Work the information to set inequalities that represent each condition or restriction.

2) Name the variables.

c: number of color copies
b: number of black-and-white copies

3) Model each restriction:

i) It takes 3 minutes to print a color copy and 1 minute to print a black-and-white copy.

3c + b


ii) He needs to print at least 6 copies ⇒ c + b ≥ 6


iv) And must have the copies completed in no more than 12 minutes ⇒

3c + b ≤ 12


4) Additional restrictions are c ≥ 0, and b ≥ 0 (i.e. only positive values for the number of each kind of copies are acceptable)

5) This is how you graph that:

i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.

ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.

iii) since c ≥ 0 and b ≥ 0, the region is in the first quadrant.

iv) The final region is the intersection of the above mentioned shaded regions.

v) You can see such graph in the attached figure.

6 0

3 years ago

Write the solution to the inequality in set - builder notation: 5r + 8 < 63

Leni [432]

First, the inequality needs to be solved. The first step is to subtract 8 from both sides of the inequality, leading to 5r < 55. Dividing 5 out from both sides, this will leave r < 11. Next, to form a set notation, the inequality is written in such form: {r | r < 11}.

7 0

3 years ago

A field has a length of 12 m and a diagonal of 13 m what is the width?

kvv77 [185]

Do Pythagorean Theorem because a rectangle divided in diagonals form right triangles
A^2+b^2=C^2
Plug in the correct numbers and solve
A and B can be switched around but C is always the longest diagonal side which is called the hypotenuse not the Adjacent sides that form a right angle
So with correct solving you should get 5.

7 0

3 years ago