Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from the drop-down menus to correctly complete the statements.

Circle Q is
Choose...
units to the
Choose...
of circle P and
Choose...
units
Choose...
it. Circle Q has
Choose...
circle P.

Circle Q is 2 units to the right of circle P and 10 units above it. Circle Q has a longer radius than circle P.

Step-by-step explanation:

A circle with center (h, k) and radius r has equation ...

(x -h)^2 +(y -k)^2 = r^2

Your circles have the following center and radius:

circle P: center (-4, -7), radius 4

circle Q: center (-2, 3), radius 5

Then the appropriate comparison is ...

Circle Q is 2 units to the right of circle P and 10 units above it. Circle Q has a longer radius than circle P

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.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.