Q: Simplify or evaluate the expression 11 + x / x^3 + 2x(5 - x)

Answer: The simplified form of the expression is $\frac{11 + x}{x^3} + 10 - 2x$. Explanation: This problem involves algebraic manipulation, including combining fractions and simplifying expressions. The key concepts used are the properties of fractions, distributive property, and combining like terms. The main goal is to write the expression in a simplified, more manageable form. Steps: Start with the original expression: \[ \frac{11 + x}{x^3} + 2x(5 - x) \] Expand the second term using the distributive property: \[ 2x \times 5 = 10x \quad \text{and} \quad 2x \times (-x) = -2x^2 \] So, \[ 2x(5 - x) = 10x - 2x^2 \] Rewrite the entire expression with the expanded form: \[ \frac{11 + x}{x^3} + 10x - 2x^2 \] To combine or simplify further, note that the terms $10x$ and $-2x^2$ are not like terms with the fraction, so the expression in its simplified form is: \[ \boxed{\frac{11 + x}{x^3} + 10x - 2x^2} \] Optional step: If desired, express all terms over a common denominator $x^3$, but since the problem only asks for simplification, the above form is sufficient.

Q: What is the number who chose Italian dressing?

Answer: The number of customers who chose Italian dressing is 90. Explanation: This problem involves understanding the distribution of salad dressing choices among customers, which is represented by a circle graph (pie chart). The key concepts involved are percentage calculations and proportions. The problem asks to find the difference in the number of customers choosing Italian dressing and vinaigrette dressing, given the total number of customers and the percentage distribution. The method involves: Calculating the number of customers for each dressing based on the percentage. Finding the difference between the two numbers. Steps: Identify the total number of customers: Total customers = 200 Determine the percentage for Italian dressing: From the table, Italian dressing = 45% Calculate the number of customers who chose Italian dressing: \[ \text{Number of Italian dressing customers} = \frac{45}{100} \times 200 = 0.45 \times 200 = 90 \] Determine the percentage for Vinaigrette dressing: Vinaigrette = 30% Calculate the number of customers who chose Vinaigrette dressing: \[ \frac{30}{100} \times 200 = 0.30 \times 200 = 60 \] Find the difference between Italian and Vinaigrette dressing customers: \[ 90 - 60 = 30 \] Question asks for the difference between the number who chose Italian dressing and the number who chose vinaigrette dressing: The difference is 30. Note: The question also mentions the number who chose vinaigrette dressing, but the main calculation is to find the number for Italian dressing, which is 90.

Question

Simplify or evaluate the expression 11 + x / x^3 + 2x(5 - x)

Accepted Answer

Answer: The simplified form of the expression is $\frac{11 + x}{x^3} + 10 - 2x$.

Explanation:  This problem involves algebraic manipulation, including combining fractions and simplifying expressions. The key concepts used are the properties of fractions, distributive property, and combining like terms. The main goal is to write the expression in a simplified, more manageable form.

Steps:

Start with the original expression:

$$
   \frac{11 + x}{x^3} + 2x(5 - x)
   $$

Expand the second term using the distributive property:

$$
   2x \times 5 = 10x \quad \text{and} \quad 2x \times (-x) = -2x^2
   $$     So,     $$
   2x(5 - x) = 10x - 2x^2
   $$

Rewrite the entire expression with the expanded form:

$$
   \frac{11 + x}{x^3} + 10x - 2x^2
   $$

To combine or simplify further, note that the terms $10x$ and $-2x^2$ are not like terms with the fraction, so the expression in its simplified form is:

$$
   \boxed{\frac{11 + x}{x^3} + 10x - 2x^2}
   $$

Optional step:  If desired, express all terms over a common denominator $x^3$, but since the problem only asks for simplification, the above form is sufficient.

Simplify or evaluate the expression 11 + x / x^3 + 2x(5 – x)