🧮 algebra

1. The problem involves solving and understanding the expressions related to $y^2$ given by the equations: - $-6 = y^2$

1. **State the problem:** Simplify the expression $$\frac{\frac{xy}{6}}{\frac{2}{3} \div \frac{x}{6} - \frac{3x}{4}}$$. 2. **Recall the division of fractions rule:** Dividing by a

1. **Stating the problem:** Solve the expression: $$14.8 \times 10^{-5} + 6.02 \times 10^{-4}$$

1. **Problema:** Sumar las fracciones algebraicas dadas aplicando factorización, casos notables y eliminando factores comunes. 2. **Ejercicio 1:** $$\frac{6x}{12x - 24} + 3$$

1. **State the problem:** We are given quantities of hair colour, colour developer, conditioner, and thickener, and we need to find and simplify certain ratios as fractions. 2. **R

1. Problem 14: Yuki's cookies Yuki baked some cookies on Monday. Half were eaten on Tuesday by friends, then Yuki ate 3 on Wednesday, took 2 to school on Thursday, and 7 remained o

1. The problem is to understand and solve a Grade 7 level math question, but since no specific problem was given, let's explain a common Grade 7 algebra concept: solving simple lin

1. Problem 14: Yuki's cookies Yuki baked some cookies on Monday. Half were eaten on Tuesday, 3 eaten on Wednesday, 2 taken on Thursday, and 7 left on Friday. Find how many she bake

1. **Problem statement:** Find all roots of the biquadratic equation $x^4 - 5x^2 + 4 = 0$. 2. **Rewrite the equation:** Let $y = x^2$. Then the equation becomes a quadratic in $y$:

1. **State the problem:** We need to find the mass of 700 sheets of paper given that 500 sheets have a mass of 2.27 kg. 2. **Formula used:** The mass is proportional to the number

1. **Énoncé du problème** : Nous avons une fonction définie par morceaux avec deux branches.

1. **Stating the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} x^2 & x \leq 0 \\ \sqrt{x} & 0 < x < 4 \\ \frac{x}{2} & x \geq 4 \end{cases}$$

1. **State the problem:** We are given a proportional relationship between variables $a$ and $b$ with values $a = 0.6, 1.0, 1.5, 2$ and $b = 20.8, 34, 56, 92$. We need to write the

1. **State the problem:** Find the square root of the complex number $8 - 6i$. 2. **Formula and approach:** To find the square root of a complex number $z = a + bi$, we look for $x

1. **State the problem:** We are given a table showing a proportional relationship between $x$ and $y$:

1. **State the problem:** Simplify the expression $-5(3p - 2n + 6m^2)$. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means

1. Énonçons le problème : Trouver le domaine de la fonction définie par morceaux $$f(x) = \begin{cases} 6x - 1 & \text{si } x \geq 6 \\ \frac{1}{x - 3} & \text{si } 3 \leq x < 6 \\

1. **State the problem:** We have the function $f(x) = 6x - 50$ which represents the profit in dollars when selling $x$ shirts. We need to find $f(-2)$, $f(7)$, and $f(12.5)$ and i

1. The problem is to simplify the expression $5^4 \cdot 5^2$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: $$a^m \c

1. **State the problem:** We have the function $f(x) = 10000 + 1000x$ which represents financial aid amount based on the number of siblings $x$ in the household.

1. Énoncé du problème : On effectue le changement de variable $X = \cos x$ pour transformer une équation trigonométrique en une équation polynomiale du second degré $L_1$ équivalen