A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?

Answer:

Step-by-step explanation:

There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:

P = 2w + l; solving for l and filling in our length of fencing gives us:

l = 148 - 2w

The area then for this will be:

A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:

[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:

[tex]A=-2w^2+148w[/tex]

The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.

To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:

[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:

[tex]-2(w^2-74w)=0[/tex]

The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:

[tex]-2(w^2-74w+1369)=...[/tex]

But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:

[tex]-2(w^w-74w+1369)=-2738[/tex]

The left side can be simplified down to a perfect square binomial:

[tex]-2(w-37)^2=-2738[/tex]

Now we'll add over the -2738:

[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.

if x = 2 and y = 6 , evaluate the following expression:

100-3(3y-4x)

(Tricky question, so be careful, not as obvious as it seems)
(NO LINKS OR I WILL REPORT)

In Middletown, Main Street and Market Street are parallel to each other. Patrick Street intersects Market Street to form a 76° angle at the northeast corner, as shown in the figure below. What is the measure of the angle formed at the southeast corner of Main Street and Patrick Street? (Note: Each street is straight and has the same uniform width.)
I WILL GIVE OUT BRAINLIEST IF CORRECT!

A. 76°
B. 90°
C. 104°
D. 142°
E. 152° (NOT E)!

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n a study of academic procrastination, it was determined that for a random sample of 18 undergrad students at a mid-size public university, the mean time spent studying for the final exam in an intro statistics course was 7.74 hours with a standard deviation of 3.40 hours. Suppose we wish to compute a 95% confidence interval for the mean time spent studying for the intro statistics final exam by all students. The margin of error for this confidence interval would then be calculated using the critical value (c) determined in the previous question as: (Don't worry if your sample size changed- use the one given here).

(OFFERING 50 POINTS!) PLEASE HELP

United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different
production capacity (in tons per day) for each grade, as follows:
Mill
Aluminum
Grade 1 2
High 6 2
Medium 2 2
Low 4 10
The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5
tons of low-grade aluminum. It costs United $6,000 per day to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know the
number of days to operate each mill in order to meet the contract at the minimum cost.
Formulate a linear programming model for this problem.

i need helpppppppp ITSSSSSSSSSSSSSSSSSSSSSSS URGETTTTTTTT HELPPPPPPPPPPPPPPPP

Which is larger, a pound or a kilogram?

UVT equals what?....

In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan.

a. If they put a big ad in the newspaper asking people to log their opinions on the PTA Web site what kind of bias might they encounter.

1. response bias due to desire to give acceptable answers
2. nonresponse bias
3. bias due to the use of a voluntary response sample
4. bias due to a poor sampling frame resulting in undercoverage
5. no bias

b. If they randomly select one of the elementary schools and contact every parent by phone, what kind of bias is there?

1. bias due to the use of a voluntary response sample
2. response bias due to desire to give acceptable answers
3. undercoverage bias due to a poor sampling frame
4. no bias
5. nonresponse bias

c. Suppose they randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling was done?

1. stratified sampling
2. convenience sample
3. simple random sampling
4. voluntary response sample

Two accounts earn simple interest . The balance y in dollars in account A after x years can be modeled y = 20x + 400

Image not writing all that.

PLEASE ANSWER ASAP FOR BRAINLEST, REALLY EASY QUESTION!!!!!!!!!!!!!!!!!!!!!!!

The population of a country has been increasing for several decades. In 1990, the population was about 263 million people In 2014, the population was about 307 million people Determine the percent in + The country's population increased by about % during this time period


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Please answer the question in the pic and make the answer clear pleaseeeee I'm giving brainliest out as welll

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Natalie can type 54 words per minute when transcribing an audio recording. Natalie needs to transcribe an audio recording with 7,938 words.

How many minutes will it take Natalie to transcribe the recording?

Enter your answer in the box.

min

100
100
Students, drow anywhere on this slide!