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3 years ago

Find the L.C.M of x^2+x , x^2-1 , x^2-x

Mathematics

2 answers:

Shalnov [3]3 years ago

8 0

Answer:

$x\cdot(x+1)\cdot(x-1)=x^3-x$

Step-by-step explanation:

To find the LCM of any integer, we take the product of all the <em>highest powers</em> of the factors that appear in the numbers. Factoring our three given expressions gives us the products

$x^2+x=x\cdot(x+1)\\x^2-1=(x+1)\cdot(x-1)\\x^2-x=x\cdot(x-1)\\$

Our LCM will be a product of some powers of $x$ , $x+1$ , and $x-1$ . The most each factor occurs in the three expressions is once, so our least common multiple is

$x^1\cdot(x+1)^1\cdot(x-1)^1$

which can be simplified to $x^3-x$

grin007 [14]3 years ago

8 0

Answer:

Step-by-step explanation:

x² + x = x * (x + 1)

x² - 1 = (x - 1)(x + 1) {a² - b² = (a+b)(a-b)}

x² - x = x * (x - 1)

LCM = x * (x + 1) * (x - 1)

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4 years ago

Select True or false for each statement

PilotLPTM [1.2K]

Answer:

False

True

False

Step-by-step explanation:

1. We have to get the sum as follows :

$3\frac{4}{9} + 4\frac{6}{9}$

= $\frac{31}{9} + \frac{42}{9}$

= $\frac{31 + 42}{9}$

= $\frac{73}{9}$

= $8\frac{1}{9} \neq 7\frac{1}{9}$

So, this is false.

2. We have to get the sum as follows :

$4\frac{5}{6} + 1\frac{3}{6}$

= $\frac{29}{6} + \frac{9}{6}$

= $\frac{29 + 9}{6}$

= $\frac{38}{6}$

= $6\frac{2}{6}$

So, this is true.

3. We have to get the difference as follows :

$4\frac{5}{8} - 2\frac{4}{8}$

= $\frac{37}{8} - \frac{20}{8}$

= $\frac{37 - 20}{8}$

= $\frac{17}{8}$

= $2\frac{1}{8} \neq 2\frac{3}{8}$

So, this is false.

4. We have to get the difference as follows :

$7\frac{5}{8} - 4\frac{2}{8}$

= $\frac{61}{8} - \frac{34}{8}$

= $\frac{61 - 34}{8}$

= $\frac{27}{8}$

= $3\frac{3}{8} \neq 3$

So, this is also false. (Answer)

5 0

4 years ago

Given the point and slope, write the equation of the line

Ratling [72]

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{6-1}\implies \cfrac{-5}{5}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-1(x-1) \\\\\\ y-4=-x+1\implies y=-x+5$

$\bf (\stackrel{x_1}{-12}~,~\stackrel{y_1}{14})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-14}{6-(-12)}\implies \cfrac{-15}{6+12}\implies \cfrac{-15}{18}\implies -\cfrac{5}{6}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-14=-\cfrac{5}{6}[x-(-12)] \\\\\\ y-14=-\cfrac{5}{6}(x+12)\implies y-14=-\cfrac{5}{6}x-10\implies y=-\cfrac{5}{6}x+4$

7 0

3 years ago

Find the solutions to the system of equations. Select all that apply. Y=x^2-1 y=2x-2

Sliva [168]

Answer:

Option C (1, 0)

Step-by-step explanation:

We have a system with the following equations:

$y = x ^ 2-1\\\\y = 2x-2$

The first equation is a parabola.

The second equation is a straight line

To solve the system, substitute the second equation in the first and solve for x.

$2x-2 = x ^ 2 -1$

Simplify

$x ^ 2-2x + 1 = 0$

You must search for two numbers that when you add them, obtain as a result -2 and multiplying both results in 1.

These numbers are -1 and -1

Therefore

$x ^ 2-2x + 1= (x-1)(x-1)\\\\x ^ 2-2x + 1= (x-1)^2=0$

Finally the solutions are

$x = 1\\y =0$

8 0

3 years ago

Read 2 more answers

A company had 2x10^5 employees in 2010. That was 2.5 times the number of employees in 1985.

professor190 [17]

So, we start by solving what the numbers are..

2x10^5 = 200000 IN 2010!

Now this is where you might get confused, that WAS 2.5 times the number IN 1985

So you divide 200,000 by 2.5 = 80,000

Therefore its C.

6 0

3 years ago

Read 2 more answers