The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³
<h3>Variation</h3>
x = k × w²
w = 4, x = 48
48 = k × 4²
48 = k × 16
48 = 16k
k = 48/16
k = 3
So,
x = k × w²
x = 3 × w²
x = 3w²
y = k/x³
x = 2, y = 14
14 = k / 2³
14 × 2³ = k
14 × 8 = k
112 = k
So,
y = k/x³
y = 112/x³
y = (1/112)x³
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The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
<h3>What is the right-angled triangle?</h3>
A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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1,126.25 hope this helped :)
