The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
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(a) 2x + 5x + 4 = 25 <== ur equation
7x + 4 = 25
7x = 25 - 4
7x = 21
x = 21/7
x = 3
(b) first piece = 2x....= 2(3) = 6 ft <=
second piece = 5x....= 5(3) = 15 ft <=
Answer:
4.) Silvia had the greater variation in her race results for the season because she has a higher standard deviation.
Step-by-step explanation:
hope this helps!!! :)
Answer:
16
Step-by-step explanation:
to get from 3/4 to 12/x you gotta multiple 3 times 4 which is 12 so the bottom multiple that by 4 also which 4 x 4 is 16
Answer:
6/1 · 11/4 = 66/4 = 16 1/2
-10/3 · (-17/5) = 170/15 = 11 1/3
-9/2 · 26/3 = -234/6 = -39
11/6 · (-9/1) = -99/6 = -16 1/2
