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2 years ago

HELPP ME PLEASE!!

Mathematics

1 answer:

otez555 [7]2 years ago

3 0

2 negative numbers multiplied together is always positive

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A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

If 3x + 2 = 4, what is the value of 6x – 4?

Andreas93 [3]

Answer:

Step-by-step explanation:

3x = 2

x = 2/3

plug in

12/3 - 4

4 - 4

4 0

2 years ago

Dr. Spike is a big fan of Bojangles and is particularly interested in the popularity of its celebrated wings dinner. Starting fr

Effectus [21]

Answer:

Step-by-step explanation:

If data is skewed then the upper and lower half have different amount of spread. Here there is no proof to say that data is not spread around mean or there are outliers. Therefore we can't say that the distribution of wings dinners sales in not normal.

6 0

3 years ago

Hyxetdryufgukhchfxrdtygujhftyuhuhyguhjygyu

nikklg [1K]

Answer:

so the answer is: eijieljnqwsmiqwmx

did i answer it correctly let me know

Step-by-step explanation:

Destroy your keyboard by smashing each random word on the poor broken keyboard

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3 years ago

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Use the properties of exponents to rewrite y=e^-0.75t in the form of a(1-r)^t

Ivahew [28]

Answer: y = (1 - 0.527)^t

Step-by-step explanation:

y=e^(-0.75t)

y=(e^-0.75)^t

y= 0.47236655^t

1 - 0.47236655 = 0.52763345

y = (1 - 0.527)^t

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2 years ago