The length of a rectangular park is twice its width.
The park is surrounded by a 3-foot-wide path.
Write a quadratic function to represent the total
area of the park and the path.

Answers

Answer 1

Answer:

[tex]A=2x^2+18x+36[/tex]

Step-by-step explanation:

Quadratic Function

It's given the length of a rectangular park is twice its width.

Let's call:

x = width of the rectangular park

2x = length of the rectangular park

The park is surrounded by a 3-foot-wide path. This path adds 3 ft twice to both dimensions, i.e.:

x+3+3=x+6 width of the park and the path

2x+3+3=2x+6 length of the park and the path

The total area is:

A=(x+6)(2x+6)

Operating:

[tex]A=2x^2+6x+12x+36[/tex]

[tex]\boxed{A=2x^2+18x+36}[/tex]


Related Questions

HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!!!!!!

Answers

Answer:

a. $73.75b. 57 rides

Step-by-step explanation:

a.

Initial value of the pass is $100

From the difference in values we can see the cost of one ride is $1.75

The formula:

P(r) = 100 - 1.75r, P- the value of the pass, r- the number of rides

Value of the pass after 15 rides:

P(15) = 100 - 1.75*15 = 73.75

b.

Number of possible rides:

0 = 100 - 1.75r1.75r = 100r = 100/1.75r = 57 (rounded to the whole number)

Explain how to solve 2(x-1)=-200

Answers

I attached the answer below. Please take a look. You're welcome.

A Cake mix contains sugar and flour. The mass of the sugar is 14 2/7% of the mass of the flour. What is the percent of flour in the cake mix ?
:D

Answers

Answer:

700/8% or 87.5%

Step-by-step explanation:

Answer:

700/8% or 87.5%

Step-by-step explanation:

Ur welcome

Yea I don't know this app But I heard people leaked my phone number and calling and someone saying I'm a actor yes... Please stop it it's annoying and I'm only 13

Answers

Answer: Hmm I don't know that you're an actor and hey u can report them if they leaked your phone number  

Step-by-step explanation:

Answer:

Yes. I heard, but I don't know know who are you. Don't worry I will keep an eye out.

Step-by-step explanation:

The sum of two numbers is 8. The difference between the two numbers is 2. What are the numbers? x + y = 8 x - y = 2 *Use the tables to list the possibilities

Answers

Answer:

x=5 y=3

Step-by-step explanation:

x+y=8 1

x-y=2 2

x+y=8

y=8-x

substitute into 2

x-(8-x)=2

x-8+x=2

2x=10

x=5

substitute x into 1

5+y=8

y=3

5+3=8

5-3=2

I need help ... please help

Answers

Answer:

the answer would be 35

Step-by-step explanation:

when u go up, you go up by 35 and run 1. therefore the answer is 35

how to do area for this problem​

Answers

the answer is 568 in in degrees tysm

find the greatest common factor of the following:
c) 2xy⁵, 6x³y³
d) 6x²y², 9xy³, 3x⁴y⁴
f) 10ab, 20bc, 30ca​

Answers

Answer:

c

[tex]2x {y}^{3} [/tex]

d

[tex]3x {y}^{2} [/tex]

f.10

Step-by-step explanation:

C. first you have to find the HCF of 2 and 6 then the HCF of

x and

[tex] {x}^{3} [/tex]

and

[tex] {y}^{5} and \: {y}^{3} [/tex]

Then:

[tex]2x {y}^{3} [/tex]

D.first you have to find the HCF of 6 ,9 and 3 then the HCF of

[tex] {x}^{2} \: \: x \: and \: {x}^{4} [/tex]

then the HCF of

[tex] {y}^{2} \: \: {y}^{3} and \: {y}^{4} [/tex]

then:

[tex]3x {y}^{2} [/tex]

F. I'm not sure but 10

if its helpful ❤❤❤❤

THANK YOU.

Mrs. Femandez starts out with $255 in her checking account. She deposits $35 on Monday. Tuesday afternoon she
writes a check for $75
Which expression could be used to find Mrs. Femandez's new account balance?

Answers

Answer:

255+35-75

Step-by-step explanation:

Since we are trying to find the account balance, we consider anything in or going to the account to be positive.

255 is positive since it is in the account

35 is positive since it is going into the account

75 is negative because it is going out of the account

so the final expression to express the amount is the checking account would be 255+35-75

Please help with these questions there due today.

