Rick's lumberyard has 360 yd of fencing with which to enclose a rectangular area. If the enclosed area is x yards​ long, express its area as a function of its length.

Answers

Answer 1

Answer:

180x - x²

Step-by-step explanation:

Since the yard has 360 yd. of fencing, hence the perimeter of Rick's lumberyard has 360 yd.

Given that the yard is x yards long. Let y represent the width of the yard. Hence:

Perimeter of the yard = 2(length + width) = 2(x + y)

Substituting:

360 = 2(x + y)

180 = x + y

y = 180 - x

Therefore the width of the yard is (180 - x) yard.

The area of the yard is the product of the length and the width, hence:

Area (A) = length * width

A = x * (180 - x)

A = 180x - x²

Answer 2

Expression for the area as a function of its length will be, Area = (180x - x²) square yards

It's given in the question,

Length of the fence with Rick's lumberyard = 360 yardsLength of the enclosed area = x yards

Since, length of the fence = Perimeter of the rectangular area

And Perimeter of the rectangular area = 2(length + width)

By substituting the values of area and the length in the expression,

360 = 2(x + width)

180 = x + width

Width = (180 - x) yards

Since, area of a rectangle is given by the expression,

Area = Length × Width

By substituting the values in the expression,

Area = x(180 - x)

        = (180x - x²) square yards

      Therefore, expression for the area in terms of its length will be, Area = (180x - x²) square yards.

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Related Questions

Triangle ABC IS dilated using the origin as the center of dllation to create triangle A'B'C'. What rule best represents the dilation applied to triangle ABC to ​

Answers

The scale factor is 3 so B would be your answer because all coordinates are multiplied by 3

PLEASE HELP!

I WILL MARK BRAINLIEST!

If ZY = 2x + 3 and WX = x+4, find WX.

Your answer will be so appreciated.

Answers

i need more info on this ? to answer.

Simplify the fraction to lowest terms.
56/
182

Answers

the answer to your question is 4/13.

Find the area of a circle with
radius, r = 5.52m.
answer rounded to 2 DP.​

Answers

Answer:

Step-by-step explanation:

Formula = A=πr2

Putting values in the equation

A = (3.14) (5.52)^2

= 95.73

Answer:

95.73

Step-by-step explanation:

2 decimal points is what the question MEANS:

formula for finding a cirlce (and this is not from the internet)

r^2 times pi

(5.52)^2 times pi

which (5.52) squared becomes a sickly: 30.4704 in decimals

lets say you WANT to keep the decimals, then multiply 30.4704 by 3.14159265359 and absolutely get every single decimal place added in and THEN round it to 2 decimal places (once i didn't do this, i got bad grades in math class)

the answer is 95.7255847919

the decimal place of this is 95.73 not 95.72 or something,

the answer is 95.73

Which equation represents the function y - 5 = –2(x+3) in slope-intercept form?
Oy= 2x + 1
Oy = 2x - 1
Oy= -2x - 1
Oy = -2x + 11
Oy = -23 - 11

Answers

Answer:

-2x-1

Step-by-step explanation:

when you graph the equation it gives you a decreasing slope with the y intercept of -1. the slope is 2 and since its decreasing it is -2. therefore its -2x-1

The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .

What is a straight line?

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

the function y - 5 = –2(x+3)

now, we have to find  in slope-intercept form.

now, we have,

function has a decreasing slope with the y intercept of -1. the slope is 2

and since its decreasing it is -2.

again, we have,

y - 5 = –2(x+3)

or, y = -2x - 6 + 5

or, y = -2x -1

here, slope = m = -2

and, y-intercept = c = -1

as, we know that,

slope-intercept form is: y = mx+ c

so, we get,  y = -2x -1

Hence, The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .

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Use slopes and y-intercepts to determine if the lines y=−2/3x+2 and −3x+2y=−4 are parallel.

Answers

Answer:

the answer is no

Step-by-step explanation:

y = -2/3x+2

2y = 3y-4

y = 3/2y-2

but here's a comment: it is perpendicular because it is it's opposite reciprocol

Graph the image of trapezoid ABCD after a translation 3 units left .​

Answers

Answer:

A: (-8, -1)

B: (2, -1)

C: (2, 5)

D: (-6, 5)

Step-by-step explanation:

If the trapezoid ABCD was able to translate 3 units to the left, we'll only need to calculate for all the input values!

