24% in simplest form

Find the smallest positive integer k such that 3240/k is a square number

sashaice [31]

Answer:

10

Step-by-step explanation:

First, factorize the number 3,240:

$3,240=2\cdot 1,620=2\cdot 2\cdot 810=2\cdot 2\cdot 2\cdot 405=2\cdot 2\cdot 2\cdot 2\cdot 5\cdot 81=2^3\cdot 5\cdot 9^2$

So,

$3,240=2^2 \cdot 2\cdot 5\cdot 9^2=18^2\cdot 10$

Now consider the fraction

$\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{k}$

If k = 10, then

$\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{10}=18^2$

is a square number.

For all k < 10, the fraction tex]\dfrac{3,240}{k}[/tex] is not a square number (this follows from factorization).

Or you can simply check the values of the fraction for all k < 10:

k = 1, $\dfrac{3,240}{1}=3,240$ is not a square number;
k = 2, $\dfrac{3,240}{2}=1,620$ is not a square number;
k = 3, $\dfrac{3,240}{3}=1,080$ is not a square number;
k = 4, $\dfrac{3,240}{4}=810$ is not a square number;
k = 5, $\dfrac{3,240}{5}=648$ is not a square number;
k = 6, $\dfrac{3,240}{6}=540$ is not a square number;
k = 7, $\dfrac{3,240}{7}$ is not a square number;
k = 8, $\dfrac{3,240}{8}=405$ is not a square number;
k = 9, $\dfrac{3,240}{9}=360$ is not a square number.

5 0

3 years ago

Which zero pair could be added to the function fon) = x2 + 12x + 6 so that the function can be written in vertex form?

Oksanka [162]

ANSWER

36,-36

EXPLANATION

The given function is:

$f(x) = {x}^{2} + 12x + 6$

To write this function in vertex form;

We need to add and subtract the square of half the coefficient of x.

The coefficient of x is 12.

Half of it is 6.

The square of 6 is 36.

Therefore we add and subtract 36.

Hence the zero pair is:

36, -36.

The correct answer is D.

4 0

3 years ago

Read 2 more answers

What is the slope of the line shown below

gizmo_the_mogwai [7]

Answer:

A. 4

Step-by-step explanation:

1. Use the SLOPE FORMULA: M= rise/run= y2-y1/x2-x1

2. Plug in the two coordinates that were plotted on the equation: (1,1) & (3,9)

3. Label the coordinates

( 1 , 1 ) = ( x1, y1 )& ( 3, 9 ) = ( x2, y2 )

4. SOLVE & PLUG IN

m = 9 - 1 / 3 - 1 = 8 / 2

5. Simplify 8/2 (Divide by 2)

6. answer: 4/1 = 4

8 0

2 years ago

Read 2 more answers

Help with this polynomial problem.

Anastasy [175]

Answer:

i cannt see it

Step-by-step explanation:

3 0

2 years ago

I used 2/3 for tickits and 1/6 on popcorn how much money is left

posledela

Answer:

You would have 1/6 of your money remaining.

Step-by-step explanation:

Let's write an equation for this.

1 - (2/3 + 1/6)

First, let's multiply the numerator and denominator of 2/3. You get 4/6!

1 - (2/3 + 1/6)

1 - (4/6 + 1/6)

Next, let's add 4/6 and 1/6. You get 5/6!

1 - (4/6 + 1/6)

1 - 5/6

Finally, let's turn 1 into 6/6 and do 6/6 - 5/6!

1 - 5/6

6/6 - 5/6

1/6

You would have 1/6 of your money remaining.

3 0

2 years ago