the equation for the line of best fit is $f(x)=1.8x - 5.4$ for the set of values in the table. using the…

the equation for the line of best fit is $f(x)=1.8x - 5.4$ for the set of values in the table. using the equation for the line of best fit, what is a good approximation for $x$ when $f(x)=30$?\n| $x$ | $f(x)$ |\n| ---- | ---- |\n| 4 | 5 |\n| 5 | 2 |\n| 6 | 5 |\n| 6 | 6 |\n| 8 | 8 |\n| 9 | 7 |\n| 10 | 18 |\no 14\no 20\no 45\no 54

the equation for the line of best fit is $f(x)=1.8x - 5.4$ for the set of values in the table. using the equation for the line of best fit, what is a good approximation for $x$ when $f(x)=30$?\n| $x$ | $f(x)$ |\n| ---- | ---- |\n| 4 | 5 |\n| 5 | 2 |\n| 6 | 5 |\n| 6 | 6 |\n| 8 | 8 |\n| 9 | 7 |\n| 10 | 18 |\no 14\no 20\no 45\no 54

Answer

Explanation:

Step1: Substitute f(x) value

Given $f(x)=1.8x - 5.4$ and $f(x) = 30$. Substitute $f(x)$ into the equation: $30=1.8x - 5.4$.

Step2: Isolate the term with x

Add 5.4 to both sides of the equation: $30 + 5.4=1.8x-5.4 + 5.4$, which simplifies to $35.4 = 1.8x$.

Step3: Solve for x

Divide both sides by 1.8: $x=\frac{35.4}{1.8}\approx19.67$. Rounding to the nearest whole - number, $x\approx20$.

Answer:

20