 10) / 80

= 1500/80

x= 18.75 miles

easy

Answer:

Step-by-step explanation:

10 miles- 80 minutes

            ?- 150 minutes

1500+80x

X= 10.75 miles

Number Theory- Find all sets of the two consecutive positive integers with a sum that is at least 8 and less less than or equal to 24.

Answers

Answer:

Step-by-step explanation:

Let the smaller number = x

Let the larger number = x + 1

(4,5)

(5,6)

(6,7)

(7,8)

(8,9)

(9,10)

(10,11)

(11,12)

what is tan 11pie divided by 6?

Answers

Answer:

1/6 tan(11 π) = 0

Alternate representations:

1/6 tan(11 π) = -1/6 cot((21 π)/2)

1/6 tan(11 π) = -1/6 cot((23 π)/2)

1/6 tan(11 π) = 1/(6 cot(11 π))

Step-by-step explanation:

A fast-food restaurant sold 54 burgers with cheese. If the ratio of burgers sold with cheese compared to without cheese was 9: 5, how many burgers did they sell total?

Answers

Answer:

Step-by-step explanation:

We can write an relationship for this as:

3

:

2

24

:

b

Where  

b

is the number of burgers sold without cheese.

We can rewrite the relationship as an equation and solve for  

b

:

3

2

=

24

b

2

3

=

b

24

24

×

2

3

=

24

×

b

24

48

3

=

24

×

b

24

16

=

b

b

=

16

The restaurant would of sold  

16

burgers without cheese with the information provided in the problem.

the 200th term of the arithmetic progression 10 97,94,91,.............is​

Answers

Answer:

-500

Step-by-step explanation:

Given sequence;

    97, 94, 91 ......

Unknown;

The 200th term of the sequence;

Solution:

Since we were given an arithmetic progression, we need to first find the common difference;

 Common difference  = second term - first term

                                     = 94 - 97  

                                     = -3

To find the 200th term, we use the expression below;

     Sn  = a + (n-1)d

   a is the first term

    n is the nth term

   d is the common difference

 S₂₀₀ = 97 + (200 - 1 ) x -3 = -500

Find the balance of an account after 7 years if &700 is deposited into an account paying 4.3% interest compounded monthly.

Answers

The required balance is $939.9

Given,

Time=7 years

Principal=700

Rate=4.3%

Compound Intrest:

Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

The formula of the compound interest is,

[tex]A=P(1+\frac{r}{100})^T[/tex]

Now, substituting the given values into the above formula we get,

[tex]A=P(1+\frac{r}{100})^T \\A=700(1+\frac{4.3}{100})^7\\ A=939.9[/tex]

Learn More about Compound Intrest:

https://brainly.com/question/21072972

say periodt as many times as you can will give brainly

Answers

Answer:

periodtperiodtperiodtperiodtperiodtperiodtperiodtperiodt

Step-by-step explanation:

periodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodttperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodttperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodttperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodteriodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperdtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodtperiodttperioodtperiodtperiodtperi

Answer:

anna oooppppddpkddkjdjdfhjndjd-

Step-by-step explanation:

¿De qué forma calcularía Luisa la medida de la tira bordada?

Answers

Do you have instructions or summmmm?

Solve eight and four eighths minus five and five sixths.

(Giving extra points on this one)

A) two and twelve forty eighths

B) two and thirty forty eighths

C) three and one fourteenth

D) three and twelve fourteenths

(Here is an image if needed) :

Answers

Answer:

B: 2 32/48

Step-by-step explanation:

8 4/8 - 5 5/6

Turn to fractions:

8 4/8 = 68/8

5 5/6 = 35/6

Common denominator: 24

68 x 3 = 204

8 x 3 = 24

35 x 4 = 140

6 x 4 = 24

Set-up:

204/24 - 140/24

Solve:

64/ 24

Simplifying to Mixed Number:

64/24 = 8/3 = 2 2/3 = 2 32/48

Answer:

b

Step-by-step explanation:

Susie has 26 baskets of apples. Each basket can hold 12 apples. Can Susie fit all her apples in her baskets?

Answers

Answer: Yes, Susie can fit all her apples in her baskets.

Step-by-step explanation: If she has 26 baskets filled of apples and can hold 12 apples each, then she can fill 2 baskets with apples and have a remainder of 2 apples left.

hey, I wanted to know if anybody was kind enough to help me solve this! I'm super confused and I just don't know what to do. please help me, it'll mean a lot to me. actually

Answers

Answer:

The answer should be B

need someone’s help with this please!!!

Answers

Answer:

Option 3

Step-by-step explanation:

Since lines a and b are intersecting, x+5=2x-5. Because they are vertical angles.

x+5=2x-5

2x-x=5+5

x=10

X=10



HahauajNaguajmanavshananahsus

Pat bounces a basketball 25 times in 30 seconds. At that rate, approximately how many times will Pat bounce the ball in 150 seconds?

Answers

125 times because 150 divided by 30 is 5 and 5 times 25 is 125

What is the answer for Expanding
2t(6t-3)

Answers

Answer:

Step-by-step explanation:

12t2 - 6t

In the equation
2
3
x
=
10
, what is the value of x?

Answers

Answer:

23/10 or 15

Step-by-step explanation:

PLEASE HELP ASAP!!!!

Write the slope-intercept form of the equation of each line. Identify the slopes y-intercept

Answers

Answer:

19) slope=2  y-intercept is 1   equation is y=2x+1

20) slope=-4  y-intercept is 4   equation is y=-4x+4

21) slope=-1/3  y-intercept is -5   equation is y=-1/3x-5

22) slope=-2/3  y-intercept is -5   equation is y=-2/3x-5

23) slope=-8  y-intercept is is -4   equation is y=-8x-4

24) slope=5  y-intercept is -3   equation is y=5x-3

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

2 3/9+3/7
fraction please answer fast​

Answers

Answer:

2 16/21

Step-by-step explanation:

Find the midpoint of the line segment from (0,4) to (-1,3)
MIDPOINT=

Answers

Answer:

Midpoint = (-0.5, 3.5)

Step-by-step explanation:

Describe 3 types of maps

Answers

Answer:

population-amount of people per sq ft

climate- the average climate in that are

physical- elevation, landmarks,

Step-by-step explanation:

4. The binomial 12x+15 is equivalent to
(1) 2(6x +15)
(3) 6(6x+9)
(2) 5(12x+3)
(4) 3(4x+5)

Answers

Answer is (4) 3(4x+5)

what is 5+5 and then divided by 8

Answers

Answer: 1.25

Step by step:

= 10/8

= 1.25

Look at this coordinate plane



Which equation can be used to find the y-coordinate of point B?




y/1=23


y/2=56


y−1/2=4/6


y−1/2=y−5/4

Answers

Answer:

Hrmm

Step-by-step explanation:

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