How do I find the prime factorization least common multiple and greatest common multiple

jeka57 [31]

Answer:

Options 1 and 3

Step-by-step explanation:

We should know that, the system of linear equations can be treated as matrices, i.e: we can modify or make any operations provide that we must apply the same operation for all terms of each equation.

Given: the solution for the following system is (2,9)

Px + Qy = R ⇒(1)

Tx + Uy = V ⇒(2)

We will check which system of equation has the same solution.

System A) Px + Qy = R

(P+T)x + (Q+U)y = R+V ⇒(3)

So, By summing (1) and (2) we will get the equation (3)

So, system A has the same solution (2,9)

System B) Px + Qy = R

(P+2T)x + (Q+2U)y = R-2V ⇒(4)

By multiplying equation (2) by 2 and add with equation (1), we will get:

(P+2T)x + (Q+2U)y = R+2V

Which is not the same as equation (4)

So, system B has not the same solution (2,9)

System C) (T-P)x + (U-Q)y = V-R ⇒(5)

Tx + Uy = V

By multiplying equation (1) by -1 and add with equation (2), we will get the equation (5)

So, system C has the same solution of (2,9)

System D) (T-P)x + (Q+U)y = V-R ⇒(6)

Tx + Uy = V

We cannot get equation (6) by the same operation over equation (1)

Note the coefficient of x and y⇒ (T-P) and (Q+U)

They must be (T+P) and (Q+U) OR (T-P) and (Q-U)

So, system D has not the same solution of (2,9)

System E) (5T-P)x + (5U-Q)y = V-5R ⇒ (6)

Tx + Uy = V

By subtract equation (1) from 5 times equation (2), we will get:

(5T-P)x + (5U-Q)y = 5V-R

Which is not the same as equation (6)

So, system E has not the same solution (2,9)

As a conclusion, the systems which have the same solution are:

Options 1 and 3

5 0

3 years ago

How does an outlier effect the median of a population?

neonofarm [45]

An outlier causes the median to move slightly towards the outlier.

5 0

3 years ago

Please help me Evaluate 7+2^3 Answer:________

Natalija [7]

Answer:

9^...................

7 0

3 years ago

Read 2 more answers

Help please due today

Vadim26 [7]

Answer:

Line a. goes to table 3, line b. goes to table 2, and line c. goes to table 1.

Step-by-step explanation:

Here are the 3 lines graphed (I even labeled each for you) so you can have a bit of a visual.

Hopefully you can find the points on each graph.

(Hint: The x row represents the x coordinate of an ordered pair, and the y row represents the y coordinate of an ordered pair.)

Ordered pairs look like this btw (x,y)

Hope this helps :)

6 0

3 years ago

Duck #1 lays eggs whose weights are normally distributed with a mean of 70gramsand a standard deviation of 6 grams.Duck #2 lays

Genrish500 [490]

Answer:

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If an egg is randomly chosen from each duck, what is the probability that Duck #2’s egg weighs more than Duck #1’s egg?

Duck #2 egg will weigh more if the subtraction of duck's 2 egg by duck's 1 egg is larger than 0.

When we subtract normal distributions, the mean is the subtraction of the means. So

$\mu = 65 - 70 = -5$