🧮 algebra

1. **State the problem:** The theater department charges $5$ dollars per ticket plus a donation of $x$ dollars per ticket. They sold $80$ tickets. We want to find expressions that

1. **State the problem:** We need to find the result of dividing $\frac{2}{3}$ by $\frac{2}{7}$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as

1. **State the problem:** We need to find the result of dividing $\frac{1}{4}$ by $\frac{2}{5}$. 2. **Recall the formula:** Dividing by a fraction is the same as multiplying by its

1. **State the problem:** Simplify the expression $2\sqrt{616}$. 2. **Recall the formula and rules:** The square root of a product can be expressed as the product of square roots:

1. The problem is to simplify the expression $2\sqrt{616}$.\n\n2. Recall the property of square roots: $a\sqrt{b} = \sqrt{a^2 b}$. Here, $2\sqrt{616}$ can be rewritten as $\sqrt{2^

1. المشكلة: حل المعادلة $x + 5 = 12$. 2. القاعدة المستخدمة: لحل المعادلة التي تحتوي على متغير، نريد عزل المتغير على أحد جانبي المعادلة.

1. نبدأ بملاحظة التعبير المعطى: $4n - 4$. 2. نبحث عن العامل المشترك الأكبر بين الحدين، وهو 4.

1. **State the problem:** We need to find the quadratic function $f(x)$ in the form $a(x - c)(x - d)$ given the roots and vertex.

1. **State the problem:** Solve the quadratic equation $$3x^2 - 7x - 268 = 0$$. 2. **Formula used:** To solve a quadratic equation $$ax^2 + bx + c = 0$$, use the quadratic formula:

1. **State the problem:** We need to find the cost of one package of white chocolate chip cookie dough (let's call it $x$) and one package of oatmeal cookie dough (let's call it $y

1. **State the problem:** Solve the quadratic equation $$3x^2 - 7x - 288 = 0$$ for $x$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ whe

1. **State the problem:** Simplify the expression $[4(3 + 2) - 4] + 42$. 2. **Apply the order of operations:** First, solve inside the parentheses.

1. **State the problem:** We need to find the price of a senior citizen ticket ($x$) and a child ticket ($y$) given two days of sales:

1. **State the problem:** Calculate the product of the mixed fraction $2 \frac{1}{3}$ and the fraction $\frac{4}{7}$.\n2. **Convert mixed fraction to improper fraction:** $2 \frac{

1. The problem is to evaluate the expression $20 + 2^3 \times 3 - 1$. 2. According to the order of operations (PEMDAS/BODMAS), we first evaluate exponents, then multiplication and

1. **State the problem:** Multiply the mixed number $2 \frac{2}{3}$ by the fraction $\frac{4}{7}$. 2. **Convert the mixed number to an improper fraction:**

1. **Solve the equation:** $$4 - \frac{x + 1}{2} = \frac{2 - x}{7}$$ 2. **State the problem:** We want to find the value of $x$ that satisfies the equation.

1. **State the problem:** Graph the line given by the equation $$9x + 63y = 630$$ using intercepts. 2. **Formula and rules:** To graph a line using intercepts, find where the line

1. **State the problem:** We need to graph the line given by the equation $$18x - 48y = 1440$$ using intercepts. 2. **Rewrite the equation:** Start by isolating $$y$$ to find the s

1. **State the problem:** Evaluate the sum $$\sum_{k=0}^4 (3k - 2)$$. 2. **Recall the formula:** The sum of a sequence $$\sum_{k=a}^b f(k)$$ is the sum of the values of the functio

1. The problem asks to draw the graph of $y = -f(x)$ given the graph of $y = f(x)$. 2. The function $y = -f(x)$ is the reflection of $y = f(x)$ about the x-axis. This means every y