The work of a student to solve a set of equations is shown below:

Equation 1: m = 6 + n
Equation 2: 2m = 8 + 8n

Step 1: −2(m) = −2(6 + n)
2m = 8 + 8n

Step 2: −2m = −12 − 2n
2m = 8 + 8n

Step 3: −12 − 2n = 8 + 8n

Step 4: −20 = 10n

Step 5: n = −2

In which step did the student first make an error?
Step 2
Step 3
Step 4
Step 5

Suppose there is a simple index of three stocks, stock abc, stock xyz, and stock qrs. stock abc opens on day 1 with 4000 shares at $3.15 per share. stock xyz opens on day 1 with 5000 shares at $4.30 per share. stock qrs opens on day 1 with 6000 shares at $4.60 per share. the price of stock abc on day 8 begins at $3.50. the price of stock xyz on day 8 begins at $3.90. stock qrs opens on day 8 with a price of $4.50 per share. assume that each stock has the same number of shares that it opened with on day 1. what is the rate of change of this simple index over 1 week?

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

How can constraints be used to model a real-world situation?