Help stuck on methods question

x=3

Explanation:

Let's write an equation for the area of this figure.

This figure can be divided into 2 rectangles, a vertical and horizontal rectangle.

Area of rectangle= length× breadth

Area of vertical rectangle= 6x

Length of horizontal rectangle= (7 -x) cm

Area of horizontal rectangle= x(7-x)

Since total area= 30 cm^2,

6x+ x(7-x)= 30

6x +7x -x^2= 30 (expand)

-x^2 +13x-30= 0 (bring all terms to one side)

x^2 -13x +30= 0 (divide by -1)

(x -10)(x -3)= 0 (factorise)

x -10= 0 or x -3= 0

x= 10 or x= 3

(reject)

We reject x=10 since from the diagram, x cm is less than 6cm.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: