🧮 algebra

1. **State the problem:** We need to find the slope of the line passing through points approximately (-7, -9) and (6, 10) on the Cartesian plane. 2. **Formula for slope:** The slop

1. The problem involves comparing different reading speeds given in pages per hour: 0.08, 0.25, 12.5, and 25 pages per hour. 2. To understand these speeds, we can analyze how long

1. **State the problem:** Solve the equation $$1 + 4x \sin\left(\frac{1}{x}\right) - 2 \cos\left(\frac{1}{x}\right) = 0.$$\n\n2. **Rewrite the equation:** We want to find $x$ such

1. **State the problem:** Solve the equation $$\frac{4x - 2}{6} = \frac{3}{2x + 7}$$ for $x$. 2. **Use the cross-multiplication rule:** When two fractions are equal, their cross pr

1. **Simplify the algebraic expressions:** i. Simplify $9x + 2y - 4z + 8y - 3x + 11z$

1. **State the problem:** Simplify the expression $(8x+7y-5)-(5xy+y-3x)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to each term

1. The problem asks us to write a function notation statement based on the given temperature graph $h(t)$, where $t$ is the number of hours since midnight. 2. From the graph descri

1. **State the problem:** We need to find the total weight in kilograms if 350 grams is 20% of it. 2. **Formula used:** If $x$ is the total weight in kilograms, then 20% of $x$ equ

1. **State the problem:** Simplify the expression $3 \times (x - 2)$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses. The distributive propert

1. **State the problem:** Calculate $\log_6 \left( \frac{216 \cdot 1296 \cdot \sqrt[3]{6}}{\sqrt{1296}} \right)$. 2. **Recall logarithm properties:**

1. **State the problem:** Solve the system of equations by elimination: $$3x + y = 16$$

1. **State the problem:** We are given the quadratic function $f(x) = -0.1x^2 + 8x + 1$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally written

1. **State the problem:** Convert each percentage to a fraction in its simplest form. 2. **Formula and rules:** To convert a percentage to a fraction, use the formula:

1. **Problem:** Solve the equation $14 \times (4x + 2) = 140$ algebraically. 2. **Formula and rules:** Use the distributive property to expand and then isolate $x$ by performing in

1. Stating the problem: Simplify the expression $$\sqrt{\frac{18x^2}{z^6}}$$. 2. Recall the rule for square roots: $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ and $$\sqrt{x^

1. Planteamos el problema: Dividir el polinomio $$1000x^6 + 90x^4 + 110x^3 + 10x^2 + 40x + 50$$ entre $$100x^3 - x + 1$$ y hallar el mayor coeficiente del resto. 2. Usamos la divis

1. **State the problem:** We are given the function $$y=\frac{1}{x-3}$$ and want to understand its behavior and key features. 2. **Formula and rules:** This is a rational function

1. **State the problem:** Solve the quadratic equation $$q_i^2 + 2q_i p_i - 2q_i = 0$$ for $q_i$, where $q_i$ and $p_i$ are allele frequencies. 2. **Rewrite the equation:** Factor

1. **State the problem:** We need to multiply the expression $9(c + 2d)$ using the area model and find the partial products. 2. **Recall the distributive property:** The distributi

1. **State the problem:** We want to multiply $7(20r + 10)$ using the area model. 2. **Formula used:** The distributive property states that $a(b + c) = ab + ac$.

1. **State the problem:** Given the functions \(f(x) = 3x - 7\), \(g(x) = 2x^2 - 3x + 1\), \(h(x) = 4x + 1\), and \(k(x) = -x^2 + 3\), find the value of \(f(x) - g(x)(-2)\). 2. **R