To solve for [tex]\( A \)[/tex] given the equation [tex]\( y = \frac{Ax + B}{C} \)[/tex] and the known values [tex]\( y = 10.7 \)[/tex], [tex]\( x = 3.03 \)[/tex], [tex]\( B = 5.98 \)[/tex], and [tex]\( C = 8.94 \)[/tex], follow these steps:
1. Rewrite the given equation:
[tex]\[
y = \frac{Ax + B}{C}
\][/tex]
2. Isolate [tex]\( A \)[/tex] by first multiplying both sides of the equation by [tex]\( C \)[/tex]:
[tex]\[
y \cdot C = Ax + B
\][/tex]
3. Substitute the known values for [tex]\( y \)[/tex] and [tex]\( C \)[/tex] into the equation:
[tex]\[
10.7 \cdot 8.94 = Ax + B
\][/tex]
4. Calculate the left-hand side of the equation:
[tex]\[
10.7 \cdot 8.94 = 95.418
\][/tex]
So the equation becomes:
[tex]\[
95.418 = Ax + B
\][/tex]
5. Subtract [tex]\( B \)[/tex] from both sides to isolate [tex]\( Ax \)[/tex]:
[tex]\[
95.418 - 5.98 = Ax
\][/tex]
6. Calculate the subtraction:
[tex]\[
95.418 - 5.98 = 89.438
\][/tex]
So now the equation is:
[tex]\[
89.438 = Ax
\][/tex]
7. Finally, divide both sides by [tex]\( x \)[/tex] to solve for [tex]\( A \)[/tex]:
[tex]\[
A = \frac{89.438}{3.03}
\][/tex]
8. Calculate the division:
[tex]\[
A = 29.59669966996699
\][/tex]
So, the value of [tex]\( A \)[/tex] is [tex]\( 29.59669966996699 \)[/tex].
