How many real number solutions does this have 3x^2 + 8x +7=0

  zero

Step-by-step explanation:

The answer to that question is best found by looking at the value of the discriminant.

For quadratic ax^2 +bx +c = 0, the value of the discriminant is ...

  d = b^2 -4ac

Here, you have a=3, b=8, c=7, so the discriminant is ...

  d = 8^2 -4(3)(7) = 64 -84 = -20

When the discriminant is negative, both solutions are complex (not real).

There are zero real solutions to this equation.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: