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3 years ago

Complete the table for the given rule.

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

6 0

Answer:

X Y

10 7

8 5

6 3

Step-by-step explanation:

Not much to explain - just put a number 3 smaller than X into column Y

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Find the solution for the system of linear equations by substitution: y = 3x + 4 and y = x + 2. Explain how

gavmur [86]

Answer:

(-1, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations by substitution/elimination

Step-by-step explanation:

Step 1: Define systems

y = 3x + 4

y = x + 2

Step 2: Solve for x

Substitute: 3x + 4 = x + 2
Subtract x on both sides: 2x + 4 = 2
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3 years ago

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Write an equation of the line passing through the point (5, 1) that is perpendicular to the line 5x+3y=15. An equation of the li

pochemuha

Answer:

$\displaystyle y = \frac{3}{5}\, x + (-2)$ .

Step-by-step explanation:

The slope of a line in a plane would be $m$ if the equation of that line could be written in the slope-intercept form $y = m\, x + b$ for some constant $b$ .

Find the slope of the given line by rearranging its equation into the slope-intercept form.

$3\, y = (-5)\, x + 15$ .

$\displaystyle y = \frac{(-5)}{3} \, x + 5$ .

Thus, the slope of the given line would be $(-5) / 3$ .

Two lines in a plane are perpendicular to one another if and only if the product of their slopes is $(-1)$ .

Let $m_{1}$ and $m_{2}$ denote the slope of the given line and the slope of the line in question, respectively.

Since the two lines are perpendicular to each other, $m_{1}\, m_{2} = (-1)$ . Apply the fact that the slope of the given line is $m_{1} = (-5) / 3$ and solve for $m_{2}$ , the slope of the line in question.

$\begin{aligned}m_{2} &= \frac{(-1)}{m_{1}} \\ &= \frac{(-1)}{(-5) / 3} = \frac{3}{5}\end{aligned}$ .

In other words, the slope of the line perpendicular to $5\, x + 3\, y = 15$ would be $(3 / 5)$ .

If the slope of a line in a plane is $m$ , and that line goes through the point $(x_{0},\, y_{0})$ , the equation of that line in point-slope form would be:

$(y - y_{0}) = m\, (x - x_{0})$ .

Since the slope of the line in question is $(3 / 5)$ and that line goes through the point $(5,\, 1)$ , the equation of that line in point-slope form would be:

$\begin{aligned} (y - 1) = \frac{3}{5}\, (x - 5) \end{aligned}$ .

Rearrange this equation as the question requested:

$\begin{aligned} y - 1 = \frac{3}{5}\, x - 3 \end{aligned}$ .

$\begin{aligned} y = \frac{3}{5}\, x - 2 \end{aligned}$ .

$\begin{aligned} y = \frac{3}{5}\, x + (-2) \end{aligned}$ .

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2 years ago