🧮 algebra

1. **State the problem:** We are given a table of distances and fares and need to construct a linear function that models the fare based on distance. 2. **Find the slope $m$:** The

1. **State the problem:** Simplify the expression $$\sqrt{2 + \frac{5}{\sqrt{3}}}$$. 2. **Rewrite the expression:** The expression inside the square root is $$2 + \frac{5}{\sqrt{3}

1. **State the problem:** Simplify the expression $[-3]x 2x$. 2. **Understand the expression:** The expression can be interpreted as multiplication of $-3x$ and $2x$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{3} \left(3 + \sqrt{\frac{2}{3}}\right) \sqrt{3}}{\sqrt{3}}$$. 2. **Rewrite the expression:** The numerator is $$\sqr

1. **State the problem:** Simplify the expression $4x[-2x]$. 2. **Recall the rule:** Multiplying a number by a product inside brackets means multiplying the number by each term ins

1. The problem is to simplify the surd expression or understand what a surd is. 2. A surd is an irrational root that cannot be simplified to remove the root, such as $\sqrt{2}$ or

1. The problem is to graph a linear function representing the fare (AED) as a function of distance (km). 2. Typically, the fare can be modeled by a linear equation of the form $$y

1. **State the problem:** We are given a fare rule for a taxi fare: $$\text{Fare} = 2 + 0.5d$$ where $d$ is the distance in kilometers. We need to complete the fare table for given

1. نبدأ بطرح التمرين: لنفترض أن لدينا دالة خطية تمثل العلاقة بين المتغيرين $x$ و $y$، ونريد إيجاد معادلة الدالة التي تمر بالنقاط $(1,3)$ و $(4,15)$. 2. نستخدم صيغة ميل المستقيم الت

1. **State the problem:** We are given the quadratic function $$y = 2x^2 - 6x + 4$$ and asked to find the value of $$y$$ when $$x = -2$$. 2. **Substitute the value of $$x$$ into th

1. The problem is to find the value of $\log_{10} 1$. 2. Recall the definition of logarithm: $\log_b a = c$ means $b^c = a$.

1. **State the problem:** Solve for $x$ in the equation $$\log_a(4x) - \log_a(2x+1) = \frac{1}{2} \log_4 4.$$\n\n2. **Recall logarithm properties:**\n- The difference of logarithms

1. **State the problem:** Solve the equation $$\frac{2x - 5}{6} - \frac{3x - 4}{8} = 0$$. 2. **Formula and rules:** To solve equations involving fractions, find a common denominato

1. **Stating the problem:** For problem 9, we have a fraction $\frac{3}{4}$ on the left and the number 20 on the right of a U-shaped graph with a square box inside near the right s

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **State the problem:** We need to find the value of $x$ in the proportion $\frac{15}{66} = \frac{x}{99}$.\n\n2. **Use the cross-multiplication formula:** For two ratios $\frac{a

1. **State the problem:** We need to find a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ such that it passes through the points $(1,24)$, $(3,120)$, $(5,336)$, and $(7,720)$. The

1. **State the problem:** We need to find the pounds of chocolate eaten per capita in the U.S. given the total population and total chocolate consumption. 2. **Given data:**

1. The problem is to find the least common multiple (LCM) of given denominators. 2. The LCM of denominators is the smallest number that each denominator divides into without leavin

1. **State the problem:** Find the least common multiple (LCM) of the fractions $\frac{3}{7}$, $\frac{5}{5}$, and $\frac{1}{6}$.\n\n2. **Recall the formula for LCM of fractions:**

1. **State the problem:** Solve for $c$ in the equation $$\frac{1}{4}(1+3c) + \frac{1}{4}(1-c) + \frac{1}{4}(1+2c) + \frac{1}{4}(1-4c) = 1.$$\n\n2. **Write the equation clearly:**\