🧮 algebra

1. **State the problem:** We need to find the number of solutions to the system of equations: $$y = x - 6$$

1. **State the problem:** We are given a cubic polynomial $f(x) = 3x^3 + 10x^2 + 9x + 2$ and told that $f(-2) = 0$. We need to determine the factors of $f(x)$. 2. **Recall the Fact

1. **State the problem:** Solve the quadratic equation $$\frac{2}{3}x^2 - 5x + \frac{7}{2} = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}

1. **Problem:** Factor the expression $15x - 12$ completely. 2. **Formula and rules:** To factor an expression, find the greatest common factor (GCF) of all terms and factor it out

1. **State the problem:** Simplify the expression $5x^2 - 6x$. 2. **Identify common factors:** Both terms have a common factor of $x$.

1. **State the problem:** Solve the equation $$\sqrt{7x - 10} = x$$ and check the solutions. 2. **Recall the domain:** The expression under the square root must be non-negative, so

1. **State the problem:** Solve the equation $$-6\sqrt[3]{10x} + 11 = -19$$ and check the solution(s). 2. **Isolate the cube root term:** Subtract 11 from both sides:

1. **State the problem:** Simplify the expression $v^{\frac{5}{7}} \times v^{\frac{1}{7}}$ assuming all variables are positive. 2. **Recall the rule for multiplying powers with the

1. The problem is to graph the function $$y=\sqrt{x+5}-4$$ by translating the graph of $$y=\sqrt{x}$$. 2. The base function is $$y=\sqrt{x}$$, which starts at the origin (0,0) and

1. **State the problem:** Analyze the key features of the function $$g(x) = \sqrt[3]{x - 8} + 4$$ and determine which statements A to E are true. 2. **Recall the parent function:**

1. The problem asks to describe the translations that transform the graph of $f(x)=\sqrt[3]{x}$ into the graph of $j(x)=\sqrt[3]{x-2}+3$. 2. The general form for horizontal and ver

1. The problem asks us to write an expression for the function $g(x)$ which is a translation of the function $f(x) = \sqrt{x}$. 2. The translation is 3 units down and 5 units to th

1. The problem states that the graph is a translation of the function $f(x) = \sqrt[3]{x}$. We need to write the function for the translated graph. 2. The original function is $f(x

1. The problem asks to find the function equation for a graph that is a translation of the cube root function $f(x) = \sqrt[3]{x}$.\n\n2. The general form for a horizontal and vert

1. The problem is to graph the function $$y=\sqrt{x}+4$$. 2. The square root function $$y=\sqrt{x}$$ starts at the origin (0,0) and increases slowly to the right.

1. **State the problem:** We need to show that dividing $\frac{1}{2}$ by a fraction can sometimes result in a value less than $\frac{1}{2}$ and sometimes not. 2. **Recall the divis

1. **State the problem:** Simplify or factor the expression $$a^3 - a^2b + 4a - 4b$$. 2. **Identify the formula or method:** We will try to factor by grouping, which involves group

1. **State the problem:** Factor the expression $9x^2 - 49y^2$. 2. **Formula used:** This is a difference of squares, which factors as $$a^2 - b^2 = (a - b)(a + b)$$

1. Risolvi l'equazione $$2x + 3 = 7$$. 2. Trova il valore di $$x$$ in $$5x - 4 = 16$$.

1. Il problema: Creiamo un compito semplice di calcolo letterale per la scuola secondaria di primo grado. 2. Formula e regole importanti: Nel calcolo letterale si usano le lettere

1. Solve the equation: $$4a + 9a - 6a = 42$$ 2. Combine like terms on the left side: