Answer:
The point of intersection is (6, 8). This indicates that in 6 days, asteroid A and B will collide at a point that is 8 million miles away from asteroid A's current position and 12 million miles away from asteroid B's current position.
Answer:
1 to 3
Step-by-step explanation:
3 blue: 9 yellow
Divide each side by 3
3/3 : 9/3
1 blue: 3 yellow
1 to 3
The answer is B.
When you set up a ratio of all the corresponding sides, the ratios all equal 2:1
Answer:
Prove set equality by showing that for any element
,
if and only if
.
Example:
.
.
.
.
.
Step-by-step explanation:
Proof for
for any element
:
Assume that
. Thus,
and
.
Since
, either
or
(or both.)
- If
, then combined with
,
. - Similarly, if
, then combined with
,
.
Thus, either
or
(or both.)
Therefore,
as required.
Proof for
:
Assume that
. Thus, either
or
(or both.)
- If
, then
and
. Notice that
since the contrapositive of that statement,
, is true. Therefore,
and thus
. - Otherwise, if
, then
and
. Similarly,
implies
. Therefore,
.
Either way,
.
Therefore,
implies
, as required.
Answers: Choice A and Choice E
0.82B and B-0.18B
========================================================
Explanation:
B is the cost of the game (some unknown amount). Subtract off 0.18B to indicate a 18% reduction in the price. That's how we get choice E.
Simplifying choice E leads us to choice A. Notice that 1 - 0.18 = 0.82; which represents 100% - 18% = 82%. After the discount, Bo is paying 82% of the original price.
Side note: Choice B indicates an 18% increase. Choices C and D don't represent percentage decreases (rather they're decreasing by a fixed amount regardless of what B is).