C is the answer to your question
x = time in minutes
y = distance remaining
Steve starts at home when the time is x = 0 minutes. The y value y = 40 pairs up with this x value. This is shown by the point (0,40) on the diagonal line, aka the y intercept. The y intercept is where the line crosses the y axis.
The y = 40 indicates that Steve has 40 miles remaining when he starts at home. In other words, the distance from home to work is 40 miles.
The x intercept is where the diagonal line crosses or touches the x axis. The x intercept is (45,0) which represents the idea that 45 minutes have passed by. The y = 0 means that he has 0 miles left go to. Steve has reached the office at this point.
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Answers:
Steve's office is located 40 miles from home
It takes him 45 minutes to travel this distance
This question involves direct proportion which has the formula (y=kx) where y and x are the values which are proportional and k is the constant of proportionality.
The constant of proportionality is basically the value that stays the same even if the x and y values change.
In this case, the constant of proportionality would be 3/7.
Answer:
a. it is arithmentic - this is because for each term there is a constant increase of 4, and the change between each term <u>doesn't change</u>
b. you need to find the nth term, by using the equation difference x n + 0th term: the difference is (+)4 and the 0th term is -9 (-5 is the 1st term, so to go one back we subtract 4 - the inverse operation), so the nth term is 4n -9. Now we do the inverse operation on 119 to see if it's a term (it is a term if it's an integer. So, first we do 119 <u>plus</u> 9 (inverse of - 9) to get 128, then divide it by 4 rather than multiplying. This gives us 32, and that tells us that 119 is the 32nd term of the sequence.
The prime factorization of 50 is 2x5x5
