Nick's printing press promptly sold 5-cent pencils and 10-cent pens to the public. it sold 1000 writing utensils and took $74.50 in sales. how many pens and how many pencils did nick's printing press sell?

Step-by-step explanation:

Let p represent the number of pens Nick sold. Then the revenue is ...

  0.10p +0.05(1000 -p) = 74.50

  0.05p = 24.50 . . . . . . eliminate parentheses, subtract 50

  p = 490 . . . . . . . . . . . . multiply by 20

The number of pencils sold is then ...

  pencils = 1000 -490 = 510

Nick's Printing Press sold 490 pens and 510 pencils.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is