🧮 algebra

1. The problem asks to express the number 0.0062143 in standard form. 2. Standard form (also called scientific notation) expresses numbers as $a \times 10^n$ where $1 \leq |a| < 10

1. **State the problem:** Solve the equation $$\frac{5x + 1}{2} - \frac{x - 2}{6} = \frac{2x + 4}{3}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fract

1. The problem asks which graph represents the relation $y = -x$. 2. The equation $y = -x$ is a linear function where the slope is $-1$ and the y-intercept is $0$.

1. **Problem:** Solve the equation $$x^4 - 6x^2 + 8 = 0$$. 2. **Formula and approach:** This is a quartic equation but can be treated as a quadratic in terms of $y = x^2$.

1. **State the problem:** We are given the equation $$5x + 12 - x - 26 = 2x + 43$$ and need to find which of the given options is equivalent to this equation. 2. **Simplify the ori

1. The problem asks which graph represents a given relation. However, the relation itself is not specified in the question. 2. To determine which graph represents a relation, we ne

1. **State the problem:** We have two parking plans, A and B, each with a fixed monthly fee plus a cost per day parked. We want to find the system of equations representing the tot

1. **State the problem:** We are given the function $$g(a) = \frac{5a + 3}{2a}$$ and need to find the expression for $$g(a) - g(2a)$$. 2. **Write the expressions:**

1. **State the problem:** Simplify the expression $ (2x+3) + (4x-5)(2x+3) + (4x-5) $. 2. **Recall the distributive property:** To simplify expressions with parentheses, multiply te

1. **Problem statement:** Solve for $x$ given the equation $\left(3^x\right)^2 = 7.5$. 2. **Rewrite the equation:** Using the power of a power rule, $\left(a^m\right)^n = a^{mn}$,

1. The problem is to understand the value of $n$ given as 42. 2. Here, $n$ is simply a variable representing a number, and it is stated that $n=42$.

1. **Stating the problem:** We need to multiply the fraction $\frac{3}{4}$ by several fractions: $\frac{2}{2}$, $\frac{6}{6}$, $\frac{3}{3}$, $\frac{4}{4}$, and $\frac{5}{5}$. We w

1. **Énoncé du problème :** Étudier la fonction $g$ définie par $g(x) = x^3 + x^2 + 3x - 1$. 2. **Dresser le tableau de variations (TV) de $g$ :**

1. **State the problem:** Determine if the equation $5(3-2x) = 5x - 2(8x-7)$ is an identity (true for all $x$) or not. 2. **Expand both sides:**

1. **State the problem:** We need to compare the fractions $\frac{6}{8}$, $\frac{6}{9}$, and $\frac{6}{10}$ by finding a common denominator (LCD) to easily compare their sizes.

1. **State the problem:** Solve the equation $$x^{5} - 9x^{5} + 14 = 0$$. 2. **Simplify the equation:** Combine like terms:

1. **State the problem:** Divide the polynomial $8x^2 - 45y^2 + 18xy$ by the binomial $2x - 3y$. 2. **Formula and approach:** Polynomial division can be done using long division or

1. **State the problem:** Solve the equation $$8x^4 - 3 = 2$$ for $x$. 2. **Rewrite the equation:** Add 3 to both sides to isolate the term with $x$:

1. **State the problem:** Solve the equation $$\frac{4}{x - 3} = 8$$ for $x$. 2. **Formula and rules:** To solve for $x$, we will isolate $x$ by first eliminating the denominator.

1. The problem is to arrange the given mathematical expressions from smallest to biggest. 2. Let's evaluate or understand each expression:

1. The problem asks why the fraction $\frac{10}{10}$ was used in the expression $\frac{2a}{3b}$ to find an equivalent fraction. 2. To find an equivalent fraction, we multiply the n