Determine whether a tangent line to circle O is shown in the diagram, for AB = 7, OB = 3.75, and AO = 8. Explain your reasoning. (The figure is not drawn to scale.)

The line AB is not tangent to circle O

Step-by-step explanation:

we know that

If AB is tangent to circle O at point B

then

AB is perpendicular to OB (radius) and ABO is a right triangle

Verify

Applying the Pythagorean Theorem

substitute the given values

-----> is not true

so

The triangle not satisfy the Pythagorean Theorem

therefore

The line AB is not tangent to circle O

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.