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3 years ago

14

Pls help Describe how to find the product of the two terms 3x^2y^5 and 4x^3y^7

2 answers:

zvonat [6]3 years ago

8 0

Answer:

12 x^5y^12

Step-by-step explanation:

3x^2y^5 * 4x^3y^7

Multiply the constants

3*4 = 12

Multiply the x terms

x^2 * x^3

We know a^b* a^c = a^(b+c)

x^(2+3) = x^5

Multiply the y terms

y^6 * y^7 = y&(5+7) = y^12

Put them back together

12 x^5y^12

Rzqust [24]3 years ago

6 0

The answer above me is correct

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Find the reduced row echelon form of the following matrices and then give the solution to the system that is represented by the

GaryK [48]

Answer:

a)

Reduced Row Echelon:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]$

Solution to the system:

$x_3=-4\\x_2=-\frac{7}{4}x_3=7\\x_1=-\frac{1}{2}x_2=-\frac{7}{2}$

b)

Reduced Row Echelon:

$\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]$

Solution to the system:

$x_3=-\frac{17}{2}\\x_1=\frac{7-3x_2}{4}$

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

Step-by-step explanation:

To find the reduced row echelon form of the matrices, let's use the Gaussian-Jordan elimination process, which consists of taking the matrix and performing a series of row operations. For notation, R_i will be the transformed column, and r_i the unchanged one.

a) $\left[\begin{array}{cccc}0&4&7&0\\2&1&0&0\\0&3&1&-4\end{array}\right]$

Step by step operations:

1. Reorder the rows, interchange Row 1 with Row 2, then apply the next operations on the new rows:

$R_1=\frac{1}{2}r_1\\R_2=\frac{1}{4}r_2$

Resulting matrix:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&3&1&-4\end{array}\right]$

2. Set the first row to 1

$R_3=-3r_2+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]$

3. Write the system of equations:

$x_1+\frac{1}{2}x_2=0\\x_2+\frac{7}{4}x_3=0\\x_3=-4$

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

$x_3=-4\\x_2=-\frac{7}{4}x_3=7\\x_1=-\frac{1}{2}x_2=-\frac{7}{2}$

b)

$\left[\begin{array}{cccc}4&3&0&7\\8&6&2&-3\\4&3&2&-10\end{array}\right]$

1. $R_2=-2r_1+r_2\\R_3=-r_1+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]$

2. Write the system of equations:

$4x_1+3x_2=7\\2x_3=-17$

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

$x_3=-\frac{17}{2}\\x_1=\frac{7-3x_2}{4}$

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

7 0

3 years ago

-3x - (2y)^2 <br><br> pls help

DENIUS [597]

Answer:

$- 3x - 4y ^{2}$

Step-by-step explanation:

$- 3 - 2 ^{2} y ^{2}$

$- 3x - 4y ^{2}$

8 0

3 years ago

Morgan uses 1/4 of her supply of raisins to make trail mix and 3/8 of her supply of raisins to make cookies. If morgan uses 5 po

arlik [135]

First, we need to find the total fraction of her raisins she used:

1/4 + 3/8 = 2/8 + 3/8

She used 5/8 of her supply.

Knowing this:

5/8x = 5

We multiply by 8 (the LCD)

5x = 40

x = 8

Her supply was 8 pounds, and after making the food, she now has 3 pounds

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3 years ago

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A line is perpendicular to y=(-1/5)×+1 and intersects the point (-5,1)

svet-max [94.6K]

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Answer:

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