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Sagot :
The answer would be C=10d+12
Hope this helps
Have a great day/night
The total cost for the guitar lessons includes an initial cost fee which is
added to the unit cost.
Where the cost of 7 lessons is a and the cost of 11 lessons is b, we have
- The total cost of lessons is; [tex]\displaystyle y = \mathbf{ \frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]
Where the cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;
- The total cost of lessons is; f(x) = y = 10·x + 12 and one lesson costs $22
Reasons:
The general equation for the total cost of lessons is;
Let a represent the cost of 7 guitar lessons, and let b represent the cost of
9 guitar lessons, given that the cost increases linearly with the number of
lessons, we have;
The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson
Therefore;
[tex]\displaystyle Slope = \frac{b - a}{11 - 7} = \mathbf{\frac{b - a}{4}}[/tex]
Expressing the equation in the slope and intercept form, we have;
[tex]\displaystyle (y - a) = \frac{b - a}{4} \cdot (x - 7)[/tex]
[tex]\displaystyle y = \frac{b - a}{4} \cdot x - 7 \times\frac{b - a}{4} + a = \frac{b - a}{4} \cdot x+ \frac{11\cdot a - 7 \cdot b}{4}[/tex]
[tex]\displaystyle y = \frac{b - a}{4} \cdot x+ \frac{11\cdot a - 7 \cdot b}{4} = \mathbf{\frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]
- The total cost is; [tex]\displaystyle \underline{y = \frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]
Where, in a similar question, a = $82, b = $122, we have;
[tex]\displaystyle y = \frac{1}{4} \cdot(122 - 82) \cdot x+ \frac{1}{4} \cdot (11\times 82 - 7 \times 122)= 10 \cdot x + 12[/tex]
y = 10·x + 12
- The total cost of x lessons is; f(x) = y = 10·x + 12
The total cost of a lessons is; y = 10 × 1 + 12 = 22
- The cost of a lesson, f(1) = $22
Learn more about linear relationships here:
https://brainly.com/question/2154877
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