Response:
Initial step=13x+7x=18+42
Sequential breakdown:
13x-42=18-7x
First step
Combine like terms in the equation
13x+7x=18+42
20x=60
x=60/20
x=3
Answer: We discover two outcomes:
1000 - 998 = 2
1001 - 999 = 2
Step-by-step explanation:
The problem can be stated as:
****-*** = 2
Where each asterisk symbolizes a distinct digit; here with a 4-digit number subtracting a 3-digit number to yield a difference of 2.
This can be represented as 99*, where we can increase any digit from 1 to 9 and we will achieve a 4-digit result:
So we rewrite it this way:
1000 - 998 = 2
When we add one to each side, the difference remains preserved, maintaining equal digit counts:[
1000 - 998 + 1 - 1 = 2
(1000 + 1) - (998 + 1) = 2
Thus, 1001 - 999 = 2
A simple case would also yield further solutions where digits can be zeros, for instance:
0004 - 0002 = 2
However, this trivial solution may be disregarded. This leads us to conclude that we have two unique solutions.
Response:
The bike positioned higher on the y-axis is the one that has traveled a greater distance.
Step-by-step explanation:
If Dorrian charted the positions of the bikes with time in seconds on the x-axis and distance traveled on the y-axis, the x-coordinates for both bikes would align.
However, the bike that finished faster would achieve a higher y-coordinate, while the slower one trail behind with a lower y-coordinate.
Thus, the bike with the higher y-coordinate is the victor of the race.
Response:
69
Detailed steps:
To calculate the total score for all tests, you take 93 and multiply it by 7 to get 651. Then, multiplying 90 by 8 results in 720. Subtracting 651 from 720 gives you 69.
