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jeka57 [31]
2 years ago
14

The scatter plot shows the amount of sleep Aria got the night before a test and her test scores. Use the points (0, 62) and (6,

80) from the line on the scatter plot. What is the equation of the trend line?
Mathematics
1 answer:
Minchanka [31]2 years ago
5 0

Answer:

y = 3x + 62

Step-by-step explanation:

Using the points :

(0, 62) and (6, 80)

Equation of trend line is in the form:

y = mx + c

Where m = slope ; c = intercept

Slope (m) = (y2 - y1) / (x2 - x1)

m = (80 - 62) / (6 - 0)

m = 18 / 6

m = 3

Intercept, c = value of y when x = 0

From (0, 62)

x = 0 ; y = 62

Then c = 62

Hence,

y = 3x + 62

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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
Please help me I need an answer
Mumz [18]
1) 2/4 = 1/4 + 1/4
2) 4/6 = 1/6 + 1/6 + 1/6 + 1/6
3) 3/5 = 1/5 + 1/5 + 1/5
4) 3/3 = 1/3 + 1/3 + 1/3
5) 7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
6) 6/2 = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2
7) 5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6
8) 9/5 = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5
9) 8/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 
10) 1/2 * 8 = 8/2 = 4

11) Unit fractions are fractions where its numerators are 1 and its denominators are positive integer. example: 1/2 ; 1/3 ; 1/4

12) D.) 5/2 = 5 * 1/2

7 0
3 years ago
A 2 -gallon container of window costs 31.36. what is the price per cup
irinina [24]

Answer:

0.98 $/cup

Step-by-step explanation:

The final answer asks for price/cup, as "per" means "divided by".

So, our final units will be in $/cup.

We are given that for every 2 gallons, it will cost $31.36.

In order to get from gallons to cups, we need to convert units.

In 1 gallon, there are 16 cups.

So, our conversion factor will be 16 cups/1 gallon.

\frac{31.36}{2} *\frac{1}{16} \\\\= 0.98$/cup

Important things to note:

- With these types of problems, it makes it much easier if you just figure out what units you need in the final answer, and then use conversions and dimensional analysis to get the answer

8 0
2 years ago
How to i solve number 9
Katyanochek1 [597]

Answer: the answer is B. 90√2


Step-by-step explanation:

It is a 45 45 90 triangle and the hypotenuse is always the smaller side (x) root 2

Or x√2

3 0
3 years ago
Read 2 more answers
Carla has $45. Pineapples cost $5 each and mangos cost $2 each. Let p stand for pineapples and let m stand for mangos. Write an
LenKa [72]

Answer

24

Step-by-step explanation:

2:2 = 8

45 / 5 = 168

168 - 45 = 123

123 - 45 = 78

78 take away the 7 is 8 , 8 x 5 = 40 / 8 = 24

5 0
2 years ago
Read 2 more answers
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