James invested $300 in a bank account that earns simple interest. He earns $24 at the end of 12 months. James invests $500 at the same rate for 12 months. How much money will James receive on his $500 investment after 12 months

$40

Step-by-step explanation:

The key formula to use for this problem is the simple interest formula, which is ; where I is the interest earned, p is the principal (initial) amount, r is the interest rate, and t is the amount of time that passes.

Since we know that both investments have the same interest rate, we can use the information from the first part of the problem to solve for the interest rate. Using algebra, we can rearrange the simple interest formula to solve for the interest rate:  . We know that our interest earned is $24 and our principal amount is $300. To make things easier, we'll also convert months to years, which is easy to do since we know that 12 months = 1 year. This gives us our value for the amount of time that passes. Now, all we have to do is plug in our values into the rearranged equation above.

We should now have:

Now, to find the interest earned from the $500 investment, we just need to plug in our values from the second part of the problem, along with our calculated interest rate of 0.08, into the original formula of

This should result in

Therefore, James will receive $40 on his $500 investment after 12 months.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form