4 divided by 1/2 Pls help

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:

brainly.com/question/145452

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8 0

1 year ago

Pls help! will mark branliest!!! :)

Ket [755]

The area of the house is the amount of space on the house.

The length of the addition is x + 20
The area of the original house is $x^2 + 30x + 200$

<h3>The length of the addition</h3>

The area of the addition is given as:

$Area = x^2 + 10x - 200$

Expand

$Area = x^2 + 20x - 10x - 200$

Factorize

$Area = x(x + 20) - 10(x + 20)$

Factor out x + 20

$Area = (x -10)(x + 20)$

The width of the addition is x - 10.

Hence, the length of the addition is x + 20

<h3>The area of the original house</h3>

The dimension of the original house is

x + 20 by x + 10

So, the area is:

$Area =(x + 20)(x + 10)$

Expand

$Area =x^2 + 20x + 10x + 200$

This gives

$Area =x^2 + 30x + 200$

Hence, the area of the original house is $x^2 + 30x + 200$

Read more about areas at:

brainly.com/question/24487155

8 0

2 years ago

Like in Utah, license plates in the great state of Wisconsin consist of 2 letter and 4 digits. However, only digits can repeat a

sveta [45]

Answer:

The correct option is B) 26x26x10^4.

Step-by-step explanation:

Consider the provided information.

It is given that the Wisconsin consist of 2 letter and 4 digits. And two letters always precede the digits.

There are 26 Alphabet so that means for alphabets we have 26 choices also we for digits we have 10 choices (0 to 9).

However, only digits can repeat. For first letter we have 26 choices for second we have only 25 choices left, similarly for digits we have 10 choices but repetition is allow so we can choose same number. the number of possible plates are:

26×25×10×10×10×10

Which also can be written as:

$26 \times 25 \times 10^{4}$

Hence, the correct option is B) 26x26x10^4.

8 0

3 years ago

Find the length of BC

bazaltina [42]

Answer:

BC = 19.78

Step-by-step explanation:

using sin(x) rule

sin(54)= 16/BC

sin(54)=0.80

∴0.80=16/BC (divied both side by 0.80)

BC=16/0.80 =19.78

8 0

2 years ago

Help me with all of them plzzz eleven<br><br> Points

irina [24]

122 with 58
35 with 145
62 with 118
105 with 75

5 0

3 years ago

Read 2 more answers