🧮 algebra

1. **State the problem:** We need to find the area of the entire large rectangle, which is divided into three smaller rectangles horizontally. 2. **Identify dimensions:** The heigh

1. **State the problem:** We need to check the type of the function $$g(x) = 2x^{3} + 3x + 1$$ given the domain $$\{0,1,2,3\}$$ and range $$\{1,6,15,28,35\}$$. 2. **Recall the func

1. The problem is to solve question number 2 (the exact problem statement is not provided, so I will assume it is a typical algebraic problem). 2. Since the problem statement is mi

1. **State the problem:** Solve the equation $$\frac{g}{4} + \frac{5g}{10} = \frac{9}{4}$$. 2. **Identify the formula and rules:** To solve for $g$, combine like terms and isolate

1. **Problem 15:** Find the equation of line L passing through points (-3,4) and (3,-2). 2. Use the slope formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$ where $(x_1,y_1)=(-3,4)$ and $(x_2,

1. The problem asks if $\sqrt{16+25} = 4+5$ is true. 2. First, calculate inside the square root: $16 + 25 = 41$.

1. **State the problem:** Calculate the value of $$\sqrt[3]{0.0089} \times 65.4 - 0.94^2$$. 2. **Recall the formulas and rules:**

1. The problem asks if $\sqrt{3} + \sqrt{2} = \sqrt{5}$ is true. 2. Recall the property of square roots: $\sqrt{a} + \sqrt{b} \neq \sqrt{a+b}$ in general.

1. **State the problem:** Solve the equation $$y^{2} + 48y - 64 = 0$$ for $y$. 2. **Identify the type of equation:** This is a quadratic equation in standard form $$ay^{2} + by + c

1. **State the problem:** We need to find the equation of a line $L_2$ that is perpendicular to the line $L_1$ given by $2y = 6x - 5$ and passes through the point $(9, -1)$. The an

1. The problem is to verify if $\sqrt{3+2} = \sqrt{5}$. 2. Recall the property of square roots: $\sqrt{a+b} = \sqrt{a+b}$, so we first simplify inside the root.

1. **State the problem:** Solve the equation $$100\sqrt{x} = \frac{1}{10}(-2)$$. 2. **Rewrite the equation:** The right side simplifies to $$\frac{1}{10} \times (-2) = -\frac{2}{10

1. **Fill in the missing numbers:** **a)** Given $\frac{1}{4} = \frac{?}{100}$.

1. **State the problem:** Solve the equation $$2^{2x} - 3 \cdot 2^{x+2} + 32 = 0$$. 2. **Rewrite the equation using properties of exponents:** Recall that $$2^{2x} = (2^x)^2$$ and

1. **State the problem:** Solve the equation $2x + 3 = 7$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse oper

1. **Problem:** Solve the linear equation $2x - 18 = 44$ for $x$. 2. **Formula and property:** Use the property of equality which states that if you do the same operation on both s

1. **State the problem:** We are given the sequence 10, 15, 25, 40, ... and need to find the generator formula of the form $An^2 + Bn + C = a_n$ where $a_n$ is the $n$th term. 2. *

1. **State the problem:** Find the equation of the line $L_2$ which is perpendicular to the line $L_1$ given by $2y = 6x - 5$ and passes through the point $(9, -1)$. The answer sho

1. **State the problem:** We need to graph the linear equation $$-\frac{1}{2}x + y = \frac{3}{4}$$ in two variables $x$ and $y$. 2. **Rewrite the equation in slope-intercept form:*

1. The problem is to solve the equation directly as requested. 2. Since no specific equation is given, I cannot solve it directly.

1. **Problem:** Factorize the following expressions: i) $2x^2 - 16xy + 24y^2$