Answers

q5=2 q6=5 q7=12 q8=2

Round each number to the nearest hundred and then estimate the answer.
then
349 + 1,978
2,300
2,400
2,500
2,200

Answers

Answer:

300 + 2,000 = 2,300

Step-by-step explanation:

349 = 300

1,978 = 2,000

because the 4 is less than 5 and any number greater than 5 is rounded up and any number less than 5 is rounded down

solve for x please. this if for geometry

Answers

Answer: 76

Step-by-step explanation: 104 + 76 = 180

1) Alex bought some chips and pop for his class party. He bought a total of
32 items. Each bag of chips cost $0.75 and each bottle of pop cost $2.19.
He spent a total of $39.84. How many bags of chips and how many bottles
of pop did he buy?

Answers

Answer:

21 bags of chips and 11 bottles of pop

Step-by-step explanation:

(0.75 × 21)+(2.19 × 11) = $39.84

Answer:

18

Step-by-step explanation:

Divide the 39.84 to 2.19 because the question was find how much pop bought

What is the initial value of the function represented by this graph?

Answers

Answer:

We conclude that the initial value of the function is 6.

Hence, option D is correct.

Step-by-step explanation:

The initial value of the function can be determined by setting x = 0 and determining the corresponding y value.

In other words, the initial value is basically the y-intercept of the graph.

It is the output value when the input value x = 0.

Given the graph, it is clear that:

at x = 0, y = 6

Thus, at x = 0, the value of y is 6.

i.e. the y-intercept b = 6.

Therefore, we conclude that the initial value of the function is 6.

Hence, option D is correct.

Answer:

6

Step-by-step explanation:

The initial value is the y-intercept or where the line crosses the y axis.

Solve for X

[tex]lnx^{2} =-2[/tex]

please show steps

I have the answer,

I just want to know how to do this :)

Answers

Answer:

[tex]x = \pm e^{-1}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Algebra I

Solving quadraticsMultiple roots

Algebra II

LogarithmsEuler's number e

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle ln(x^2) = -2[/tex]

Step 2: Solve for x

Raise both sides by e:                    [tex]e^{\displaystyle ln(x^2)} = e^{-2}[/tex]Simplify equation:                           [tex]x^2 = e^{-2}[/tex]Square root both sides:                 [tex]x = \pm e^{-1}[/tex]

Answer:

Step-by-step explanation:

lnx^n=nlnx

[tex]\ln x^2=-2\\2\ln x=-2\\\\\ln x=-1\\\\x>0\\x=e^{-1}\\or~x=\frac{1}{e}[/tex]

Carlos drove to the train station and back. The trip there took five hours and the trip back took four hours. What was Carlos' average speed on the trip there if he averaged 68 mph on the return trip?

Answers

Answer: 54.4 mph

Step-by-step explanation:

First find the distance to the train station. If it took Carlos 4 hours to come back driving at 68 mph, the distance is:

= Speed * time

= 68 * 4

= 272 miles

This means that Carlos drove for 5 hours to cover 272 miles the first time. His average speed was therefore:

= Distance / time

= 272/5

= 54.4 mph

4/-2 flipped over the x axis

Answers

Answer:

I suppose that here we have:

"(4, - 2) flipped over the x-axis"

Regardless of that, i will answer this in a kind of general way.

When we have a point (x, y) and we do a reflection over the x-axis (or the line y = 0, is the same) the reflected point will be (x, - y)

If we instead had a reflection over the y-axis (or the line x = 0) the reflected point will be (-x, y)

Then if we have the point (4, -2) and we have a reflection over the x-axis, the sign of the y-component needs to change.

Then the reflected point will be (4, -(-2)) = (4, 2)

The original price of last year's gaming system was $699. It is now selling at a 19% discounted price. What is the sale price?

Answers

Answer:

$566.19

Step-by-step explanation:

If there is a 19% discount, the product is selling at 100-19=81% of the original price. Multiply and you get- 699*(81/100)=566.19 :)

Please help if you can :)
(98 ÷ 14 + x - 9/ 24) × 40 = 480

(the slash is a fraction of x-9 over 24)

Answers

hi! im chimken and i have your answers!

x = 43/8

( 98 ÷ 14 + x - 9 / 24 ) • 40 = 480

( 7 + x - 9 / 24 ) • 40 = 480

( 53 / 8 + x ) • 40 = 480

265 + 40x = 480

40x = 480 - 265

40x = 215

x = 43 / 8

i hope this helped! have a good day! :)

praise bingus!

Answer: x = 43/8

HOPE THIS HELPS

Complete the statement. Round to the nearest hundredth if necessary.

