🧮 algebra

1. **State the problem:** We need to graph the inequality $y > -2x - 1$ on the coordinate axes. 2. **Understand the inequality:** The inequality $y > -2x - 1$ means that $y$ is gre

1. **State the problem:** We need to graph the linear inequality $$3x + y \leq -3$$ on the Cartesian coordinate system. 2. **Rewrite the inequality in slope-intercept form:** To gr

1. **State the problem:** Simplify the expression $$\frac{x^{2} + 14x + 49}{x^{2} + 15x + 56}$$. 2. **Recall the factoring formula:** For a quadratic expression $ax^2 + bx + c$, we

1. **State the problem:** We need to graph the linear inequality $$3x + y \leq -3$$ on a coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, express

1. **Problem Statement:** We need to graph the linear inequality $$3x + y \leq -3$$ on the coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, expres

1. **State the problem:** Solve for the positive value of $x$ in the equation $$2|4 - x| + 3|4 - x| = 25.$$\n\n2. **Combine like terms:** Since both terms have $|4 - x|$, add the c

1. **State the problem:** Solve the equation $$\frac{7}{2} - \frac{7}{2x} = 7$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, find a common den

1. **State the problem:** Solve the equation $$\frac{7}{2} + \frac{5}{2x} = 3$$ and understand the rectangle with length $x+2$ and width $x$ positioned in the first quadrant. 2. **

1. **State the problem:** Solve the equation $$\frac{6x - 18}{8} = \frac{2x + 3}{8x}$$ for $x$. 2. **Understand the equation:** We have a rational equation where both sides are fra

1. **State the problem:** We need to sketch the graph of the quadratic function $$f(x) = 2x^2 - 4x - 2$$. 2. **Recall the general form and properties:** A quadratic function is gen

1. **State the problem:** We have two functions, A and B, with different rates of change (slopes). We want to find the equation of a new linear function whose slope is an integer b

1. **Problem Statement:** We need to sketch the graph of the quadratic function $$f(x) = 2x^2 - 4x - 2$$.

1. **Stating the problem:** We want to create an exponential function that fits given $x$ and $y$ coordinates. 2. **Formula used:** An exponential function generally has the form $

1. **Problem 1:** Solve the equation $$\frac{3x}{x-2} - \frac{6}{x-2} = \frac{3(x-2)}{x-2}$$ Since the denominators on the left side are the same, combine the fractions:

1. **State the problem:** We need to sketch the graph of the quadratic function $$f(x) = 2x^2 - 4x - 2$$.

1. **State the problem:** We are given the quadratic function $f(x) = 2x^2 - 4x - 2$ and some points on its graph: $(0, -2)$, $(2, -6)$, $(\frac{1}{2}, -3)$, and $(-1, 0)$. We want

1. مسئله: حل و ساده‌سازی توابع داده شده از ۱۶ تا ۲۹. 2. تابع ۱۶: $y=\frac{1}{|x|} - x$

1. The problem involves evaluating powers and solving for unknowns in number patterns and graphs. 2. For powers, recall the rule: $a^1 = a$ and $a^2 = a \times a$.

1. The problem involves understanding the summation and product notation along with some special mathematical symbols. 2. The summation \(\sum_{i=1}^{n} i^2\) means to add the squa

1. Állítsuk fel a változókat: legyen $J$ János kora, és $M$ Mihály kora. 2. Az első feltétel szerint: amikor Mihály annyi idős lesz, mint János most ($J$), akkor együtt 35 évesek l

1. **State the problem:** We have two equations: $$3a + 14s = 99000$$