🧮 algebra

1. The problem asks for the equation of a vertical line crossing the x-axis at $x=10$. 2. A vertical line has an equation of the form $x = a$, where $a$ is the x-coordinate where t

1. **Problem Statement:** Find the x-coordinate of every point along the given vertical line and determine the equation of the line.

1. **State the problem:** Multiply the fractions $\frac{4}{7}$ and $3 \frac{1}{3}$ and express the answer as a fraction in its lowest terms. 2. **Convert the mixed number to an imp

1. **State the problem:** Find the value of $\log \frac{1}{8}$. 2. **Recall the logarithm rule:** $\log \frac{a}{b} = \log a - \log b$.

1. We are asked to factor the quadratic expression $x^2 - x - 30$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=-1$, and $c=-30$.

1. **State the problem:** Simplify the expression $2x (x-3) + (x-3)$. 2. **Identify the common factor:** Notice that both terms contain the factor $(x-3)$.

1. **State the problem:** Simplify the expression $a(a^2 + ab + b^2) - b(a^2 + ab + b^2)$.\n\n2. **Identify the common factor:** Notice that both terms share the common factor $(a^

1. The problem is to understand and simplify surds, which are irrational numbers expressed with roots, such as square roots. 2. The key formula to remember is that $$\sqrt{a} \time

1. **State the problem:** Simplify the expression $3 \sqrt{18} \times 5 \sqrt{2}$. 2. **Recall the properties of square roots:**

1. **State the problem:** We are given that a 15% discount equals 180, and we need to find the marked price (MP). 2. **Formula and explanation:** The discount is calculated as a pe

1. **Problem statement:** સપનાએ ₹20,800 સદા વ્યાજ પર અંશત: વાર્ષિક 11% દરે અને અંશત: વાર્ષિક 9% દરે રોકાણ કર્યા છે. 6 વર્ષ પછી બંને રોકાણોમાંથી સમાન વ્યાજ મળે છે. 11% દરે રોકાણ કરે

1. The problem is to continue with the operations, but since no specific operations were given, let's assume we are continuing a general algebraic operation. 2. Suppose we have an

1. **Problem Statement:** Show that if a line passes through points $(x_1, y_1)$ and $(h, k)$ with slope $m$, then the equation $k - y_1 = m (h - x_1)$ holds.

1. **State the problem:** We are given two equations:

1. **Problem statement:** We are given two lines where the slope of one line is double the slope of the other. The tangent of the angle between these two lines is $\frac{1}{3}$. We

1. **State the problem:** Solve the system of equations:

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

1. **State the problem:** Solve the system of equations by elimination: $$13x + 48 = 8y$$

1. The problem is to find the sequence pattern in the given multipliers: 1.06x, 4.35x, 8.83x, 259.21x, 1.48x, 1.26x, 12.29x, 1.69x, 1.25x, 4.95x, 1.00x, 1.49x, 2.80x, 1.86x, 1.22x,

1. Vamos a resolver una ecuación cuadrática más difícil: $$2x^2 - 7x + 3 = 0$$. 2. La fórmula para resolver ecuaciones cuadráticas es la fórmula cuadrática:

1. **State the problem:** Simplify the expression $-0.12 \div 13$. 2. **Formula and rules:** Division of decimals by whole numbers can be done by dividing the decimal number direct