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Firdavs [7]
2 years ago
9

The ordered pairs (−4,−3)

Mathematics
1 answer:
lilavasa [31]2 years ago
3 0

The equations and inequality expresses the relationship between the variables.

The correct responses are;

  • First part; The rule that represent the function is; <u>y = 0.5·x - 1</u>
  • Second part; the correct option is the inequality; <u>2·n - 6 ≥ 35</u>
  • Third part; \displaystyle \underline{b = \frac{- a\cdot x^2 - c}{x}}
  • Fourth part; <u>Table 4</u>
  • Fifth part; \displaystyle  \underline{y < -\frac{1}{2} \cdot x - 4}
  • Sixth part; <u>75·w + 55 ≤ 400</u>

Reasons:

First part;

The difference between y-values following a change in 2 units of the x-value is a constant, and is equal to 1;

The rate of change of the function, <em>m</em>, is therefore;

\displaystyle m = \frac{2 - 1}{6 - 4}  = \frac{1}{2} = 0.5

The slope and intercept form of the equation of the function is therefore;

y - 3 = 0.5·(x - 8) = 0.5·x - 4

y = 0.5·x - 4 + 3 = 0.5·x - 1

The rule that represent the function is; <u>y = 0.5·x - 1</u>

Second part;

2·n represent twice the number

The difference between twice the number and 6 = 2·n - 6

At least 35 = ≥ 35

Therefore, the inequality is; <u>2·n - 6 ≥ 35</u>

Third part;

The given quadratic equation is; a·x² + b·x + c = 0

Therefore;

\displaystyle \underline{b = \frac{-c - a\cdot x^2}{x}}

Fourth part;

The best correct option is table 4, given that the table is as follows;

\begin{tabular}{|c|cc|}In&&Out\\Not clear&&\\9&&17\\10&&19\end{array}\right]

Fifth part;

The y-intercept of the graph is -0.5

The slope is -4 ÷ 8 = -0.5

Therefore, the equation is; y = -0.5·x - 4

The shaded area is the area lower than the y-values, with broken lines (indicating < relationship) which gives, the correct inequality as follows;

\displaystyle  \underline{y < -\frac{1}{2} \cdot x - 4}

Sixth part;

The amount Jordan part-time job pays = $75

The amount he has already saved = $55

The cost of the iPhone = $400

Let <em>w</em> represent the number of weeks Jordan works, at his part-time job to purchase the iPhone, we have;

<u>75·w + 55 ≤ 400</u>

Learn more about writing equations and inequalities here:

brainly.com/question/14321394

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