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2 years ago

Using the equation below, find the slope and y-intercept of the equation it would create.

Mathematics

1 answer:

IRISSAK [1]2 years ago

4 0

Answer: m=-1, b=-2

Step-by-step explanation:

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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

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

Find the area of the rectangular playground

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

Find the value of x: 3(6x - 4x) = -30 (Provide Step-By-Step)

Olegator [25]

Answer:

x = -5

Step-by-step explanation:

Multiply 3 by (6x - 4x) = 18x - 12x

18x - 12x = -30

6x = -30

x = -30 /6

x = -5

5 0

2 years ago

Read 2 more answers

kali has a 6 centimeter ladder and puts the base of the ladder 2 meters away from the tree how high into the tree will the lader

weqwewe [10]

I am going to assume ‘centimetre’ was a typo.

A^2 + B^2 = C^2

C^2 - A^2 = B^2

32 = B^2

Square root both sides

B = 5.7m high

The ladder will reach 5.7 meters high

5 0

3 years ago

Need answers asap pls bae<3 ill mark you the whatever if you answer bae

ValentinkaMS [17]

Answer: Justin is shown in 15 pictures with friends, 6 with family, and 8 with only him

Step-by-step explanation: Hope this helps :)

5 0

2 years ago

For the following rectangular prism, find the length of the diagonal connecting A to B. Round to the nearest tenth.

meriva

Answer:

I think it is 192

Step-by-step explanation:

Volume of cube: 5 x 4 x 8 = 160

Area of diagonal: 160/2 = 80

Length of diagonal: 80 / 0.5 x 3 = 480

AB = 480 / 5 x 2 = 192

8 0

1 year ago