A insurance salesperson earns a salary of $4,200 per month plus a commission of 3% of sales. How much must the salesperson have to sell to make an income of at least $4,500?

x = 10,000

Step-by-step explanation:

commision earned = $4500. - $4200

commision = 300

therefore:

commision = 3% of the amount of the sales

300 = 3% of x( the price isn't known)

300 = 3/100 * x

300 = 3x /100

multiplying both sides by 100

300 x 100 = 3x/100 x 100

30000 = 3x

Divide through by 3

x = 10,000.

the amount of the sales = 10,000

To check

commision = 3% of 10,000

commision = 300

b

Step-by-step explanation:x-intercepts:

factor the function

f(x)=(x+3)(x+1)

zeros at x=-3,-1

x-intercepts  --> (-3,0),(-1,0)

y-intercepts:

set x=0 in f(x)

f(0)=(0)^2+4(0)+3=3

y-intercept  --> (0,3)

find minimums and maximums

The max or min of a quadratic function occurs at x=-b/(2a). If a is negative, the max value of the function is f(-b/(2a)).  if a is positive, the minimum value of the function is f(-b/(2a)).

f(x)=ax^2+bx+c

f(x)=x^2+4x+3

here a is positive so you are looking for a minimum,

x=-b/(2a)

x=-4/(2*1)

x=-2   > plug into f(x), f(-2)=(-2)^2+4(-2)+3=-1

minimum (-2,-1)