Mathematics High School

A farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). The farmer has
30 feet of fence and wants the garden to have an area of 108 sq-feet. What should the dimensions of the
garden be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides);
the length with be the longer dimežision (needing one side). Additionally, the length should be as long as
possible.)

Answers

Answer 1

length×width = 108

length + 2×width = 30

length = 30 - 2×width

using that in the first equation

(30 - 2×width)×width = 108

-2×width² + 30×width - 108 = 0

the general solution to such a quadratic equation like

ax² + bx + c = 0

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-30 ± sqrt(30² - 4×-2×-108))/(2×-2) =

= (-30 ± sqrt(900 - 864))/-4 =

= (-30 ± sqrt(36))/-4 = (-30 ± 6)/-4

width1 = (-30 + 6)/-4 = -24/-4 = 6 ft

width2 = (-30 - 6)/-4 = -36/-4 = 9 ft

for width = 6 ft

length = 30 - 2×width = 30 - 12 = 18 ft.

for width = 9 ft

length = 30 - 2×width = 30 - 18 = 12 ft

given the request that the length sound be as long as possible,

width = 6 ft

length = 18 ft

is our solution.

Related Questions

solve the following equation 23 + 23 = 5y + 11

Answers

Answer:

Step-by-step explanation:

Since 23 + 23 = 46

We just have to multiply 5 by something. 11 + 5 x 7 = 46

Y is = 7

btw im in middle school

your answer could be 72

i did a lot of math

and if you have what y means to me its y = 3 so i did 5*3

PLEASE HELP FASTTT ILL MARK BRAINLIEST

Answers

Answer:

[tex]2\sqrt{2}[/tex]

Doing RSM I see... lol gl. (tell me if this is wrong, I'll correct it if it is) :]

Step-by-step explanation:

h(6)=2

g(2) = [tex]\sqrt{2\\}[/tex]

f(sqrt2) = [tex]2\sqrt{2}[/tex]

Eric orders 3 large cheese pizzas. There is a $2 delivery fee for each pizza. He pays a total of $42. Which equation can be used to find the price, r, of each pizza?

Answers

we have that he paid 4 dollars due the delivery. So each pizza costs

[tex]\frac{38}{2}=19[/tex]

so the equation to find the price r is

[tex]r=\frac{42-4}{2}[/tex]

A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.
a. Which information is not needed to compute the bill after tax and tip?
b. What was the total bill?

Answers

well, the bill was actually "x", which oddly enough is the 100%, but we also know that the tip was $1.05 and that's 15% of the whole bill plus tax.

so if we know that 1.05 is 15% of "x", what the dickens is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1.05 & 15\\ x& 100 \end{array} \implies \cfrac{1.05}{x}~~=~~\cfrac{15}{100} \\\\\\ 105=15x\implies \cfrac{105}{15}=x\implies 7=x[/tex]

well, as you can see, we know the tax was 8%, but, it doesn't really matter if it had been 25% or who knows, so long we know that 1.05 is 15% of the whole smack.

please help asap
during a snow storm the temperature drops from 0 degress f to - 12 degress f in 3 hour. on averge by how many degress is the temperature changing per hour?

A, -4f

B. 12f

C. 15f

D. -9f

Answers

The average change per hour is: -4 F/h

So the temperature decreases by 4 degrees Fahrenheit each hour.

How to get the average change in temperature?

To get the average change in degrees per hour, we need to take the quotient between the change in temperature and the number of hours in which this happens.

We know that initially the temperature is 0F

The final temperature is -12F

and this happens on an interval of 3 hours, then the average change per hour is:

(-12F - 0F)/3h = -12F/3h = -4 F/h

Learn more about average rates of change:

https://brainly.com/question/8728504

#SPJ1

Alvin's
age Is three times Elga's age. The sum of their ages Is 96. What Is Elga's age?
years old

Answers

Answer: Elga is 16 years old

Step-by-step explanation: so first you divide 96 by 2 and get 48, 48 divided by 3=16,

please mark brainliest if this helps :)

Answer: 24 years old

Work Shown:

x = Elga's age

3x = Alvin's age since he is 3 times older

x+3x = 4x = sum of their ages

4x = 96

x = 96/4

x = 24 is Elga's age

3x = 3*24 = 72 is Alvin's age

Check: 24+72 = 96 which confirms the answer.

x = -4z - 19
y= 5x + z - 4
-5y - z = 25

Answers

Answer:

x = 1, y = -4, z = -5

Step-by-step explanation:

Solve the following system:

{x = -4 z - 19 | (equation 1)

{y = z + 5 x - 4 | (equation 2)

{-z - 5 y = 25 | (equation 3)

Express the system in standard form:

{x + 0 y + 4 z = -19 | (equation 1)

{-(5 x) + y - z = -4 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Swap equation 1 with equation 2: