🧮 algebra

1. **State the problem:** Simplify the expression $$(3 - )(9 - 2i)(1 + 3i)$$. Since the first term is incomplete, assuming it is $3$ (without any imaginary part), the expression be

1. **State the problem:** Simplify the expression $$(9x^2 + 8x - 8) + (-9x^2 - 3x - 9) - (-7x^2 + 4x + 7).$$ 2. **Write the expression clearly:**

1. **State the problem:** Simplify the expression $$(9x^2 + 8x - 8) + (-9x^2 - 3x - 9) - (-7x^2 + 4x + 7)$$. 2. **Write the expression clearly:**

1. **State the problem:** Add the complex numbers $(3 - 5i)$ and $(7 - 2i)$. 2. **Formula:** To add complex numbers, add their real parts and their imaginary parts separately:

1. **State the problem:** Add the two complex numbers $ (3 - 5i) $ and $ (7 - 2i) $. 2. **Formula and rules:** To add complex numbers, add their real parts and their imaginary part

1. **State the problem:** We have two linear relationships: - Relationship R: $$0.2x - 0.01y = 0.03$$

1. **State the problem:** Solve the system of linear equations: $$-2x - 5y = -15$$

1. **State the problem:** Find the slope of a line perpendicular to the line given by the equation $$y - 9 = 12(x + 2)$$. 2. **Rewrite the given line in slope-intercept form:** The

1. The problem is to solve the equation $$\frac{2x+4}{3} = 6$$ for $x$. 2. The formula used is to isolate $x$ by multiplying both sides by the denominator to eliminate the fraction

1. **Stating the problem:** We are given two quadratic expressions and two factored expressions. We will analyze and verify the factored forms and expressions.

1. **State the problem:** We need to graph the absolute value function $$y = 6|x + 4| - 2$$ and identify its key features. 2. **Formula and rules:** The general form of an absolute

1. The problem asks to write the number 321,000,000 in scientific notation. 2. Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.

1. The problem is to write the number 5,430,000 in scientific notation. 2. Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.

1. Planteamos el problema: completar el cuadrado para la expresión cuadrática $x^2 - 3x - 14$. 2. Recordemos que para completar el cuadrado en una expresión $x^2 + bx + c$, se usa

1. **State the problem:** Verify if the simplification of $\log_2 \left( \frac{x}{3} + 5 \right) - \log_2 (16)$ to $\log_2 \left( \frac{x}{48} + \frac{5}{16} \right)$ is correct. 2

1. **State the problem:** We need to verify if the expression $$\log_2 \left( \frac{x}{3} + 5 \right) - \log_2 (16)$$ is correctly simplified to $$\log_2 \left( \frac{x}{48} + \fra

1. **State the problem:** Simplify the expression $5^6 \times 5^{-3}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents

1. **State the problem:** Solve the inequality $x + 5.4 < -1.6$. 2. **Write the inequality:**

1. Stated problem: Find the vertex coordinates of the quadratic function $f(x) = 2(x + 1)^2 + 1$. 2. Formula and rules: The vertex form of a quadratic function is $f(x) = a(x - h)^

1. **State the problem:** We have a square sheet with area 900 cm\(^2\), so each side is $\sqrt{900} = 30$ cm.

1. The problem is to solve for $x$ in the equation $2x + 3 = 11$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides to undo