An image of two concentric circles is shown with r2 = 6 and r1 = 2: in order to prove the two circles are similar, the radius r2 was decreased to make the circles congruent. what is the scale factor used in the above image?

The radius of the Outer circle (with r₂) is 6 and the radius of the inner circle (with r₁) is 2. When objects are similar, they have a proportional relationship. If we take the outer circle and squeeze by one third, we get a radius of 6 x 1/3 = 2. On the other hand, if we start with the inner circle and stretch it by 3, we get a radius of 2 x 3 = 6.

Thus, to make r₂ similar, we use a scale factor of 1/3. The third choice is best.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system