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3 years ago

Find 7x+y when x=4 and y=5. *

Mathematics

1 answer:

Alexeev081 [22]3 years ago

7 0

Answer:

7x+y, when x+4 and y+5

7(4) + 5=

28+5=

Step-by-step explanation:

Hope this helps. :)

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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:

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:

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

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:

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

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

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

What is the discriminant of 3x^2 -10x=-2

Firdavs [7]

The discriminant is −8

f(x)=−3x2−2x−1 is of the form ax2+bx+c ,with a=−3 , b=−2 and c=−1

7 0

3 years ago

Which number gives you a rational sum when you add it to 4/7?

dlinn [17]

Answer:

Thus, the rational number 93/77 should be added to -7/11 so as to get 4/7.

8 0

3 years ago

Help pls!! Use 3.14 for pi.

krok68 [10]

<h3>Find the area of the circle</h3>

To find the area, we take into account that your data is:

r = 6 cm
π = 3.14

To calculate the area of the circle, we use the following formula:

Area: π * r²

We substitute the data in the formula, and we begin to solve.

A = 3.14 * (6 cm)²

taking the square root

A = 3.14 * 36 cm²

Multiply the two numbers

A = 113.04 cm²

Therefore, the area of the circle is 113.04 cm². The correct alternative is option "A".

See more about the area of a circle at: brainly.com/question/23422024

4 0

2 years ago

Read 2 more answers

Substitution method x=2y 2x+5y=4

Dvinal [7]

Answer:

y=4/9

Step-by-step explanation:

Substitute 2y into the x

2(2y)+5y=4

4y+5y=4

9y=4

y=4/9

6 0

3 years ago