🧮 algebra

1. The problem asks to graph the function $$g(x) = -3(x - 5)(x + 1)$$ and identify the x-intercepts, vertex, and axis of symmetry. 2. First, find the x-intercepts by setting $$g(x)

1. **Problem statement:** A runner jogs at 2 km/h and takes 2 steps per second. We need to find how many steps he takes while jogging 1.5 km. 2. **Relevant formulas and concepts:**

1. The problem is to factor the quadratic expression $d^2 + 2d - 48$. 2. The general form of a quadratic expression is $ax^2 + bx + c$.

1. **State the problem:** We need to graph the system of linear inequalities: $$y > -2x - 1$$

1. **State the problem:** We are asked to describe the slope of the line passing through the points $(-1, -2)$ and $(3, -2)$ and then find its slope. 2. **Recall the slope formula:

1. The problem is to graph the system of linear inequalities: $$x + y > -3$$

1. نبدأ بحل التعبير المعطى: $\left(\frac{1}{6} + 1\right) \left(\frac{1}{5} + 1\right) \left(\frac{1}{3} + 1\right) \left(\frac{1}{1} + 1\right)$. 2. نجمع الكسور مع الواحد في كل قو

1. **State the problem:** We are given a function $$f(x) = \frac{1}{50} \left[ c(x-1) + \frac{1}{2} \right]$$ for $$x=1,2,...,10$$ and the condition $$\sum_{x=1}^{10} f(x) = 1$$. W

1. **State the problem:** We need to graph the system of inequalities: $$x + y > -3$$

1. **State the problem:** Find the equation of the line passing through points $(0,3)$ and $(5,0)$ and write it in standard form. 2. **Find the slope $m$ using the formula:**

1. The problem is to analyze the quadratic function given by the equation $y = kx^2 + 2x + 3$. 2. This is a quadratic function of the form $y = ax^2 + bx + c$, where $a = k$, $b =

1. **State the problem:** Solve the equation $$\sqrt{x^{2} - 8x + 16} + \sqrt{x^{2} - 4x + 4} = 2.$$\n\n2. **Recognize perfect squares:** Notice that \(x^{2} - 8x + 16 = (x-4)^2\)

1. **State the problem:** Solve the equation $\frac{32}{a} = a - 4$ for $a$. 2. **Rewrite the equation:** Multiply both sides by $a$ (assuming $a \neq 0$) to eliminate the denomina

1. **State the problem:** Decompose the rational function $$\frac{x^2+x+1}{(x-1)(x+2)}$$ into partial fractions. 2. **Formula and rules:** For distinct linear factors in the denomi

1. **State the problem:** Solve the equation $$3(x - 5) - 7 = -2(-2x + 4) - 9x$$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** We are given the function $$f = 5x^2 + \sqrt{9x - x - 3} - x - 3$$ and asked to understand and graph it. 2. **Simplify inside the square root:** Simplify

1. Solve the inequality $1 < \frac{x}{2} < 3$. 2. Multiply all parts of the inequality by 2 (positive number, so inequality signs remain the same):

1. The problem is to find the remainder when one number is divided by another. 2. The remainder is the amount left over after division when one number cannot be divided evenly by a

1. The problem is to find the value of $i^{45}$, where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Important rule: Powers of $i$ cycle every 4 steps because:

1. **Problem Statement:** Aghar lost 35 by selling a body for 430. We need to find the loss percentage. 2. **Given:**

1. დავწეროთ მოცემული პირობა: $a-b$ არის $a+b$ რიცხვის 20%, რაც ნიშნავს: $$a-b=0.2(a+b)$$