Which of the following equations describes a circle with radius 10 that passes through the origin when graphed in the xy-plane?

Which of the following equations describes a circle with radius 10 that passes through the origin when graphed in the xy-plane?

A) (x – 5)² + (y+5)² = 10

B) (x – 5)² + (y+5)² = 100

C) (x – 10)² + (y+10)² = 10

D) (x – 5√2)² + (y+5√2)² = 100

Clearly, A) is out because that one does not have a radius of 10. What is the most time-efficient way to solve this? Sketch and eyeball?

In the xy-plane what is the slope of the line that passes through the origin and makes a 42° angle with the positive x-axis? A. 0.67 B. 0.74 C. 0.90 D. 1.11

Trigonometry does the trick here. Below is that line making a 42° angle with the positive x-axis. I’ve also drawn a dotted segment to make myself a neat little right triangle. Remember that slope is rise over run—how high the line climbs divided by how far it travels right. In this case, the dotted segment (more…)

In the xy plane above, f and g are functions defined by f(x)=abs[x] and g(x)=-abs[x] + 3 for all values x. What is the area of the shaded region bounded by the graphs of the two functions?

Hi mike! This question is from the May 2015 SAT.

(will post photo)

In the xy plane above, f and g are functions defined by f(x)=abs[x] and g(x)=-abs[x] + 3 for all values x. What is the area of the shaded region bounded by the graphs of the two functions?