the instructions for a fashion design project require three different cuts of silk. The longest piece must be twice the length of the middle-sized piece, and the shortest piece must be ten inches shorter than the middle sized piece. The total length of the piece of silk you are given to work with is 70 inches. How long should each of the three cut pieces be?

5x+2x=49

7x=49

x=7. 35 apples

this would be 35. 35 + 5 = 40. you take the known constant and subtract by the answer of the equation and you get y.

  b:   ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°

step-by-step explanation:

this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.

if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that

  x/sin(x) = y/sin(y) = z/sin(z)

and all of these ratios must be greater than 15, the longest side length.

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if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.

  z² = x² +y² -2xy·cos(z)

  z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°

now you can find y from the law of sines

  y = arcsin(y/z·sin(z)) = 31.242°