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11.03.2020 •
Mathematics
Suppose that $a$ is a positive integer for which the least common multiple of $a+1$ and $a-5$ is $10508$. What is $a^2 - 4a + 1$?
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Ответ:
21022.
Step-by-step explanation:
Find the prime factors of 10508:
2 ) 10508
2 ) 5254
37 ) 2627
71.
50208 = 2*2*37*71.
Now there is no integer value for a that would fit (a+ 1)(a - 5) = 10508 .
But we could try multiplying the LCM by 2:-
= 21016 = 2*2*2*37*71.
= 2*2*37 multiplied by 2 * 71
= 148 * 142.
That looks promising!!
a - 5 = 142 and
a + 1 = 148
This gives 2a - 4 = 290
2a = 294
a = 147.
So substituting a = 147 into a^2 - 4a + 1 we get:
= 21022.
Ответ:
Answer & Step-by-step explanation:
The problem tells us that ΔABC ≅ ΔDEF. Since we know that this is true, then we also know that ∠A ≅ ∠D, ∠B ≅ ∠E, and ∠C ≅ ∠F.
So, since we are looking for the measurement of ∠F, then all we have to do is know the measurements of ∠C because they are congruent angles.
So, the measurement of ∠F is 63°