Based on the Hypotenuse-LengthTheorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:
Recall:
Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.
Use this to create two equations and solve to get the value of x and y.
(eqn. 1)
(eqn. 2).
(eqn. 1)
Therefore, based on the Hypotenuse-LengthTheorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:
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Answer:
x = 8 and y = 4
Step-by-step explanation:
For congruency the hypotenuse and a leg must be congruent, that is
3y = x + 4 → (1) ( Equating the hypotenuse )
x = y + 4 → (2) ( equating corresponding legs )
Substitute x = y + 4 into (1)
3y = y + 4 + 4
3y = y + 8 ( subtract y from both sides )
2y = 8 ( divide both sides by 2 )
y = 4
Substitute y = 4 into (2)
x = 4 + 4 = 8
The probability that the spinner stops at purple and a pink card is selected is 1/20
The given parameters are:
There is 1 purple color on the spinner and 1 pink card in the card.
So, the probability that the spinner stops at purple and a pink card is selected is:
P(Purple and Pink) = 1/5 * 1/4
Evaluate the product
P(Purple and Pink) = 1/20
Hence, the probability that the spinner stops at purple and a pink card is selected is 1/20
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