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There are essentially two ways that I know to solve this.
One is to guess.
The other is to find the prime factors of 96. For an integer to be a perfect square, each prime factor has to occur an even number of time. Therefore k would need to be the product of whatever primes occur in 96 an odd number of times.
Given that 9+6 is divisible by 3, we know that 96 is divisible by 3. Doing the division, we find that 96 = 3 * 32.
The prime factor 3 only occurs once. Therefore k must be a multiple of 3.
32 is 2 raised to the 5th power. This is an odd number of 2’s. We need one more. Therefore k must be a multiple of 2.
Therefore the smaller possible value of k is 6.
96 * 6 is a perfect square. It is the same as 64 * 9, or 24 * 24.
Hope it helps!
Answer:
B
Step-by-step explanation:
Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:
The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:
Solve for BC. We can take the reciprocal of both sides:
Multiply:
Use a calculator. Hence:
BC measures approximately 11.62 units.
Our answer is B.
{11X+8Y=158
{5X+17Y=152
{55X+40Y=790
-
{55X+187Y=1672
147Y=882
Y=6
Cost of the ticket for student is $6