Trapezoid in present:

A - -5

B - 5

C - 5

D - -3

Now move the units to the left!

Trapezoid in the future:

A - -8

B - 2

C - 2

D - -6

Then add the y values into the units

A: (-8, -1)

B: (2, -1)

C: (2, 5)

D: (-6, 5)

*************************************************

Tell wether x and y show a proportional relationship.

x 1 2 3 4
y 4 8 12 16

Answers

Answer:

They do because y is always 4 times of x.

Step-by-step explanation:

Factorise 12x3-9x2 please help

Answers

Answer:

18

Step-by-step explanation:

12x3=36=36-9x2=18=36-18=18

NEED HELP DUE IN 3 MINUTES!!!!

Answers

Answer:

y = -1/3 x+9

Step-by-step explanation:

First find the slope between the two points

m = ( -1 -8)/(2 - 5)

    -9/-3

   =3

We want a line that is perpendicular so it is the negative reciprocal

-1 /(3)

The slope of the perpendicular line is -1/3

y= mx+b where m is the slope and b is the y intercept

y = -1/3x+b

We have a point of (6,7)

7 = -1/3 (6) +b

7 = -2 +b

Add 2 to each side

7 +2 = -2+b+2

9 = b

The equation of the line is y = -1/3 x+9

1/3 x9







Bc I need help

A market research firm conducts telephone surveys with a 42% historical response rate. What is the probability that in a new sample of 375 telephone numbers, at least 150 individuals will cooperate and respond to the questions

Answers

Answer:

The right answer is "0.7823".

Step-by-step explanation:

Given that,

P = 42%

or,

  = 0.42

n = 375

[tex]\hat{P}[/tex] = 0.4

The z-score will be:

= [tex]\frac{\hat{P}-\mu_P}{\sigma_p}[/tex]

By putting the values, we get

= [tex]\frac{0.4-0.42}{\sqrt{\frac{0.42\times (1-0.42)}{0.375} } }[/tex]

= [tex]-0.784706[/tex]

hence,

The probability will be:

⇒ [tex]P(\hat {P}>0.04)[/tex] = [tex]P(z>-0.7847)[/tex]

                        = [tex]1-P(z<-0.7847)[/tex]

                        = [tex]1-0.21770[/tex]

                        = [tex]0.7823[/tex]

I neeed the answer plssss

Answers

Answer:

300km

Step-by-step explanation:

if 1 hr=80

then take 80 and multiply it by 3.75

hope this helps!

please give brainiest if you want<3

Answer:

300km

Step-by-step explanation:

What is half of 3/4 in fraction?

Answers

Answer:

3/8

Step-by-step explanation:

1/2 times 3/4= 3/8

i have two points, (3,5) and (2,18) i need to find the exponential equation using these points. how do i do this?

Answers

Answer:  y = (5832/25)*(5/18)^x

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

Explanation:

Any general exponential function is of the form

y = a*b^x

Plug in (x,y) = (3,5) and we get

y = a*b^x

5 = a*b^3

If you plug in (x,y) = (2,18), then we'll get this other equation

18 = a*b^2

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

So we have this system of equations

[tex]\begin{cases}5 = ab^3\\18 = ab^2\end{cases}[/tex]

From here, we divide the two equations straight down. The left hand sides divide to 5/18. The right hand sides divide to (ab^3)/(ab^2) which simplifies to b. The 'a' terms cancel and we subtract the exponents for the b terms.

Overall, we end up with b = 5/18

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

Use that value of b to find 'a'

18 = a*b^2

18 = a*(5/18)^2

18 = a*(25/324)

18*(324/25) = a

a = 5832/25

You could use the other equation as well to find 'a'

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

Therefore, the equation in y = a*b^x form is y = (5832/25)*(5/18)^x

To verify this, plugging in x = 3 should lead to y = 5. Similarly, plugging in x = 2 should lead to y = 18.

En una P.A. el t(18) es 125 y el t(36) es 251. hallar el término que ocupa el lugar 45.

Answers

Answer:

161 correo o no ............

