Question

NEED HELP WITH THESE QUESTIONS

Answer 1

For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

$\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =$

Applying double C we have:

$\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =$

By definition of multiplication of powers of the same base we have to place the same base and add the exponents:$\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =$

Canceling common terms:

$\frac {mn ^ 5} {p ^ 4}$

Answer:

Option A

Question 2:

We should simplify the following expression:

$\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}$

So, we have:

$\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =$

Simplifying common terms:

$\frac {1} {y ^ 2z ^ 2}$

Answer:

Option D

Question 3:

We factor the following expressions to rewrite the experience:

$r ^ 2 + 7r + 10$: We look for two numbers that multiplied give 10 and added 7:

$(r + 5) (r + 2)$

$r ^ 2-5r-50:$ We look for two numbers that multiplied give -50 and added -5:

$(r-10) (r + 5)$

$3r-30 = 3 (r-10)$

Rewriting the given expression we have:

$\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =$

We simplify common terms in the numerator and denominator we have:

$(r + 2)$

Answer:

Option D

Answer 2

Answer:

17. The correct answer option is A.

18. The correct answer option is D.

19. The correct answer option is D.

Step-by-step explanation:

17. $\frac{m^2n^3}{p^3} \times \frac{mp}{n^2}$

Changing division to multiplication by taking reciprocal of the latter fraction to get:

$\frac{m^2n^3}{p^3} \times \frac{n^2}{mp}$

$\frac{mn^5}{p^4}$

The correct answer option is A. $\frac{mn^5}{p^4}$.

18. $\frac{3xyz^2}{6y^4} \times \frac{2y}{xz^4}$

$\frac{1}{y^2z^2}$

The correct answer option is D. $\frac{1}{y^2z^2}$.

19. $\frac{r^2+7r+10}{3} \times \frac{3r-30}{r^2-5r-50}$

Factorizing the terms to get:

$\frac{(r+2)(r+5)}{3} \times \frac{3(r-10)}{(r+5)(r-10)}$

Cancelling the like terms to get:

$r+2$

The correct answer option is D. $r+2$.