Question

1. find the product of the monomials.

b. $5x^{2}y^{3}cdot(- 2\frac{3}{4}xy^{6})$
ch.1: 123. compare each expression to zero. do not calculate!
d. $-\frac{57}{88}cdot92.3 - 75$
e. $\frac{-88\frac{1}{15}}{-19.6}$
ch.1: 104. the midpoint between $x$ and 27 is -3. find $x$.
ch.1: 110. the arithmetic mean of 3, 15, and my number is 40. what is my number?
ch.1: 127. find the roots of each equation.
a. $5x^{2}-3x = 0$

Explanation:

1127b. Find the product of the monomials

Step1: Multiply coefficients

Multiply 5 and $- 2\frac{3}{4}=-\frac{11}{4}$. So, $5\times(-\frac{11}{4})=-\frac{55}{4}$.

Step2: Multiply variables with same base

For $x$ - terms: $x^{2}\cdot x=x^{2 + 1}=x^{3}$ (using $a^{m}\cdot a^{n}=a^{m + n}$). For $y$ - terms: $y^{3}\cdot y^{6}=y^{3+6}=y^{9}$.

Step3: Combine results

The product is $-\frac{55}{4}x^{3}y^{9}$.

Step1: Analyze the first - term sign

$-\frac{57}{88}\cdot92.3$ is negative since $-\frac{57}{88}$ is negative and $92.3$ is positive. Let $a =-\frac{57}{88}\cdot92.3$.

Step2: Consider subtraction

We have $a - 75$, where $a$ is negative and we are subtracting a positive number 75. So the result is negative.

Step1: Analyze the sign of the numerator and denominator

The numerator $-88\frac{1}{15}=-\frac{88\times15 + 1}{15}=-\frac{1321}{15}$ is negative and the denominator $- 19.6$ is negative.

Step2: Determine the sign of the fraction

A negative divided by a negative is positive.

Answer:

$-\frac{55}{4}x^{3}y^{9}$

Ch.1:123d. Compare the expression to zero