Select the correct answer.
Which expression is equivalent to the glven expression?
(3m-4)^3(3m^5)
A. 81/m^2 B.27/m^7 C. 27/m^2 D.81/m^7

Answers

The answer for this question is D

The correct expression which is equivalent to the given expression is,

⇒ 81 / m⁷

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (3m⁻⁴)³ (3m⁵)

Now, We can simplify as;

⇒ (3m⁻⁴)³ (3m⁵)

⇒ (3³m⁻¹²) (3m⁵)

⇒ (27m⁻¹²) (3m⁵)

⇒ 81 m⁻¹²⁺⁵

⇒ 81 m⁻⁷

⇒ 81 / m⁷

Thus, The correct expression which is equivalent to the given expression is,

⇒ 81 / m⁷

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Which expression is equivalent to 5^15 x 5^5

Answers

Answer:

[tex]5^{15} * 5^{5}[/tex]

= [tex]25^{20\\}[/tex]

I would really appreciate if someone could answer this:)

Answers

Answer:

first you need to know that the the sum of the co-interior angle is  180 degree and the sum of the opposite side of  parallelogram is always equal.

now x+140=180(being co - interior angle)

or, x= 180-140

therefore, x =40 degree

y= 140 degree because sum of the opposite side of  parallelogram is always equal.

x= z=40 degree (sum of the opposite side of  parallelogram is always equal.

when you are again confused go in this link

 ----> https://www.scholr.com/ncert-solutions/consider-the-following-parallelograms-fi/40087/

plz mark me brainliest + thanks

Sally generates an input-output table using two rules. The input rule is “add 2 2” and the starting number is 3 3. The output rule is “add 4 4” and the starting number is 6 6. The table is shown. ​ ​ Which ordered pairs follow the same rules as the pattern in the table? Select two answer choices. A (9,12)(9,12) B (11,22)(11,22) C (15,25)(15,25) D (17,36)(17,36) E (21,42)(21,42)

Answers

9514 1404 393

Answer:

  B  (11, 22)

  E  (21, 42)

Step-by-step explanation:

The numbers in the input sequence are ...

  [tex]i_n=i_1+d(n-1)\\\\i_n=3+2(n-1) = 2n+1[/tex]

The numbers in the output sequence are ...

  [tex]o_n=o_1+d(n-1)\\\\o_n=6+4(n-1)=4n+2=2(2n+1)\\\\o_n=2\times i_n[/tex]

So, the ordered pairs we're looking for have an output value that is double the input value.

The two that match this characteristic are ...

  B(11, 22) and E(21, 42)

Simplify (2 1/6 - 1 2/3) - 2 2/3​

Answers

Answer:

[tex]- 2\frac{1}{6}[/tex]

Step-by-step explanation:

[tex](2\frac{1}{6} -1\frac{2}{3}) - 2 \frac{2}{3}[/tex]

[tex](\frac{13}{6} -\frac{5}{3}) - 2 \frac{2}{3}[/tex]

[tex](\frac{13}{6} -\frac{10}{6}) - 2 \frac{2}{3}[/tex]

[tex]\frac{3}{6} - 2 \frac{2}{3}[/tex]

[tex]\frac{3}{6} - \frac{8}{3}[/tex]

[tex]\frac{3}{6} - \frac{16}{6}[/tex]

[tex]- \frac{13}{6}[/tex]

[tex]- 2\frac{1}{6}[/tex]

Identify the x-intercept points of the parabola

Answers

Answer:

(3,0) and (-1,0)

Step-by-step explanation:

The X intercept are the point(s) where the line croses the X axis (the horizontal/leftright line). the points for this graphing system are always listed (x,y) so to find a certain point you find the X value then the Y value

Cindy took a multiple choice test. The ratio of number of problems Cindy got incorrect to the number of problems she got correct was 2:6. If Cindy missed 14 problems, how many problems did Cindy get correct?

Answers

Answer:

42

Step-by-step explanation:

Divide 14/2 *6 to get your ratio.

Hope this helps!

:)

Answer:

42

Step-by-step explanation:

Divide 14/2 *6 to get your ratio.

