🧮 algebra

1. **State the problem:** Graph the quadratic function $g(x) = -3x^2$, plot points, sketch the curve, and find domain and range. 2. **Make a table of values:** Choose $x$ values: $

1. The problem is to understand why subtracting $\pi$ from 2 is done or what it means. 2. Subtraction is a basic arithmetic operation where you take away one number from another.

1. **Problema:** Semplifica l'espressione $2x(x^2+1)-3x(x^2-x+1)-(-x^3+x^2-x)$. 2. **Formula e regole:** Per semplificare, applichiamo la proprietà distributiva $a(b+c) = ab + ac$

1. **State the problem:** Solve the equation $$(x + 5)^2 - 16 = 0$$ for $x$. 2. **Use the formula:** Recognize this as a difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ where

1. **State the problem:** Find the magnitude of the vector $\vec{v} = (-3, -10)$. The magnitude of a vector $\vec{v} = (x, y)$ is given by the formula: $$|\vec{v}| = \sqrt{x^2 + y^

1. **State the problem:** We have a city population of 89,000 in 2010.

1. **State the problem:** We want to find for which values of $b$ the quadratic expression $$x^2 + bx + 12$$ is factorable over the integers. 2. **Recall the factorization rule:**

1. **State the problem:** We are given the equation $$(a \times 10^b) \times (5.3 \times 10^8) = 2.226 \times 10^4$$ where $a \times 10^b$ is in standard form. We need to find the

1. **State the problem:** Calculate $\left(5.46 \times 10^{-4}\right)^3 + \left(2.23 \times 10^{-5}\right) \times \left(1.39 \times 10^{-6}\right)$ and express the answer in standa

1. **State the problem:** We are given two quadratic functions: - $g(x) = 3x^2$

1. The problem is to solve the quadratic equation $x^2 - 7x + 12 = 0$ by graphing the related function and finding its zeros. 2. The related function is $y = x^2 - 7x + 12$.

1. The problem is to solve the equation $2x^2 - 10x = -12$ by graphing the related function and finding its zeros. 2. First, rewrite the equation in standard form by moving all ter

1. **State the problem:** Solve the equation $3x^2 + 9x = -6$ by graphing the related function and finding its zeros. 2. **Rewrite the equation:** Move all terms to one side to set

1. **State the problem:** Simplify the expression $$\frac{3f^3}{12f^{18}}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{

1. **State the problem:** Solve the quadratic equation by graphing and finding its zeros: $$x^2 + 4x = 5$$ 2. **Rewrite the equation in standard form:** Move all terms to one side

1. Das Problem: Wir wollen alle wichtigen Regeln zu Potenzen verstehen und wissen, was man dazu wissen muss. 2. Definition: Eine Potenz hat die Form $a^n$, wobei $a$ die Basis und

1. **State the problem:** We are given the equation $$x^4 + x^3 + x^2 + x + 1 = 0$$ and asked to find the value of $$\left(x^{33} + \frac{2}{x^{22}}\right)\left(x^{22} + \frac{3}{x

1. **State the problem:** Simplify the expression $\sqrt{\frac{5}{11}}$. 2. **Recall the rule:** The square root of a fraction can be written as the fraction of the square roots: $

1. **State the problem:** Rearrange the formula $$y = \frac{3x - 2}{x + 1}$$ to make $$x$$ the subject. 2. **Start with the given equation:**

1. Das erste Thema ist Potenzen und ihre Regeln. 2. Übungsaufgabe 1: Berechne $$2^3 \times 2^4$$.

1. Problema: Calculați radicalii cubici pentru următoarele valori: a) ³√216; b) ³√-512; c) ³√0,027; d) ³√\frac{729}{125}; e) ³√\frac{125}{64}; f) ³√-0,001; g) ³\sqrt{(ab)^5}. 2. Fo