I NEED HELP ASAP!!!!! In one version of a trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another versio
n of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes? Explain your reasoning.
2 answers:
so so to start you're going to want to find the lowest common factor of 3 cups peanuts and 4.5 cups of peanuts. and then you're going to want to multiply both to get to the lowest common factor. then you end up with 9 cups peanuts to 6 cups of raisins for the first ratio. for the second one you end up with the same ratio of 9 cups peanuts and 6 cups of raisins.
so both mixes are the same .
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Answer:
Options (2) and (3)
Step-by-step explanation:
Let,
-8 + 8i√3 = a² + b²i² + 2abi
-8 + 8i√3 = a² - b² + 2abi
By comparing both the sides of the equation,
a² - b² = -8 -------(1)
2ab = 8√3
ab = 4√3 ----------(2)
a =
By substituting the value of a in equation (1),
48 - b⁴ = -8b²
b⁴ - 8b² - 48 = 0
b⁴ - 12b² + 4b² - 48 = 0
b²(b² - 12) + 4(b² - 12) = 0
(b² + 4)(b² - 12) = 0
b² + 4 = 0 ⇒ b = ±√-4
b = ± 2i
b² - 12 = 0 ⇒ b = ±2√3
Since, a =
For b = ±2i,
a =
=
=
But a is real therefore, a ≠ ±2i√3.
For b = ±2√3
a =
a = ±2
Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)
Options (2) and (3) are the correct options.