<h3><u>Question:</u></h3>
Serena uses chalk to draw a straight line on the sidewalk. The line is 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long. How many sections will the line be divided into?
<h3><u>Answer:</u></h3>
The number of sections that the line is divided is 4
<h3><u>Solution:</u></h3>
Given that, Serena uses chalk to draw a straight line on the sidewalk
The line is 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long
From given,
To find: Number of sections can be made
The number of sections that can be made is found by dividing the total length of line by length of each section
Substituting the values, we get,
Thus number of sections that the line is divided is 4
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.
Learn more about prime numbers here:
brainly.com/question/145452
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T. Pitagora twice => new street = 2
= 8.94 miles;
135*8.94 = 1206.9$;
Answer: The answer is B. 0.208.
Step-by-step explanation: Just took the test on e2020
Step-by-step explanation:
i can't see ur question the pic is black can u resend
