🧮 algebra

1. The problem is to find the product of the fractions $\frac{13}{52}$ and $\frac{12}{51}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \fra

1. **State the problem:** Bill drives 320 km each week. His car consumes 7 liters of gas per 100 km, and gas costs 1.02 per liter. We need to find his weekly gas expense.

1. The problem is to verify if $\frac{13}{52} \times \frac{12}{52} = \frac{1}{17}$.\n\n2. Start by multiplying the numerators and denominators: $$\frac{13 \times 12}{52 \times 52}

1. The problem is to find the lowest terms of the fraction $\frac{3}{52}$. 2. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD)

1. **State the problem:** We need to solve the multiplication of two fractions: $\frac{13}{52} \times \frac{12}{52}$. 2. **Formula used:** To multiply fractions, multiply the numer

1. Let's start by stating the problem clearly: You want to simplify the expression or solve the problem in a way that is easy to understand and shows your work clearly. 2. The key

1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$2x + 3y = 11$$

1. The problem is to find the equation of the line that passes through two points (setch both of them). 2. The formula to find the slope $m$ of a line passing through points $(x_1,

1. The problem is to solve the permutation equation $P(n,7) = 8,648,640$ where $P(n,7)$ represents the number of permutations of $n$ items taken 7 at a time. 2. The formula for per

1. The problem is to sketch the lines for the equations: $$1)\ 4x + 3y = 11$$

1. **State the problem:** Solve the system of equations using the elimination method: $$-2x + 2y = -12$$

1. **State the problem:** Solve the system of equations using the elimination method: $$6x - 5y = 50$$

1. **State the problem:** Simplify the expression $\frac{2}{3} \times \frac{3}{5}$.\n\n2. **Recall the multiplication rule for fractions:** To multiply two fractions, multiply the

1. المشكلة: لماذا نستخدم الأزواج 12*12 و 8*8 في المسألة السابقة؟ 2. في مسائل الجبر أو الهندسة، عندما نستخدم أزواج مثل 12*12 أو 8*8، غالبًا ما يكون ذلك بسبب الحاجة إلى حساب مربع عدد

1. **State the problem:** Simplify the algebraic expression: $$-02 + 2x - 11 - 5x - 9x - 5 + 11x + 7x - 6x$$

1. **Problem 16:** Write $y = x^2 - 8x + 12$ in vertex form, identify axis of symmetry, extrema, and zeros. 2. **Formula:** Vertex form is $y = a(x-h)^2 + k$ where $(h,k)$ is the v

1. **Problem statement:** Given the sum of a geometric series \( \sum_{p=k}^{10} 3^{p-1} = 29520 \), find the value of \( k \). 2. **Formula for the sum of a geometric series:**

1. نبدأ بحل المتباينة الأولى: $\alpha + 10 > \beta$. 2. نطرح 10 من كلا الطرفين لعزل $\alpha$:

1. **State the problem:** Convert the quadratic function $y = -2x^2 + 20x - 42$ into vertex form, identify the axis of symmetry, extrema (maximum or minimum), and zeros (x-intercep

1. **State the problem:** Convert the quadratic function $y = x^2 + 2x - 5$ into vertex form and identify the axis of symmetry, extrema, and zeros. 2. **Recall the vertex form:** T

1. **Problem:** Find the equation of a line with gradient 5 passing through the point $(-1, -3)$. 2. **Formula:** The equation of a line with gradient $m$ passing through point $(x