Beth simplified the expression 8 + 10 + 8 + 2 minus (4 times 1.4) minus (4 times 1.4) to find the perimeter of the figure on the grid. On a coordinate plane, a figure has side lengths of 8, 10, 8, 2, (4 times 1.4), (4 times 1.4).

What error did Beth make?
She found the area of the figure instead of the perimeter.
She subtracted the lengths of the diagonal lines instead of adding them.
She used 4 times 1.4 to represent the length of each diagonal line instead of 4.
She added the horizontal and vertical lengths instead of multiplying them.

- "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."

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.