What's the LCM OF 90 show your work

If the Greatest Common Factor of L and M is 6, write the expression for the Least Common Multiple of these numbers.

zhuklara [117]

Answer:

$\frac{(L x M)}{6}$

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

$\frac{(L x M)}{6}$

7 0

3 years ago

Which of the following set can be sets of a right triangle

pav-90 [236]

Where are the triangles :)

4 0

4 years ago

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Suppose a certain population satisfies the logistic equation given by dP

Ksenya-84 [330]

Answer:

The population when t = 3 is 10.

Step-by-step explanation:

Suppose a certain population satisfies the logistic equation given by

$\frac{dP}{dt}=10P-P^2$

with P(0)=1. We need to find the population when t=3.

Using variable separable method we get

$\frac{dP}{10P-P^2}=dt$

Integrate both sides.

$\int \frac{dP}{10P-P^2}=\int dt$ .... (1)

Using partial fraction

$\frac{1}{P(10-P)}=\frac{A}{P}+\frac{B}{(10-P)}$

$A=\frac{1}{10},B=\frac{1}{10}$

Using these values the equation (1) can be written as

$\int (\frac{1}{10P}+\frac{1}{10(10-P)})dP=\int dt$

$\int \frac{dP}{10P}+\int \frac{dP}{10(10-P)}=\int dt$

On simplification we get

$\frac{1}{10}\ln P-\frac{1}{10}\ln (10-P)=t+C$

$\frac{1}{10}(\ln \frac{P}{10-P})=t+C$

We have P(0)=1

Substitute t=0 and P=1 in above equation.

$\frac{1}{10}(\ln \frac{1}{10-1})=0+C$

$\frac{1}{10}(\ln \frac{1}{9})=C$

The required equation is

$\frac{1}{10}(\ln \frac{P}{10-P})=t+\frac{1}{10}(\ln \frac{1}{9})$

Multiply both sides by 10.

$\ln \frac{P}{10-P}=10t+\ln \frac{1}{9}$

$e^{\ln \frac{P}{10-P}}=e^{10t+\ln \frac{1}{9}}$

$\frac{P}{10-P}=\frac{1}{9}e^{10t}$

Reciprocal it

$\dfrac{10-P}{P}=9e^{-10t}$

$P(t)=\dfrac{10}{1+9e^{-10t}}$

The population when t = 3 is

$P(3)=\dfrac{10}{1+9e^{-10\cdot 3}}$

Using calculator,

$P=9.999\approx 10$

Therefore, the population when t = 3 is 10.

8 0

3 years ago

WXY is a right triangle.<br> A. True<br> B. False

mojhsa [17]

Answer:

need a picture

Step-by-step explanation:

can u give us a picture of the triangle? we can't determine whether point WXY is a right triangle without an image.

4 0

4 years ago

Fuaad solved an absolute value inequality and expressed the solution as -12 < x > 7. What is another way to show Fuaad’s s

seropon [69]

Solution: The another way to show the Fuaad's solution is $x>7$ .

Explanation:

It is given that the solution of an inequality is $-127$ .

It can be break in two parts $-12$ and $x>7$ .

The inequality $-12$ means the values of x is greater than $-12$ and the inequality $x>7$ means the value of x is greater that than 7.

When we combine both results we get $x>7$ it means the value of x is greater than 7.

It can also represented by number line as shown in given figure.

The number line shows the values of x and red lines shows the solution of both inequalities $-12$ and $x>7$ .

The common region shows the combination of both the possible inequalities, therefore the another way to show the Fuaad's solution is $x>7$ .

4 0

3 years ago

Read 2 more answers