A kite is inscribed in a rectangle. Everything outside of the kite is shaded. The points of the kite split the lengths of the rectangle into a length of 3x and x. The points of the kite split the height of the rectangle into lengths of x and x. The total length of the rectangle is 4 x and the height is 2 x. The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region?

2x2
4x2
6x2
8x2

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

f(x) is   are being squared

g(x) is   increasing by 2

h(x) is adding .25 each time

k(x) is taking the square root

f(x) and k(x) are exponential functions