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UNO [17]
2 years ago
11

What is the first step to prove that 9n - 4n is divisible by 5?

Mathematics
1 answer:
EleoNora [17]2 years ago
3 0

Answer:

Collect like terms, ie do 9n-4n = 5n ...

5n will then be exactly divisible by 5 as 5n / 5 = n

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The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the
Ivenika [448]

Answer:

26; the cheetah's rate in miles per hour

Step-by-step explanation:

4 0
3 years ago
Solve the given system of equations using either Gaussian or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTI
cricket20 [7]

Answer:

The system has infinitely many solutions

\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}

Step-by-step explanation:

Gauss–Jordan elimination is a method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

An Augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

There are three elementary matrix row operations:

  1. Switch any two rows
  2. Multiply a row by a nonzero constant
  3. Add one row to another

To solve the following system

\begin{array}{ccccc}x_1&-3x_2&-2x_3&=&0\\-x_1&2x_2&x_3&=&0\\2x_1&+3x_2&+5x_3&=&0\end{array}

Step 1: Transform the augmented matrix to the reduced row echelon form

\left[ \begin{array}{cccc} 1 & -3 & -2 & 0 \\\\ -1 & 2 & 1 & 0 \\\\ 2 & 3 & 5 & 0 \end{array} \right]

This matrix can be transformed by a sequence of elementary row operations

Row Operation 1: add 1 times the 1st row to the 2nd row

Row Operation 2: add -2 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1

Row Operation 4: add -9 times the 2nd row to the 3rd row

Row Operation 5: add 3 times the 2nd row to the 1st row

to the matrix

\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]

The reduced row echelon form of the augmented matrix is

\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]

which corresponds to the system

\begin{array}{ccccc}x_1&&-x_3&=&0\\&x_2&+x_3&=&0\\&&0&=&0\end{array}

The system has infinitely many solutions.

\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}

7 0
3 years ago
How to find The point midway
Vadim26 [7]

Step-by-step explanation:

The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.

4 0
3 years ago
Read 2 more answers
Whats 125% as a fraction and a decimal
ZanzabumX [31]
125% as a fraction is 1 25/100 and in decimal form it is 1.25.
5 0
3 years ago
Suppose you pay back $575 on a $525 loan you had for 75 days. What was your simple annual interest rate? State your result to th
KengaRu [80]

The <em>simple annual interest</em> rate for the $ 525 loan is equal to 46.35 %.

<h3>What is the interest rate behind a pay back?</h3>

In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the <em>interest</em> rate for paying the loan back 75 days later is:

575 = 525 · (1 + r/100)

50 = 525 · r /100

5000 = 525 · r

r = 9.524

The loan has an <em>interest</em> rate of 9.524 % for 75 days. <em>Simple annual interest</em> rate is determine by rule of three:

r' = 9.524 × 365/75

r' = 46.350

The <em>simple annual interest</em> rate for the $ 525 loan is equal to 46.35 %.

To learn more on interests: brainly.com/question/26457073

#SPJ1

7 0
2 years ago
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