🧮 algebra

1. **State the problem:** Solve the algebraic expression $3((6-0.5q)-2q)$. 2. **Understand the expression:** Inside the parentheses, we have $6 - 0.5q - 2q$. We will simplify this

1. **State the problem:** We are given the system of equations: $$2x + y = 6$$

1. **State the problem:** We want to understand why the graphs of $\log(1000x)$ and $\log x + 3$ are the same. 2. **Recall the logarithm property:** The logarithm of a product can

1. Solve the equation: $$6 - \left[\frac{3}{2} \div \left(0.5 + \frac{1}{4}\right)\right] = 4$$ 2. First, simplify inside the parentheses:

1. **Problem:** Solve $3.6 + 2.4 \div 0.6 - 1.25$ using the order of operations. 2. **Formula and rules:** According to the order of operations (PEMDAS/BODMAS), division and multip

1. **Problem 4:** Given the equation $$520 \div x = 40n$$, find the value of $$x$$ in terms of $$n$$. 2. **Step 1:** Write the equation clearly:

1. **Problem 4:** Given the equation $$520 \div x = 40n$$, find an expression equal to $$nx$$. 2. **Step 1:** Start with the given equation:

1. The problem asks: What is 55% of 20? 2. To find a percentage of a number, use the formula:

1. **State the problem:** We need to graph the rational function $$f(x) = \frac{-2}{-x - 2}$$ and identify its vertical and horizontal asymptotes. 2. **Rewrite the function:** Simp

1. **State the problem:** We need to find the discriminant and the number of real solutions for the quadratic equation $$3x^2 - 7x + 1 = 0$$. 2. **Recall the formula for the discri

1. **State the problem:** We need to graph the parabola given by the equation $$y = -x^2 + 4x - 2$$ and plot five points: the vertex, two points to the left, and two points to the

1. **State the problem:** Expand the logarithmic expression $$\log(xz^3)$$ using the properties of logarithms. 2. **Recall the properties of logarithms:**

1. **State the problem:** Evaluate the expressions $\frac{5}{4^3}$ and $\left(-\frac{3}{5}\right)^2$. 2. **Evaluate the first expression:**

1. **State the problem:** Find values of A and B given the system:

1. Find the 2nd estimate for $\sqrt{341}$ using Newton's Iteration Method with initial estimate 18. Newton's formula: $$x_{n+1} = \frac{x_n + \frac{S}{x_n}}{2}$$ where $S$ is the n

1. The problem is to find the inverse of the linear function $f(x) = -x + 2$ in slope-intercept form $y = mx + b$. 2. To find the inverse function $f^{-1}(x)$, we start by replacin

1. **State the problem:** Solve the system of linear equations: $$4x + 8y = 20$$

1. **State the problem:** Solve the system of linear equations: $$4x + 8y = 20$$

1. **Stel het probleem vast:** We hebben een ellips gegeven door de vergelijking $$\frac{x^2}{36} + \frac{y^2}{16} = 1$$ met lastigere getallen dan het origineel. 2. **Formule en r

1. **State the problem:** We are given two expressions for angles: $(5x + 23)^\circ$ and $(17x - 41)^\circ$, and we want to find the value of $x$ when these two angles are equal. 2

1. The problem is to rewrite the formula for the area of a rectangle, $A = b \cdot h$, to solve for the height $h$ by isolating it on one side of the equation. 2. The formula for t