🧮 algebra

1. **State the problem:** Find the equation in the form $y = mx + 6$ of the line containing the point $(2, 5)$ and perpendicular to the line $2x + y = -3$. 2. **Identify the slope

1. **State the problem:** Solve the equation $$-\frac{1}{4}h = -\frac{5}{6}$$ for $h$. 2. **Formula and rules:** To solve for $h$, we need to isolate $h$ on one side of the equatio

1. **State the problem:** Solve the equation $\frac{3}{7} = -\frac{9}{14}d$ for $d$. 2. **Formula and rules:** To solve for $d$, we want to isolate $d$ on one side of the equation.

1. **State the problem:** We are given two speed lines for Ariana and Glenn and need to complete ratio/rate tables, find unit rates, list points, and answer distance/time questions

1. **Problem:** How many widgets can the factory produce in 5 days? Given data: Widgets produced each day increase by 800 per day: 800, 1600, 2400, 3200, 4000.

1. Masalah: Buktikan bahwa elemen identitas pada grup adalah unik. 2. Definisi: Dalam teori grup, elemen identitas $e$ adalah elemen yang memenuhi $e \cdot a = a \cdot e = a$ untuk

1. **State the problem:** Calculate the value of the expression $-8 \times (-10) - 7 \times \left(\frac{1}{-1}\right)$. 2. **Recall the rules:** Multiplying two negative numbers re

1. **State the problem:** Calculate the product $$(-3 \cdot 10^{4}) \cdot (2 \cdot 10^{-3})$$. 2. **Recall the multiplication rule for powers of 10:** When multiplying powers of 10

1. **State the problem:** Simplify the expression $$\frac{8r}{5} - \frac{rs^2}{4}$$. 2. **Find a common denominator:** The denominators are 5 and 4. The least common denominator (L

1. The problem states that we have a line passing through the points $(-2, -8)$ and $(2, 8)$. We need to find the slope of this line and represent the "rise" and "run". 2. The form

1. The problem asks to identify which given functions are polynomial functions. 2. A polynomial function is defined as a function of the form $$p(x) = a_n x^n + a_{n-1} x^{n-1} + \

1. **State the problem:** We are given two equations: $$y = \frac{\sqrt{3x}}{3}$$

1. The first problem asks to simplify the expression $9 - 6x - 42 + 4x - 45$. 2. To simplify, combine like terms. Like terms are terms that have the same variable raised to the sam

1. **State the problem:** Simplify the expression $-8 + 2x + 17 - 9x + 20$ and solve the equations $8x + 23 = 79$, $6x - 23 = 79$, and $8x + 15 = 79$. 2. **Simplify the expression:

1. **State the problem:** Simplify the expression $12pr - 8pr - 19$. 2. **Identify like terms:** The terms $12pr$ and $-8pr$ are like terms because they both contain the variables

1. **State the problem:** Solve the equation $x^2 - 5x + 6 = 0$ for $x$. 2. **Formula and rules:** This is a quadratic equation of the form $ax^2 + bx + c = 0$. We can solve it by

1. Chapter 1 - Quadratic Functions: Solve the quadratic equation $$x^2 - 5x + 6 = 0$$ by factoring. 2. Chapter 2 - Nonlinear Functions: Sketch the graph of the piecewise function $

1. **Énoncé du problème :** On considère les suites $(U_n)$ et $(V_n)$ définies par

1. **Énoncé du problème :** Calculer $V_0$ et $U_1$ pour les suites $(U_n)$ et $(V_n)$ définies par :

1. The problem is to solve an exponential equation, for example, solve for $x$ in the equation $$2^x = 16$$. 2. The formula used here is based on the property of exponents: if $a^x

1. The problem is to solve part 2 a) of a given question, but since the exact problem statement is not provided, please provide the full details of 2 a) for a precise solution. 2.