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4 years ago

Find the equation of the line specified. The line passes through the points ( 2, 1) and ( 5, 4).

Mathematics

2 answers:

Aleksandr [31]4 years ago

8 0

Answer:

y=x-1

Step-by-step explanation:

A line passes through the points (x,y) if they correspond to the equation so we have to prove the points with each of the given equations

a) y=x+1 replacing x with 2 we obtain

y=2+1= 3 ≠ 1 so it can´t be the equation

c) y=x-1 replacing x with 2 que obtain

y=2-1= 1 so we have that this equation passes through the point (2,1)

now we have to prove that it passes through (5.4)

So we repeat again replacing x with 5 so we have that

y=5-1=4 So it proves that it passes through the point (5,4)

Just to be sure let´s replace the point (2,1) in the other two equations

y=-2-1=-3≠1

y=2+3=5≠1

Hence the answer is C

lutik1710 [3]4 years ago

4 0

I THINK it might be y = x + 1, though i am not sure. Please do tell me if that is wrong or not.

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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

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

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