14 m= ft

Answers

14 m = 45.93 ft

(1 m = 3.28 ft)

In a group of 20 students, 8 have brown eyes. What percent of the students have brown eyes?​

Answers

8/20 = 4/10 = 0.4

0.4 x 100 = 40

40%

Answer:

40%

Step-by-step explanation:

What is the y-intercept of the equation y=3/2x+6?

Answers

Answer:

(0, 6)

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

y = 3/2x + 6

Step 2: Break Function

Identify Parts

Slope m = 3/2

y-intercept b = 6

The length of a rectangular cement patio is 3 feet less than three times the width. The sum of the length and width of the patio is 21 feet. Find the length of the patio.

Answers

Answer: The length is 15 feet.

Step-by-step explanation:

L = 3w - 3 (length is 3 feet less than three times the width)21 = w + (3w -3)21 = 4w - 3 (add like terms)24 = 4w (substract 3 from both sides)6 = w <-- width

But, the problem is asking for the length...

L = 3w - 3L = 3(6) - 3L = 18 - 3L = 15 ft

pls help I don't get this

Answers

Answer:

yeah same

Step-by-step explanation:

Answer:

The first and fourth answer.

Step-by-step explanation:

There are eight fluid ounces in one cup. One cup has eight fluid ounces.

Please help me on this and thank you!

Answers

Answer:

D

Step-by-step explanation:

We open it up, so 2/3x + -3 + -2 -1/3x, -3 + (-2) = -5.

2/3x - 1/3x - 5, 2/3x - 1/3x = 1/3x

Our final answer is 1/3x - 5

The ratio of kids to adults at a school festival is 11 : 7. Suppose there are a total of 810 kids and adults at the festival. How many adults are at the festival?

Answers

Answer:

315

Step-by-step explanation:

So with the ratio, you can tell that 11/18 of the people at the festival are kids, and 7/18 are adults.

Since you want to find the number of adults, just multiply.

7/18 x 810

You can cross multiply to get rid of 18 and 810 will simplify into 45. So then you are left with multiplying

7 x 45

=315

So, 315 is your answer

Answer: 315 Adults.

Step-by-step explanation:

Let the number of adults is x.

Then the number of kids is (810-x).

The ratio of kids to adults is

810 - x/x = 11/7

It is your basic equation, which you get from the condition.

To solve it, cross multiply; then simplify

7*(810-x) = 11x

7*810 - 7x = 11x

7*810 = 11x + 7x

7*810 = 18x

x = 7 x 810/18 = 315.

✨1 kai 1 poso kanei✨

Answers

Answer:

i'M bOuTA.. DOIVE

Explanation:

Who can answer this ??

Answers

Answer:

I believe the answer is B. nonlinear

Step-by-step explanation:

A committee must be formed with 5 teachers and 4 students. If there are 6 teachers to choose from, and 15 students, how many different ways could the committee be mad?

Answers

Answer:

8190 ways

Step-by-step explanation:

Given

[tex]Teachers = 6[/tex]

[tex]Students = 15[/tex]

Selection

[tex]Students = 4[/tex]

[tex]Teachers = 5[/tex]

Required

Number of ways of selection

4 students can be selected from 15 students in:

[tex]Students= ^{15}C_4[/tex]

Similarly.

5 teachers can be selected from 6 teachers in:

[tex]Teachers= ^{6}C_5[/tex]

So, the required number of selection is:

[tex]Selection = ^{15}C_4 * ^6C_5[/tex]

Apply combination formula:

[tex]Selection = \frac{15!}{(15-4)!4!} * \frac{6!}{(6-5)!5!}[/tex]

[tex]Selection = \frac{15!}{11!4!} * \frac{6!}{1!5!}[/tex]

[tex]Selection = \frac{15*14*13*12*11!}{11!*4*3*2*1} * \frac{6*5!}{1*5!}[/tex]

[tex]Selection = \frac{15*14*13*12}{4*3*2*1} * \frac{6}{1}[/tex]

[tex]Selection = \frac{32760}{24} * 6[/tex]

[tex]Selection = 1365 * 6[/tex]

[tex]Selection = 8190[/tex]

A telephone company charges its customers per minute to make long-distance calls. The cost, c, can be represented by c = .12m where m is the number of minutes. Which type of number is most reasonable for the domain of the situation?

Answers

Answer:

m ≥ 0

Step-by-step explanation:

Since the cost is represented by c = 0.12m, the domain should be a positive number, this is because number of minutes can't be written in negative. Therefore, the most reasonable number for the domain would be the set of positive whole numbers which means, m≥0.

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