Lana is the oldest of four sisters. her youngest sister is half her age. the other two sisters are twins 2 years younger than lana. when the four sisters' ages are added together, the result is 45. if the youngest sister is n years old, what is n? will give meadel

If Lana's age is L, her youngest sister is L/2 (or 0.5L) and the twins L-2.  Add all these together (remember that there are two sisters who are L-2 years old):
0.5L + L-2 + L-2 + L = 45
Simplify the L's by adding them all together, we get:
3.5L - 2 - 2 = 45
3.5L - 4 = 45
Now add 4 to both sides:
3.5L = 49
Now divide both sides by 3.5
L = 49/3.5 = 14.  Now we know that Laura is 14, so her youngest sister must be 7.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

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