🧮 algebra

1. **State the problem:** We need to graph the inequality $$2x + 3y \geq -6$$ on the coordinate plane. 2. **Rewrite the inequality as an equation:** To graph the boundary line, con

1. **State the problem:** We are given the equation $$(ax + b)(ax^2 + cx + 1) = 25x^3 + 15x^2 - 28x + 7$$ where $a$, $b$, and $c$ are constants with $a > 0$. We need to find the va

1. **State the problem:** We need to graph the inequality $$-5x + 2y > -8$$ on the Cartesian coordinate system. 2. **Rewrite the inequality in slope-intercept form:** To graph, exp

1. **Noteikt doto kopu elementus.** a) Atrisinām vienādojumu $2x - 1 = 19$.

1. **Problem statement:** We have a football league where each team plays every other team exactly once. Points are awarded as follows: 3 for a win, 0 for a loss, and 1 for a draw.

1. **State the problem:** We are given a linear cost function for hiring a scooter: $$C = 0.15t + 22$$ where $C$ is the cost in pounds and $t$ is the time in minutes. 2. **Understa

1. The problem asks to find 45% of 60. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. **Problem statement:** We are given quantities of hair colour, colour developer, conditioner, and thickener, and we need to find and simplify ratios as fractions. 2. **Recall:**

1. **Noteikt, kurš no dotajiem skaitļiem nav racionāls skaitlis.** Racionāls skaitlis ir skaitlis, ko var izteikt kā divu veselumu daļu $\frac{p}{q}$, kur $q \neq 0$.

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: $$f(x) = \begin{cases} x^2 & x \leq 0 \\ \sqrt{x} & 0 < x < 4 \\ \frac{x}{2} & x \geq 4 \end{cases}$$