100 points the right answer please the set designer for a play painted some background scenery on a large piece of plywood. He used a 13-foot-long pole to hold the piece of plywood upright, as in the diagram below. What is h, the total height in of the feet of the piece of plywood
13ft 2ft 5ft

14 ft

Step-by-step explanation:

Focus on the triangle, and temporarily neglect the 2 ft measurement at the top of the triangle.  Then the 2 legs of the triangle have lengths h - 2 ft and 5 ft, and the hypotenuse is 13.

Applying the Pythagorean Theorem, we get:

13^2 =  (h - 2)^2 + 5^2, or

169 = h^2 - 4h + 4 + 25, or

144 = h^2 - 4h + 4, or

140 = h^2 - 4h, or, finally,

h^2 - 4h - 140 = 0.  We must find the value of h.

I graphed this function on a calculator and found that -10 is a zero.  Thus, the function factors into (h + 10)(h - 14) = 0, or h = 14.

The total height of the piece of plywood is 14 ft.

Check this:  does a right triangle with legs (14 - 2) and 5 have a hypotenuse of 13?  Yes.

50- 250 is correct i did that one too

step-by-step explanation:

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: