a 27 piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 3 inches more than three times the length of the first piece what's the length of the first piece

4 in, 8 in, 15 in

Step-by-step explanation:

If x, y, z are the three pieces, then:

x + y + z = 27

y = 2x

z = 3 + 3x

Substitute the second and third equations into the first.

x + 2x + 3 + 3x = 27

6x + 3 = 27

6x = 24

x = 4

y = 8

z = 15

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629