🧮 algebra

1. **State the problem:** We are given two functions, $f(x)$ and $g(x)$, defined graphically. We need to find the values of the compositions $f(g(-2.76))$, $g(f(2.46))$, and $g(g(3

1. **State the problem:** Calculate the total wall area of a room, estimate the paint needed, and compute the total cost of the paint. 2. **Formula for wall area:** The total wall

1. **State the problem:** Simplify the expression $$(2x - 3y) + (y - 4z) - (z - 3x)$$. 2. **Apply the distributive property:** Remove parentheses carefully, remembering that the mi

1. The problem asks for the coefficient in the expression $18^3y^3$. 2. The coefficient is the numerical factor multiplying the variable part of the term.

1. **State the problem:** We are given the function $f(x) = 3x^2 + 4x - k + 3$ and the condition $f(-1) = -2$. We need to find:

1. **State the problem:** We have the quadratic equation $k + 9 = (6 - x)(2x + 1)$ and need to find the range of values of $k$ for which the equation has two distinct real roots. 2

1. **State the problem:** Find the x-intercept and y-intercept of the function $$y=\frac{5x}{x-1}$$. 2. **Recall definitions:**

1. نبدأ بكتابة المسألة: ١ على س زائد ١ جمع ٢. 2. نكتب التعبير رياضيًا: $\frac{1}{x} + 1 + 2$.

1. المسألة الأولى: حل المعادلة $$0.5x^2 - 3x + 125 = 0$$ 2. نستخدم صيغة المعادلة التربيعية: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ حيث $$a=0.5$$، $$b=-3$$، و$$c=125$$.

1. المشكلة: نريد إيجاد المجال والمدى لدالة معينة. 2. المجال: هو مجموعة القيم التي يمكن أن يأخذها المتغير المستقل (عادة x) بحيث تكون الدالة معرفة.

1. نبدأ بحل المعادلة المعطاة: $$25 س^3 - 30 \times 5 س^2 + 125 \times 5 س + 5 = 0$$

1. **المسألة:** حل المعادلة $x^2 - 5x + 6 = 0$. 2. **الصيغة والقواعد:** لحل المعادلات التربيعية نستخدم صيغة التحليل أو صيغة الجذور التربيعية. المعادلة التربيعية تكون على الشكل $ax^

1. **State the problem:** Find the solution set of the simultaneous equations by graphical method for the first problem: $$2x + 2 = y$$

1. **State the problem:** Simplify the expression $$3\sqrt{8x^{2}y} + 5x\sqrt{2xy^{2}} - x\sqrt{32y}$$. 2. **Recall the rule:** $$\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$$ and $$\sqrt

1. **Stating the problem:** Solve the system of linear equations:

1. **State the problem:** We need to find the equation of a line parallel to line A, which has the equation $y = mx + c$, passing through the point $P(0,5)$. 2. **Recall the formul

1. **State the problem:** Simplify the expression $$3\sqrt{8x^2y} + 5x\sqrt{2xy^2} - x\sqrt{32y}$$. 2. **Recall the rule:** The square root of a product can be separated as $$\sqrt

1. **State the problem:** Simplify and solve the expression $$\left(\frac{a^4 b^2}{a^{-1} b^3}\right)^{-2}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$\frac{2}{3} \left( \frac{1}{4} x - 2 \right) = \frac{1}{5} \left( \frac{4}{3} x - 1 \right)$$. 2. **Write the formula and rules:** We

1. **State the problem:** Solve the equation $$\frac{2}{3}\left(\frac{1}{2}x - 2\right) = \frac{1}{3}\left(\frac{4}{6}x - 1\right)$$ using distribution of fractions. 2. **Write the

1. **State the problem:** We need to find the complex number $z = a + bi$ such that $$z^2 = -77 + 36i,$$ where $i = \sqrt{-1}$ and $a,b$ are real numbers. 2. **Use the formula:** I