🧮 algebra

1. **Problem:** Simplify the polynomial expression $6x^3 - 9x + 12$. 2. **Formula and rules:** This is a polynomial expression. Simplification involves combining like terms if any,

1. **State the problem:** We need to write a function that models the height of Emily's rosemary bush over time. 2. **Identify the variables:** Let $x$ represent the number of year

1. The problem states that Nick's camera has a total memory storage of 128 GB and he uses 20 GB each month. 2. We want to write a function $y$ that describes the remaining memory a

1. The problem is to simplify each given expression. 2. Simplification involves reducing expressions to their simplest form by combining like terms, factoring, canceling common fac

1. **State the problem:** Simplify the expression $11(3g+7-2g)-4$. 2. **Apply the distributive property:** Multiply $11$ by each term inside the parentheses.

1. **State the problem:** Factor the polynomial equation $$x^4 - 26x + 144 = 0$$. 2. **Understand the problem:** We want to express the quartic polynomial as a product of polynomia

1. **State the problem:** Distribute and simplify the expression $$(x - 7)(x - 3)$$. 2. **Recall the distributive property (FOIL method):**

1. The problem asks to rewrite the power expression $ (x - 2)^2 $ as repeated multiplication. 2. Recall the rule for powers: $ a^n $ means multiplying $ a $ by itself $ n $ times.

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 4x + 17 & \text{for } x < -4 \\ -4 & \text{for } x \geq 0 \end{cases}$$

1. **Stating the problem:** Risolvi l'equazione $$\sqrt{5(x-1)} = 2(x+1)$$. 2. **Formula and rules:** Per risolvere equazioni con radici quadrate, eleviamo al quadrato entrambi i m

1. **State the problem:** Simplify the expression $2\sqrt{-16}$.\n\n2. **Recall the formula and rules:** The square root of a negative number involves imaginary numbers. Specifical

1. The problem is to find the value of $\sqrt{-18}$. 2. The square root of a negative number is not a real number because no real number squared gives a negative result.

1. The problem asks to identify the inequality that matches the graph described. 2. The graph shows a vertical line at $x = -7$ with shading to the left of the line, indicating all

1. **State the problem:** We need to determine which inequality matches the given graph. 2. **Analyze the graph:** The line passes through the point $(2,4)$ with an open circle, me

1. **State the problem:** We are given two functions $f(x) = 3x - 8$ and $g(x) = x^3$. We need to find an expression for the composite function $g(f(x))$. 2. **Recall the definitio

1. Problemet handler om at forstå, hvad bogstaver som a og b betyder i matematik. 2. Bogstaver som a og b kaldes variable, og de repræsenterer tal, som kan ændre sig.

1. Problem statement: We have three functions: $$f(x) = 0.9 \cdot x - 2$$

1. **State the problem:** Simplify the expression $$\frac{s^{723}}{s^{721}}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same bas

1. **Stating the problem:** Simplify the expression $$(\sqrt{x} - 1)(\sqrt{x+1} + \sqrt{x-1}) - \sqrt[3]{x\sqrt{x}}$$

1. We are asked to make $y$ the subject of the equations $7x - 2y + 11 = 0$ and $6x + y + 4 = 0$. 2. For the first equation $7x - 2y + 11 = 0$, isolate $y$:

1. **State the problem:** Simplify the expression $$\frac{5^{723}}{5^{721}} \cdot \frac{3^{300}}{3^{249}} \cdot \left(\frac{3 \cdot 4^3}{3^{-2} \cdot 4^{-7}}\right)^0 \cdot \left(\