The distributive property: a(b + c) = ab + ac
127 × 32 = 127 × (30 + 2) = 127 × 30 + 127 × 2 = (130 - 3) × 30 + (130 - 3) × 2
=(130)(30) - (3)(30) + (130)(2) - (3)(2) = 3900 - 90 + 260 - 6
= 3810 + 254 = 4064
127 × 32 = (130 - 3) × 32 = 130 × 32 - 3 × 32 = 130 × (30 + 2) - 96
= (130)(30) + (130)(2) - 96 = 3900 + 260 - (100 - 4) = 4160 - 100 + 4
= 4060 + 4 = 4064
9514 1404 393
Answer:
1. b. The common difference is 0.39
2. no good answer (Zach's method is exponential; Victoria's is linear)
Step-by-step explanation:
1. The differences in mileage are ...
24.39 -24 = 0.39
24.78 -24.39 = 0.39
25.17 -24.78 = 0.39
The common difference is 0.39.
____
2. Zach's monthly times are ...
10, 20, 40, 80
The differences are ...
10, 20, 40
The ratios are ...
20/10 = 40/20 = 80/40 = 2
Zach's times have a common ratio, so are exponential.
__
Victoria's monthly times are ...
35, 50, 65, 80
The differences are ...
15, 15, 15
Victoria's times have a common difference, so are linear.
__
The choices are ...
a. both exponential; common factor . . . . correct for Zach; not for Victoria
b. Zach's is linear (has equal factor) . . . incorrect
c. both exponential; common difference . . . incorrect
d. Victoria's is linear . . . . correct for Victoria
Choice D describes Victoria's method. Choice A is correct regarding Zach's method, but incorrect regarding Victoria's.
Choices B and C are not self-consistent, so are incorrect on their face.
There is no good choice.
So,
We know that we cannot add or subtract quantities of the same kind.
-18xy can only be added/subtracted to 4yx, which is the same as 4xy. The result would be -14xy, or -14yx.
The correct option is B.
