If ben invest $5000 at 6% interest each year how much additional money must he invest at 7.5% annual interest to ensure that the interest he receives each year is 6.5% of the total amount invested

  $2500

Step-by-step explanation:

Let x represent the amount invested at 7.5%. Then the total annual interest received is ...

  0.075x + 0.06·5000 = 0.065(x+5000)

  0.01x = 25 . . . . . . simplify, subtract (.065x+.06·5000)

  x = 25/0.01 = 2500

Ben must invest $2500 at 7.5% to ensure an average return of 6.5%.

the answer is d

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is