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mel-nik [20]
3 years ago
8

Systems of Equations via Elimination

Mathematics
1 answer:
Natalka [10]3 years ago
5 0

Answer:

Step-by-step explanation:

The shop sold 70 ice cream cones. It means that x + y = 70Small cones cost 3.95 and large cones cost 5.75. The total sales made from the selling 70 ice creams is $370.10. It means that 3.95x + 5.75y = 370.1 - - - - - - - - - -1Substituting x = 70 - y into equation 1, it becomes3.95(70 - y) + 5.75y = 370.1276.5 - 3.95y + 5.75y = 370.1- 3.95y + 5.75y = 370.1 - 276.51.8y = 93.6y = 93.6/1.8y = 52x = 70 - 52x = 18. Ww

Read more on Brainly.com - brainly.com/question/14570469#readmore

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What is the smallest prime number p such that
Ne4ueva [31]

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.

  • p^3 + 4p^2 + 4p

By factorization, we have:

  • = p(p+2)²

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:

  • p₁ = 5 and p₂ = 3

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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brainly.com/question/145452

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