🧮 algebra

1. **Stating the problem:** We need to evaluate or simplify the expression $1,47 = 0,138(0+1)$. 2. **Understanding the expression:** The expression uses commas as decimal separator

1. **State the problem:** We need to factor the polynomial $$36x^2y^4 + 12x^3y^2 + 12x^4y^3$$ and match it with the given factors $$-4xy$$ and $$12x^2y^2$$. 2. **Identify the great

1. **State the problem:** We want to find how to get the numbers 7, 21, 55, 56, and 64 from the number 147. 2. **Analyze the problem:** One common approach is to check if these num

1. **State the problem:** Solve for $x$ in the equation $$\frac{1}{40} + \frac{1}{16} = \frac{1}{60} + \frac{1}{x}.$$\n\n2. **Write the formula and rules:** To solve for $x$, first

1. **State the problem:** Simplify the expression $$(2b - 3a)^3 + 8(2a - b)(a - b) - 5a(a - b)^2.$$\n\n2. **Recall formulas and rules:**\n- Cube of a binomial: $(x - y)^3 = x^3 - 3

1. **State the problem:** Determine how many solutions the system of equations has: $$y = -5x + 8$$

1. **State the problem:** We need to find how many solutions the system of equations has: $$y = 9x - 9$$

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