Television sizes are determined by the length of their diagonal measure. Michael just bought a new television. The height of the television is 40 inches and the length is 71.5 inches. Using the Pythagorean Theorem, what is the size of Michael’s new television? Round your answer to the nearest whole inch (whole number).

Part A: What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse?

Part B: Set-up your equation by substituting the correct numbers into the formula.

Part C: Solve for the missing length. Remember to show ALL work for each step.

Part D: What is the size of the television rounded to the nearest whole inch (whole number)?

Step-by-step explanation:

The height of the television is 40 inches and the length is 71.5 inches.

Part A

The part of the right angle triangle that you have been given are the legs which are also the opposite and adjacent sides. You are looking for the hypotenuse

Part B

The Pythagorean theorem is expressed as

Hypotenuse² = opposite side² + adjacent side²

The equation becomes

Hypotenuse² = 40² + 71.5²

Part C

Length ² = 1600 + 5112.25

Length ² = 6712.25

Length = √6712.25

Length = 81.9 inches

Part D

The size of the television is 82 inches

82 inches.

Step-by-step explanation:

The size , using Pythagoras,

= sqrt ( 40^2 + 71.5^2)

= sqrt (6712.25)

= 81.928 ins.

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:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb