🧮 algebra

1. **State the problem:** Solve the equation $x + 1.29 = 3.78$ for $x$. 2. **Formula and rule:** To isolate $x$, subtract $1.29$ from both sides of the equation. This uses the subt

1. The problem states that the slope $m$ of a line is $-\frac{5}{6}$. We want to understand what this means and how to use it. 2. The slope $m$ of a line is defined as the ratio of

1. The problem states Marcos spent 8.15 total on a drink and a sandwich. 2. The drink cost 1.29, so the sandwich cost is represented by $x$.

1. **State the problem:** Find the equation of a line in slope-intercept form $y=mx+b$ that passes through the point $(5,5)$ with slope $m=\frac{5}{6}$. 2. **Recall the slope-inter

1. **State the problem:** Solve the equation $-4b (3b - 5b - 7) = -5 (2b + 9) + 8$ for $b$. 2. **Simplify inside parentheses:**

1. The problem asks for the equation of a line passing through the point $(7, -9)$ with an undefined slope. 2. An undefined slope means the line is vertical.

1. **State the problem:** Find the equations of any vertical asymptotes for the function $$f(x) = \frac{3x - 11}{x^2 + 3x - 4}$$. 2. **Recall the rule for vertical asymptotes:** Ve

1. **State the problem:** Find the vertex and x-intercepts of the quadratic function $f(x) = -x^2 - 3x - 4$. 2. **Formula for vertex:** The vertex of a parabola given by $f(x) = ax

1. The problem is to graph the solution regions for each system of linear inequalities from 15 to 24. 2. Each inequality represents a half-plane bounded by a line. The solution to

1. **State the problem:** Find the vertex and x-intercepts of the quadratic function $f(x) = 3x^2 - 2x - 2$. 2. **Formula for vertex:** The vertex of a parabola given by $f(x) = ax

1. **Problem:** Verify if the given inverse relations for the original functions are correct. 2. **Understanding Inverse Relations:**

1. **Problem Statement:** Find the inverse functions for the given functions: - $f(x) = 3x + 5$

1. **Stating the problem:** Solve the equation $$\left(112128.28-60\cdot x^2\right)\cdot \left(46135.98-28.03\cdot x^2\right)-\left(-46135.98\right)^2=0.$$\n\n2. **Rewrite the equa

1. **State the problem:** Simplify the radical expression $$5\sqrt{x^5 y^5}$$. 2. **Recall the rule for nth roots:** $$\sqrt[n]{a^n} = |a|$$ if $n$ is even, and $a$ if $n$ is odd.

1. **State the problem:** Solve the equation $6x - 4 - 2x + 5 = 13$ for $x$. 2. **Combine like terms:** Group the $x$ terms and the constants separately.

1. **State the problem:** Simplify the expression $6(x + 3) - 10 + 2x$ and find which of the given options matches the result. 2. **Use the distributive property:** Multiply $6$ by

1. **Simplify the expression:** $5x - 70 + 13x + 65$ Combine like terms (terms with $x$ and constants separately):

1. **State the problem:** Solve the proportion $$\frac{24}{4} = \frac{x}{11}$$ to find the value of $x$. 2. **Formula used:** In a proportion $$\frac{a}{b} = \frac{c}{d}$$, the cro

1. **State the problem:** Alejandro sells tacos and burritos. He sold 43 tacos and wants to sell a total of 111 tacos and burritos combined. Each taco costs 4.50 and each burrito c

1. **State the problem:** The drama club sells student tickets at $6.50 each and adult tickets at $9 each.

1. The problem states: "Eight minus a number $x$ divided by three is greater than or equal to eleven." We need to translate this sentence into an inequality. 2. Let the number be $