a 12.0 cm object is 9.0 cm from a convex mirror that has a focal length of -4.5 cm. what is the distance of…

Explanation:

Step1: Recall mirror formula

The mirror formula is $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$, where $f$ is the focal - length, $u$ is the object distance, and $v$ is the image distance.

Step2: Substitute given values

Given $f=- 4.5$ cm and $u = 9.0$ cm. Substitute into the mirror formula: $\frac{1}{-4.5}=\frac{1}{9}+\frac{1}{v}$.

Step3: Solve for $\frac{1}{v}$

$\frac{1}{v}=\frac{1}{-4.5}-\frac{1}{9}$. First, find a common denominator. The common denominator of 4.5 and 9 is 9. So, $\frac{1}{-4.5}=-\frac{2}{9}$. Then $\frac{1}{v}=-\frac{2}{9}-\frac{1}{9}=-\frac{2 + 1}{9}=-\frac{3}{9}=-\frac{1}{3}$.

Step4: Find $v$

If $\frac{1}{v}=-\frac{1}{3}$, then $v=-3$ cm.

Answer:

A. -3 cm