Answer:
Santana scored 12 2-point baskets.
Step-by-step explanation:
Given that Santana converted 22 baskets in his last basketball game, totaling 54 points at the end of the game, and that in basketball the baskets are worth 2 and 3 points, to determine the number of baskets of each value that Santana converted, the following logic reasoning must be done:
If all the baskets were 2 points, the total of points made would have been 44 (22 x 2). Now, there are 10 more points, which are attributable to the 3-point baskets (that is, each extra point is a 3-point basket). Therefore, since 54 minus 44 equals 10, Santana made 10 3-point baskets and 12 2-point baskets.
This is verified through the following calculation:
(10 x 3) + (12 x 2) = X
30 + 24 = X
54 = X
Answer:
3
Step-by-step explanation:
1/2 is 3 times 1/6, because 3/1
and 3/6 is the same as 1/2. Thus, he can make 3 bowls of granola.
We are told that circle C has center (-4, 6) and a radius of 2.
We are told that circle D has center (6, -2) and a radius of 4.
If we move circle C's center ten units to the right and eight units down, the new center would be at (-4 + 10), (6 - 8) = (6, -2). So step 1 in the informal proof checks out - the centers are the same (which is the definition of concentric) and the shifts are right.
Let's look at our circles. Circle C has a radius of 2 and is inside circle D, whose radius is 4. Between Circle C and Circle D, the radii have a 1:2 ratio, as seen below:

If we dilate circle C by a factor of 2, it means we are expanding it and doubling it. Our circle has that 1:2 ratio, and doubling both sides gives us 2:4. The second step checks out.
Translated objects (or those that you shift) can be congruent, and dilated objects are used with similarity (where you stretch and squeeze). The third step checks out.
Thus, the argument is correct and the last choice is best.