Suppose you transform a square by increasing one side by 12 units and decreasing the other side by 8 units. If the area of the resulting rectangle equals 44 how many units long was the side of the original square?

The the side of the original square is 10 units

Step-by-step explanation:

Take the facts given to set up an equation:

(x +12)(x-8) = 44  Foil and create a quadratic equation

  subtract 44 from both sides so it's equal to 0, then factor.

 -10 × 14 satisfies product of 140 and difference of 4

(x + 14)(x - 10) =0  Set each factor equal to 0, and solve for x

x + 14 =0  x = -14 not viable as real polygons cant have negative side values.

x - 10 = 0  x = 10 This works.

Prove by substituting in original equation

(10 + 12)(10 - 8) = 44   22 × 2 = 44  True!

The original square was 10 x 10 units.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."