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3 years ago

Find the greatest common factor of 15x^2y^3 and -18x^3yz The Answer has to be like _x_y_

Mathematics

1 answer:

Daniel [21]3 years ago

8 0

Answer:

The greatest common factor of this would be 3x^2y

Step-by-step explanation:

In order to find this, first find the greatest common factor of the coefficients. Since 3 goes in evenly to both 15 and -18, then we know that it is a common factor.

From there we need to find the number of x's. Since the first term only has 2 x's and the second has 3, we take the lowest number. (x^2)

And since the first term has 3 y's and the second has just 1, we take the lowest number (y).

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Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.

sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

$\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ =I.

First, we have to identify the matrix I. As it was said, the matrix is the identiy matrix, which means

I = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So, $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Isolating the X, we have

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ - $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Resolving:

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]$

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X= $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ ⁻¹· $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

$\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ · $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a= $\frac{2}{11}$ ; b= $\frac{7}{33}$ ; c= $\frac{-1}{11}$ and d= $\frac{-3}{11}$ . Substituting:

X= $\left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11} \end{array}\right]$ · $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Multiplying the matrices, we have

X= $\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11} \end{array}\right]$

6 0

3 years ago

A basket contained 75 brown eggs. 40% of them were used-up, and a third of them remaining were rotten and thrown out. What fract

IceJOKER [234]

Answer:

4/15

Step-by-step explanation:

40% is the same as .4.

.4 x 75 = 30

1/3 x 75 = 25

30 + 25 = 55

75 - 55 = 20

20 / 75

Simplify. Divide by 5.

4/15

6 0

3 years ago

9x-6+11x what would the answer be

frez [133]

Answer:

20x-6

Step-by-step explanation:

5 0

3 years ago

The Nielsen Media Research Company uses people meters to record the viewing habits of about 5000 households, and today those met

expeople1 [14]

Answer:

Cross-sectional study.

Step-by-step explanation:

- In a cross-sectional study, data are observed, measured, and collected at one point in time.

- In a prospective (or longitudinal) study, data are collected in the future from

groups sharing common factors.

- In a retrospective (or case-control) study, data are collected from the past by going

back in tirme (through exanmination of records, interviews, arıd so on).

Hope this Helps!!

4 0

3 years ago

Use the graph to answer the question.

stealth61 [152]

A 180 counterclockwise rotation about the origin followed by a reflection of the y-axis

6 0

3 years ago

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