Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, r, in beats per minute, can be approximated by the formulas

r = 143 - 0.65a for women
r = 165 - 0.75a for men,

where a represents the person’s age. if the desirable heart rate for a man is 135 beats per minute, how old is he?
a.
22.5 years old
b.
40 years old
c.
45 years old
d.
42.5 years old

b.   40 years.

Step-by-step explanation:

For men  R = 165 - 0.75a

When R = 135:

135 = 165 - 0.75a

0.75a = 165 - 135 = 30

a = 30 / 0.75

=  40 years.

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.