Least common multiples of 3v^7y^2x^5 and 24y^4x^5

Sam and Carlos are bully with the plastic pins in Sam's living room. Remarkably Sam knocks down eight pins on every bowl and Car

SVEN [57.7K]

Answer:

72

Step-by-step explanation:

We are given that "Sam knocks down 8 pins on every bowl"

This means that, Sam's bowling will move in multiples of 8.

we are also given that "Carlos knocks down 9 pins on every bowl".

His bowling will also be in multiples of 9

Now we are supposed to find What is the least number of total pins that Sam and Carlos could have each knocked down.

So,The least of them is the least common multiple of 8 and 9.

So we are supposed to find the LCM of 8 and 9

2 | 8 , 9

2 | 4 , 9

2 | 2 , 9

3 | 1 , 9

3 | 1 , 3

| 1 , 1

So, LCM = 2 x 2 x 2 x 3 x 3 = 72

Hence the least number of total pins that Sam and Carlos could have each knocked down is 72.

5 0

3 years ago

FRANK has a paper clip.it has a mass of 9g and a volume of 3cm3.what is its density?

Pachacha [2.7K]

Answer:

Step-by-step explanation:

The density of a substance can be found by using the formula

$density = \frac{mass}{volume} \\$

From the question we have

$density = \frac{9}{3} = 3 \\$

We have the final answer as

Hope this helps you

7 0

3 years ago

A drawing of a man is 4 inches high. The actual man is 64

Alexxandr [17]

Answer:

Step-by-step explanation:

The scale factor is the ratio between the man's actual height and the height of the drawing.

Scale = 64/4 = 16

6 0

2 years ago

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Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 2 (a) Find the interval on which

Burka [1]

Answer:

a) $(-\infty, -1) \cup (5, \infty)$

b) $(-1,5)$

Step-by-step explanation:

The first step to solve this question is finding the roots of the derivative of x.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$f(x) = x^{3} - 6x^{2} - 15x + 2$

So

$f'(x) = 3x^{2} - 12x - 15$

Finding the roots:

$3x^{2} - 12x - 15 = 0$

Simplifying by -3

$x^{2} - 4x - 5 = 0$

So $a = 1, b = -4, c = -5$

Then

$\bigtriangleup = (-4)^{2} - 4*1*(-5) = 36$

$x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5$

$x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1$

So the function can be divided in three intervals.

They are:

Less than -1

Between -1 and 5

Higher than 5

In which it increases and which it decreases?

Less than -1

Lets find the derivative in a point in this interval, for example, -2

$f'(x) = 3x^{2} - 12x - 15$

$f'(-2) = 3*(-2)^{2} - 12*(-2) - 15 = 21$

Positive.

So in the interval of $(-\infty, -1)$ , the function increases.

Between -1 and 5

Will choose 0.

$f'(x) = 3x^{2} - 12x - 15$

$f'(0) = 3*(0)^{2} - 12*(0) - 15 = -15$

Negative.

So in the interval of $(-1,5)$ , the function decreases.

Higher than 5

Will choose 6.

$f'(x) = 3x^{2} - 12x - 15$

$f'(6) = 3*(6)^{2} - 12*(6) - 15 = 21$

Positive

So in the interval of $(5, \infty)$ , the function increases.

(a) Find the interval on which f is increasing.

Using interval notation

$(-\infty, -1) \cup (5, \infty)$

b) Find the interval on which f is decreasing.

$(-1,5)$

5 0

3 years ago

Subtract 4 from 8 and then add 9

Elodia [21]

When you subtract 4 from 8 you get 4 and this when you add 9 your final answer is 13.

7 0

3 years ago

Read 2 more answers