0.36% as a fraction in simplest form

Answers

Answer: 9/2500

Step-by-step explanation:

We start with turning it into a fraction:

0.36/100

Then, we turn every number into a whole number by multiplying by whatever the last decimal place is called (hundreth= x100)

36/10000

Lastly, we simplify as much as we can by finding the least common denominator. In this case, the smallest whole number both 36 and 10000 can be divided by is 4:

(36/4)/(10000/4)

= 9/25000

I would appreciate if someone could answer this

Answers

Answer:

x = 15

LN and MO both equal 43

Step-by-step explanation:

LN and MO are diagonals in rectangle

Diagonals of a rectangle are congruent Hence, 4x - 17 = 2x + 13

Now we solve for x

4x - 17 = 2x + 13

Add 17 to both sides

4x = 2x + 30

Subtract 2x from both sides

2x = 30

Divide both sides by 2

x = 15

Now we want to find the values of LN and MO

To do so we substitute 15 for x in it's given expression ( note: because LN = MO we only need to do this process once )

LN = 4x - 17

Substitute 15 for x

4(15) - 17

Multiply

60 - 17

Subtract

LN and MO = 43

Please answer this, I am confused (5^2)(7^2)(3^2)

Answers

Given:

The expression is:

[tex](5^2)(7^2)(3^2)[/tex]

To find:

The value of the given expression.

Solution:

We have,

[tex](5^2)(7^2)(3^2)[/tex]

On simplification, we get

[tex](5^2)(7^2)(3^2)=(25)(49)(9)[/tex]

[tex](5^2)(7^2)(3^2)=11025[/tex]

Therefore, the value of the given expression is 11025.

Which of the following functions has a rate of change that stays the same?
A. y=-4+10
B. y=1/2x^2
C. y=3^x
D. y=x^2+2

Answers

Answer:

The answer is A because the rest are parabolas

Please, I'm desperate need of help I will mark Brainliest to the one who answers with the full process! Gold will Bless You!

Two angles of a triangle are 85° and 65°, and the longest side of the triangle is 34 cm. How long is the shortest side? Include a labelled diagram.

Answers

Add 65 and 85

65+85= 150

Next subtract 180-150

The answer is 30, so that is the missing angle is 30.

The side opposite to 30 is the shortest side

Here I added the picture!

I NEED HELP NOW MY ASIGNMENT IS DUE BEFORE 8;00 PLZZZ HELP AND PUT A ANSWER THAT HASN'T BEEN USED(05.02)Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work.

Parallelogram with base of 14 feet, height of 12 feet, and triangle base of 3 feet.

Answers

Answer:

10 feet

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Area of parallelogram is

A = base of parallelogram x height of parallelogram

= 14 x 12 = 168 sq feet

Break parallelogram down into figures

There would be 2 triangles and 1 square

Area of 1 triangle = 0.5 (3 x 12) = 18

Area for 2 triangles = 2 x 18 = 36

Area of square = base x height

= 11 x 12 = 132

132 + 36 = 168

Area of parallelogram is 168 sq feet

Plz help me simply this

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt[5]{u^{10}*p^{15}}*\sqrt[4]{u^{16}*p^{18}}= \sqrt[5]{u^{2*5}*p^{3*5}}*\sqrt[4]{u^{4*4}*p^{16*2}}\\\\\\=\sqrt[5]{(u^{2})^{5}*(p^{3})^{5}}*\sqrt[4]{(u^{4})^{4}*p^{4*4}*p^{2}}\\\\=\sqrt[5]{(u^{2})^{5}*(p^{3})^{5}}*\sqrt[4]{(u^{4})^{4}*(p^{4)^{4}}*p^{2}}\\\\=u^{2}*p^{3} * u^{4}*p^{4}*\sqrt[4]{p^{2}}\\\\=u^{2+4}*p^{3+4}*\sqrt[4]{p^{2}}\\\\= u^{6}p^{7}\sqrt[4]{p^{2}}[/tex]

A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours

Answers

Answer:

The Sample Size Need To be at least 114

Step-by-step explanation:

According to the Question,

Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.

The Maximum Error(E) is given as 1.5 hours and the standard deviation(σ) is 6.2 hours.

Now, For 99% Confident the level of value α is 0.01.

α/2 = 0.01/2 ⇒ 0.005

Thus, From The table, We get that the value of [tex]Z_{alpha/2}[/tex] is 2.58.

Hence, the sample size n can be found as

n = {[tex]\frac{(Z_{alpha/2} * Standard Deviation)}{E}[/tex]}²

n = {2.58 × 6.2}² / 1.5²

n = 113.72 .

So, The Sample Size Need To be at least 114.

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