If x/0.5 + y/0.2 = 18, where x and y are positive integers, then what is the value of x ?
1 answer:
An equation without exponents and two variables, is typically a straight line. All the points on the line with integer coordinates are solutions of the equation. Since x and y have to be positive as well, there aren't that many solutions.
Let's see where the line crosses the x-axis, it is where y=0:
x/0.5 + 0 = 18, so x=9 at the intercept. y=0 there, so this is a point on the line, but not a solution to the question (y was supposed to be positive).
Possible values for x are thus limited to 1,2,3,4,5,6 and 7. You can try them all (ie., solve the equation with them) and see for which x values the y is also positive and integer.
You will find that x=4, y=2 is the only pair that satisfies these conditions.
Let's see where the line crosses the x-axis, it is where y=0:
x/0.5 + 0 = 18, so x=9 at the intercept. y=0 there, so this is a point on the line, but not a solution to the question (y was supposed to be positive).
Possible values for x are thus limited to 1,2,3,4,5,6 and 7. You can try them all (ie., solve the equation with them) and see for which x values the y is also positive and integer.
You will find that x=4, y=2 is the only pair that satisfies these conditions.
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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;
- Fourth part; <u>Table 4</u>
- Fifth part;
- 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;
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;
Fourth part;
The best correct option is table 4, given that the table is as follows;
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;
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: