HELP PLEASE !!!

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three h

neonofarm [45]

Answer:

50 ft by 75 ft
3750 square feet

Step-by-step explanation:

Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...

y = (300 -2x)/3

And the enclosed area is ...

A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)

This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.

The maximum area is enclosed when the dimensions are ...

50 ft by 75 ft

That maximum area is 3750 square feet.

_____

<em>Comment on the solution</em>

The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).

6 0

2 years ago

Give the algebraic expression by using variables and constant and arithmetic operations: i. Sum of the squares of x and y. ii.Pr

Olenka [21]

Answer:

a) x^2 + y^2

b) 9-xy

Step-by-step explanation:

Here, we want to write the algebraic statements as expressions;

a) The sum of the squares of x and y

The square of x is x^2

The square of y is y^2

The sum of the squares is x^2 + y^2

ii) Product of x and y subtracted from 9

The product of x and y is x * y = xy

Subtracting these from 9, we have;

9-xy

5 0

2 years ago

Ava graphs the function h(x) = x2 + 4. Victor graphs the function g(x) = (x + 4)2. Which statements are true regarding the two g

Firlakuza [10]

Answers:

Ava’s graph is a vertical translation of f(x) = x^2.

Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.

Ava’s graph has a y-intercept of 4.

Given:

Ava graphs the function $h(x) = x^2 + 4$ .

Victor graphs the function $g(x) = (x + 4)^2$

To find y intercept we plug in 0 for x

$h(x) = x^2 + 4$

$h(x) = 0 + 4$ = 4

So ,Ava’s graph has a y-intercept of 4.

Ava graphs the function $h(x) = x^2 + 4$

If any number is added at the end then the graph will be shifted up. 4 is added at the end so there will be vertical translation.

Hence , Ava’s graph is a vertical translation of f(x) = x^2. Also Ava moved 4 units up from f(x) = x^2 in a positive y- direction.

Victor graphs the function $g(x) = (x + 4)^2$

If any number added with x then the graph will be shifted left. the graph will be shifted in negative x direction.

7 0

3 years ago

Read 2 more answers

1.<br> Write a polynomial function in factored form with zeros at -2, 5, and 6.

Hatshy [7]

Answer:

f(x) = (x + 2) (x − 5) (x − 6)

Step-by-step explanation:

f(x) = (x − (-2)) (x − 5) (x − 6)

f(x) = (x + 2) (x − 5) (x − 6)

4 0

2 years ago

Pedro le dice a María si cambias los billetes de 10 € que tienes por billetes de 5 € y los billetes de 5 € por billetes de 10 €

Bad White [126]

Answer: Maria has 10 bills of 5€ and 10 bills of 10€.

She has a total of 150€.

Step-by-step explanation:

Let be "f" the number of 5€ bills that Maria has and "t" the number of 10€ bills that Maria has.

Set up a system of equations:

$\left \{ {{f+t=20} \atop {5f+10t=10f+5t}} \right.$

Use the Substitution method to solve the system of equations:

1. Solve for "f" from the first equation:

$f=20-t$

2. Substitute the equation obtained into the second equation and solve for "t".

Then:

$5(20-t)+10t=10(20-t)+5t\\\\100-5t+10t=200-10t+5t\\\\20t-10t=100\\\\t=\frac{100}{10}\\\\t=10$

3. Substitute the value of "t" into the equation $f=20-t$ and evaluate:

$f=20-10\\\\f=10$

Therefore, Maria has 10 bills of 5€ and 10 bills of 10 €.

So the total amount of money she has, is:

$Total=10(5)+10(10)=150$

She has a total of 150€.

5 0

3 years ago