1. **State the problem:** We are given the formula for cardiac output $D = V \cdot R$, where $D$ is the cardiac output, $V$ is the volume of blood pumped per heartbeat, and $R$ is the number of heartbeats per minute. 2. **Find $V$ in terms of $D$ and $R$:** Starting from the formula: $$D = V \cdot R$$ To isolate $V$, divide both sides by $R$: $$V = \frac{D}{R}$$ Show the cancellation step: $$V = \frac{D}{\cancel{R}} \cdot \frac{1}{\cancel{R}}$$ This simplifies to: $$V = \frac{D}{R}$$ 3. **Next problem: Factor the expression $42r^3s^2 - 35r^2s^3$** 4. **Factor out the greatest common factor (GCF):** - Coefficients: GCF of 42 and 35 is 7 - Variables: $r^2$ is common (lowest power of $r$), $s^2$ is common (lowest power of $s$) So, factor out $7r^2s^2$: $$42r^3s^2 - 35r^2s^3 = 7r^2s^2(6r - 5s)$$ 5. **Check the answer choices:** - Option A: $7rs(6s - 5r)$ - Option B: $7rs(6rs - 5rs)$ Our factorization is $7r^2s^2(6r - 5s)$, which is not exactly either option. 6. **Re-examine the factorization:** Try factoring out $7rs$ instead: $$42r^3s^2 - 35r^2s^3 = 7rs(6r^2s - 5rs^2)$$ This matches neither option exactly. 7. **Compare with option A:** Option A is $7rs(6s - 5r)$, which is not equivalent to the original expression. 8. **Compare with option B:** Option B is $7rs(6rs - 5rs) = 7rs(1rs) = 7rs(0)$ which is zero, so incorrect. 9. **Conclusion:** Neither option matches the correct factorization exactly, but option A is closest in form. **Final answers:** $$V = \frac{D}{R}$$ Equivalent expression: $$42r^3s^2 - 35r^2s^3 = 7rs(6r^2s - 5rs^2)$$ Since the options do not match exactly, the correct factorization is as above.