Simplify the expression <br><br><br> 17r-17r=

Which number is not divisible by either of the numbers 3 and 5?

Triss [41]

3and5 are both divisible by 15

8 0

3 years ago

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

The 7 grade student at palm coast muddle school made some apple pies for a bake sale . the school cafeteria also donated 9 pies

Reil [10]

Answer:

The students baked 19 pies.

Step-by-step explanation:

Least total pieces of pies sold = 224

Number of pies donated by school cafeteria = 9

Number of pieces of pies donated by school cafeteria = 9×8 = 72

Number of pieces of pies baked = 224 - 72 = 152

Number of pies baked = 152 ÷ 8 = 192

4 0

4 years ago

Read 2 more answers

Christy went jogging on Saturday. The table shows how far she had jogged after various times

irga5000 [103]

Is there more to the question

6 0

3 years ago

Read 2 more answers

Solve and graph the solutions of the equation 2|x-2|-12=0

defon

2|x-2|-12=0

Rearrange variables to the left side of the question

2|x-2|=12

Dividing both sides of the equation by the coefficent of variables

|x-2|=12/2

Reduce the fraction

|x-2|=6

Split into two variables

x-2=6 or x-2=-6

Rearrange variables to the left side of the equation

x=6+2

x=8 or x=-4

when x=8

LHS=2|8-2|-12=0

RHS=0

LHS=RHS

x=8 is valid

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

A variable is a letter or symbol that stands in for any individual integer in a group of two or more. A constant is a letter or symbol that stands for a single particular number, whether it is known or unknown.

In mathematics, variables serve as stand-ins for unknowable numbers. Variables can be utilized in formulae, equations, and expressions in mathematics. When it's necessary to find the optimum solution, variables are frequently employed.

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6 0

1 year ago

Simplify the expression 17r-17r=