In the below system,solve for y in the first equation<br> X-3y=-6<br> 2x-7y=10

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.

Learn more about prime numbers here:

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8 0

2 years ago

A chef is using vinegar for a salad dressing recipe.

Vesna [10]

40 bytdbgesdhgrecvfeewdvfewsxxeww

3 0

3 years ago

Read 2 more answers

Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A ∪ B) then how many elements are in (A

Leona [35]

Answer:

17

Step-by-step explanation:

The computation of the number of elements are in (A ∩ B) is shown below;

Given that

Set A contains 35 elements

And, set B contains 22 elements

Now if there are 40 elements in (A ∪ B)

So, the number of elements are in (A ∩ B) is

= 35 + 22 - 40

= 17

5 0

3 years ago

Consider the arithmetic sequence:

Leona [35]

Answer:

If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

Step-by-step explanation:

We are given the arithmetic sequence:

10, 12, 14, 16, ...

If n is an integer, which of these functions generate the sequence?

We need to find the nth term for the given sequence

The nth term for arithmetic sequence will be: $a_n=a_1+(n-1)d$

where aₙ is nth term, a₁ is first term and d is common difference

Looking at the sequence a₁ = 10 and d = 2

So, nth term will be:

$a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n$

So, nth term is: $a_n=8+2n$

In the options below, the only correct answer is option D. so, we can write nth term as: $d(n) = 8 + 2n\: for\: n > 1$

So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

4 0

3 years ago

Read 2 more answers

What is the slope of the line for BOTH graphs? Are the slopes the same or different?

Y_Kistochka [10]

Answer:

both are -10

Step-by-step explanation:

#1

x1 y1 x2 y2

1.5 180 6 135

(Y2-Y1) (135)-(180)= -45 ΔY -45

(X2-X1) (6)-(1.5)= 4.5 ΔX 4.5

slope= -10

B= 195

Y =-10X +195

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#2

x1 y1 x2 y2

1 175 8 105

(Y2-Y1) (105)-(175)= -70 ΔY -70

(X2-X1) (8)-(1)= 7 ΔX 7

slope= -10

B= 185

Y =-10X +185

7 0

3 years ago

In the below system,solve for y in the first equation X-3y=-6 2x-7y=10