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2 years ago

Suppose $n$ is a positive integer such that $6n$ has exactly 9 positive divisors. How many prime numbers are divisors of $6n$

Mathematics

1 answer:

zvonat [6]2 years ago

6 0

The number of prime divisors of "6n" is 2 numbers 2 and 3

Given

"n" = 6

thus 6n = 6(6) = 36

The positive divisors are 1, 2, 3, 4, 6, 9, 12, 18 and 36

So, the number of prime divisors of "6n" is 2 numbers 2 and 3.

The prime factors of a positive integer are the top numbers that divide that integer exactly. The technique of finding those numbers is known as integer factorization or prime factorization.

The fundamental theorem of mathematics says that every positive integer has a completely unique prime factorization.

Learn more about prime factorization here: brainly.com/question/1081523

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Use division to find the unit rate. <br><br> 45 buttons were needed to make 5 jackets.

frez [133]

Answer:

1 jacket = 9 buttons

Step-by-step explanation:

45 ÷ 5 = 9

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If a person walks 16 miles in 10 minutes, how far will that person walk in one hour?

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Find the equation of the quadratic function with vertex (-2,18) passing through (-5,0)?

Sliva [168]

Answer:

$y-18=-2(x+2)^2$

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

$y-k=a(x-h)^2$

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

It's been given the vertex of the parabola as (-2,18):

$y-18=a(x+2)^2$

Now substitute the point (-5,0) and find the value of a:

$0-18=a(-5+2)^2$

Operating:

$-18=a(-3)^2$

$-18=9a$

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$a = -18 / 9$

a = -2

Thus, the equation of the quadratic function is:

$\mathbf{y-18=-2(x+2)^2}$

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2 years ago

A person standing 20 feet from a streetlight casts a shadow as shown. How many times taller is the streetlight than the person?

Leviafan [203]

I don't know

Step-by-step explanation:

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Write a ratio, in the simplest form and a percent for the shaded area (there's a 5x4 box and 6 cubes are shaded)

Alexxandr [17]

Answer:

$\%Percent = 30 \%$

Step-by-step explanation:

Given

$Shaded = 6\ cubes$

$Box = 5\ x\ 4$

Required

Determine the percentage of the shaded cubes

First, we calculate the number of boxes:

$Box = 5\ x\ 4$

Express as multiplication

$Box = 5\ *\ 4$

$Box = 20$

This implies that there are 20 cubes in the box.

The percentage of the shaded cubes is:

$\%Percent = \frac{Shaded}{Box} * 100\%$

$\%Percent = \frac{6}{20} * 100\%$

$\%Percent = \frac{6* 100}{20} \%$

$\%Percent = \frac{600}{20} \%$

$\%Percent = 30 \%$

<em>30% were shaded</em>

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2 years ago