explain step by step how to arrive at a single rational number to represent the following expression. Show both a written explanation and th related math work for each step

Answers

Answer 1

Answer: Seemingly fair enough ... but impossible until you tell us what the expression is.

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During the summer, Andrew worked for 6 days each week. He worked 8 hours each day. In a week, he earned $360. How much was he paid for each hour of work?

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Answers

6 days each week and 8 hours each day so total hours = (6x8) = 48 hours.

he earned $360 in a week it means he earn that much money working 48 hours so he paid in one hour is (360/48) = $7.5 (ans)

$7.50 because 6x8 equals 48 and 360 divided by 360 equals $7.50

What is the nth term in the sequence:
4, 7, 12, 19, 28
Please show working out

Answers

The correct answer is n²+3.

Explanation:
We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.

Since these are different, this is not linear.

We now find the second differences:
5-3=2; 7-5=2; 9-7=2.

Since these are the same, this sequence is quadratic.
We use (1/2a)n², where a is the second difference:
(1/2*2)n²=1n².

We now use the term number of each term for n:
4 is the 1st term; 1*1²=1.
7 is the 2nd term; 1*2²=4.
12 is the 3rd term; 1*3²=9.
19 is the 4th term; 1*4²=16.
28 is the 5th term: 1*5²=25.

Now we find the difference between the actual terms of the sequence and the numbers we just found:

4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.

Since this is constant, the sequence is in the form (1/2a)n²+d;
in our case, 1n²+d, and since d=3, 1n²+3.

Answer:

The nth term in the given sequence will be:

$n^2+3$