🧮 algebra

1. **Problem Statement:** Show that the equation $$x^3 + 3x + 1 = 0$$ has exactly one real solution. 2. **Define the function:** Let $$f(x) = x^3 + 3x + 1$$.

1. **State the problem:** Evaluate the expression $$-\frac{2}{3}xyz$$ given $$x = -8.4$$, $$y = 0.25$$, and $$z = 3 \frac{4}{5}$$. Write the answer as a mixed number in simplest fo

1. **State the problem:** We need to find the value of $C$ in the equation $C + C + 88 = 180$. 2. **Write the equation:** The equation can be simplified by combining like terms: $$

1. **State the problem:** Evaluate $\frac{1}{2} yz$ given $y = \frac{3}{5}$ and $z = -1 \frac{7}{8}$. Write the answer as a fraction in simplest form. 2. **Convert mixed number to

1. **Simplify** $\frac{2}{a+1} + \frac{3}{2a+2}$. - Note $2a+2 = 2(a+1)$.

1. The problem appears to involve evaluating or simplifying the expression: $$\frac{5000 \times e^{4.5 \times 20}}{4.5 \times 1.5}$$. 2. First, recognize that $e$ is the base of th

1. **State the problem:** We need to evaluate $\frac{a}{b}$ where $a = -\frac{1}{4}$ and $b = 0.02$. Then, write the answer as a mixed number in simplest form. 2. **Write the expre

1. **Problem Statement:** Identify the domain and range of the given graph and determine if it represents a function and if it is one-to-one.

1. **State the problem:** Evaluate $\frac{1}{4}xy$ given $x = -\frac{2}{3}$ and $y = \frac{3}{5}$. Write the answer as a fraction in simplest form. 2. **Formula used:** The express

1. **State the problem:** We need to find the value of $8 \frac{1}{3} \div \left(-\frac{5}{9}\right)$ and write the answer in simplest form. 2. **Convert mixed number to improper f

1. **State the problem:** We need to find the value of $-3 \frac{4}{9} \div -2 \frac{1}{3}$ and express the answer as a mixed number in simplest form. 2. **Convert mixed numbers to

1. **State the problem:** Simplify the fraction $$\frac{4aw}{16a^2w}$$. 2. **Recall the rule:** To simplify a fraction, divide the numerator and denominator by their greatest commo

1. **State the problem:** We are given two sets of points representing two groups of people living with a disease from 1993 to 2000. We need to find the equations of the lines appr

1. **Stating the problem:** We have two vertical matrices (or column vectors) and their operations:

1. **Problem Statement:** We have a brass alloy made by mixing copper and zinc in the ratio 8:2. We want to find how many kilograms of copper are in 2 kg of this brass. 2. **Unders

1. **State the problem:** Calculate the value of the expression $$\frac{(110 - 82.5) \times 1.25}{110 - (82.5 \times 1.25)}$$. 2. **Recall the order of operations:** Perform operat

1. **Problem statement:** Lauren wants to arrive at station B by 12:00 on Thursday. Each bus takes 48 minutes to travel from station A to station B. It takes Lauren 13 minutes to g

1. **State the problem:** Solve the equation $x - 3 = \frac{2x - 6}{2}$ for $x$. 2. **Understand the equation:** The right side is a fraction with numerator $2x - 6$ and denominato

1. **State the problem:** We need to compare prices of various products purchased in Canada and the US by calculating unit prices in consistent units (mL or sheets) and converting

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-2x + y + 3z = 20 \\ -3x + 2y + z = 21 \\ 3x - 2y + 3z = -9 \end{cases}$$

1. The problem is to sketch the graph of the function $y = x^2 - 1$. 2. This is a quadratic function in the form $y = ax^2 + bx + c$ where $a = 1$, $b = 0$, and $c = -1$.