Answer: 7
Step-by-step explanation:
Let the number chosen by Michael be x.
We are told that he multiplied it by itself, added 1. This would be:
= = ( x × x) + 1 = x² + 1
We are further told that he multiplied the result by 10, and added 3. This would be:
= = [(x² + 1) × 10] + 3
= 10x² + 10 + 3
= 10x² + 13
Lastly, he multiplied the result by 4 and his final answer was 2012. This would be:
(10x² + 13) × 4 = 2012
40x² + 52 = 2012
40x² = 2012 - 52
40x² = 1960
x² = 1960/40
x² = 49
x = ✓49
x = 7
The number is 7
can be expressed as:
= ( x × x) + 1 = x² + 1
Answer:
1/6
Step-by-step explanation:
There are 6 sides on a die, labeled 1,2,3,4,5,6
P(6) = number of 6's / total numbers
= 1/6
Answer:
y=5.69
Step-by-step explanation:
If x=3 then y=(.23*3)+5
.23*3=.69
.69+5=5.69
y=5.69
Answer: she would catch up with Tom in 1 hour.
Step-by-step explanation:
Let t represent the time it will take for Mary to catch up with Tom.
Tom leaves his boat from a dock and travels at a rate of 25 miles per hour.
Distance = speed × time
Distance travelled by Tom in t hours is
25 × t = 25t
Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. Converting 10 minutes to hours, it becomes 10/60 hour
Time spent by Mary is (t - 10/60) hours. If she travels at a rate of 30 miles per hour, it means that the distance that she would travel in
(t - 10/60) hours is
30(t - 10/60)
= 30t - 5
By the time she catches up with Tom, they would have covered the same distance. It means that
25t = 30t - 5
30t - 25t = 5
5t = 5
t = 5/5 = 1 hour