🧮 algebra

1. The problem is to multiply $9$ by $-\frac{5}{3}$. 2. The formula for multiplication of a whole number and a fraction is:

1. **State the problem:** We have a table with two expressions: $x^2 + y$ and $xy$, and some values to find.

1. **State the problem:** We need to estimate the average rate of change of money spent on fuel with respect to average speed from $x=5$ to $x=9$. 2. **Recall the formula for avera

1. **Stating the problem:** We need to solve the equation given by the user. However, the user did not specify the equation explicitly. Since no equation was provided, I cannot sol

1. **State the problem:** Simplify or analyze the expression $$\frac{2}{(x+1)^2}$$. 2. **Recall the formula and rules:** This is a rational expression where the numerator is 2 and

1. **State the problem:** Wilbur has a rectangular pool 12 feet by 25 feet and wants to build a concrete walkway of equal width $x$ around it. The total area of the pool plus walkw

1. The problem is to evaluate the expression $i^{-23}$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Recall the powers of $i$ cycle every 4 steps:

1. **State the problem:** Evaluate the expression $4t^2 - (2t)^2$ when $t=3$. 2. **Write the formula and explain:** The expression is $4t^2 - (2t)^2$. We will substitute $t=3$ and

1. The problem asks us to find which equation is parallel to the line given by $$y = -2x + 13$$. 2. Recall that two lines are parallel if and only if they have the same slope.

1. **State the problem:** We need to find an expression for the total cost when ordering $y$ books, where the first book costs 15 and each additional book costs 12.

1. **State the problem:** We need to find the percentage change in Carly's total annual pay from last year to this year, given a 6% increase in salary and a 9% decrease in bonus.

1. **Stel het probleem vast:** We moeten de uitdrukking a) berekenen: $\frac{5^2 - 5!}{18 - 23^2}$. 2. **Formule en regels:** We gebruiken de volgorde van bewerkingen: eerst machte

1. The problem is to understand the values given: -0.7 and -0.5. 2. These are decimal numbers between -1 and 0, representing points on the number line.

1. The problem is to solve for $d$ given an equation or context (not provided explicitly). 2. Since the problem statement is incomplete, let's assume a common algebraic context whe

1. **State the problem:** We are given the quadratic function $$f(x) = -0.04x^2 + 0.48x - 0.8$$ representing the company's expected net worth over time in years.

1. **State the problem:** We are given the quadratic function $$f(x) = -x^2 + 20x - 96$$ which models the height of a soccer ball in meters as a function of horizontal distance $x$

1. **State the problem:** Simplify the expression $$(4r^3 + 3r^4) + (r^4 + 5r^3)$$ 2. **Identify like terms:** Terms with $r^4$ and terms with $r^3$ can be combined.

1. **State the problem:** Solve the equation $7[x+2]-3=4$ for $x$. 2. **Apply the distributive property:** Multiply 7 by each term inside the brackets:

1. **Problem Statement:** Convert the quadratic equation $y = 2x^2 - 8x + 7$ into graphing form (vertex form) and find the vertex and line of symmetry.

1. Problem statement: Simplify the expressions for parts a, b, and c. 2. Part a: Simplify $2x + x(4x - 2) - 6$

1. **State the problem:** Factor the polynomial $$P(x) = 2x^3 + 13x^2 + 3x - 18$$ given that $$(x + 6)$$ is a factor. 2. **Use the factor theorem:** Since $$(x + 6)$$ is a factor,