🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{25x^2 - 64}{5x^2 - 13x - 6} \times \frac{x^2 - 8x + 15}{5x + 8} - (x - 7)$$ as a single fraction in simplest form. 2. **Fa

1. **Problem 1:** Find the equation of the line $L$ passing through $(6, -4)$ and parallel to the line $y = 5 - 3x$. 2. The given line can be rewritten as $y = -3x + 5$, so its slo

1. **Simplify** $\frac{1}{2} \left( \frac{1}{\sqrt{3}} + \sqrt{2} - \frac{1}{\sqrt{3}} - \sqrt{2} \right)$. Step 1: Notice that $\frac{1}{\sqrt{3}}$ and $-\frac{1}{\sqrt{3}}$ cance

1. **Problem 1:** Find the equation of the line $L$ passing through $(6, -4)$ and parallel to the line $y = 5 - 3x$. 2. The given line can be rewritten in slope-intercept form $y =

1. **State the problem:** We are given the average speed of Aviv's cycle journey as 19 km/h (correct to the nearest whole number) and the time as 1.5 hours (correct to one decimal

1. **State the problem:** Simplify the expression $\frac{2.16 \times 10^{7}}{3000}$.\n\n2. **Recall the rules:** When dividing numbers in scientific notation, divide the coefficien

1. The problem is to understand and use examples effectively in math problems. 2. Examples help illustrate how to apply formulas and solve problems step-by-step.

1. Let's state the problem: We want to find the values of variables $A$, $C$, $F$, and $H$. 2. To solve for these variables, we need the equations or context in which they appear.

1. **State the problem:** Calculate the value of the expression $$\frac{367500000}{2500000 \times 9.8}$$. 2. **Formula and explanation:** This is a simple division problem where th

1. **Problem (a): Solve** $\frac{1 - 2y}{3} = \frac{4}{5} - \frac{2y - 1}{2}$ 2. To solve this equation, we first find a common denominator to clear the fractions. The denominators

1. **Stating the problem:** We have butterfly-shaped diagrams with values at vertices labeled as $A, B, C, D, E, F, G, H$ arranged in two adjoining triangles. We want to find relat

1. **State the problem:** Write the quadratic expression $5 + 12x - 2x^2$ in the form $a + b(x + c)^2$ where $a$, $b$, and $c$ are integers. 2. **Recall the formula:** To rewrite a

1. **State the problem:** We are given the formula $x = \frac{6a}{b - a}$ with $a = 3.46$ (3 significant figures) and $b = 6.3$ (1 decimal place). We need to find the upper bound f

1. **State the problem:** We are given the cubic function $$y = -\frac{3x^3}{3} - 2x^2 + 5x - 7$$ which simplifies to $$y = -x^3 - 2x^2 + 5x - 7$$. We need to:

1. Masalah: Selesaikan persamaan $8C_n = 4 \times 7C_n$ di mana $C_n$ adalah koefisien binomial. 2. Rumus yang digunakan: Koefisien binomial $nC_r = \frac{n!}{r!(n-r)!}$.

1. Problem 6: The sixth, seventh, and eighth grades raised money for their middle school. The sixth grade raised 40% of the total, the seventh grade raised 22%, and the eighth grad

1. **Stating the problem:** We want to understand how to solve problems involving sequences and series. 2. **Definitions:**

1. **Problem 6:** The sixth, seventh, and eighth grades raised money for their middle school. Sixth grade raised 40% of the total, seventh grade raised 22%, and eighth grade raised

1. **Problem 6:** The sixth, seventh, and eighth grades raised money for their middle school. Sixth grade raised 40% of the total, seventh grade raised 22%, and eighth grade raised

1. **Problem 6:** The sixth, seventh, and eighth grades raised money for their middle school. The sixth grade raised 40% of the total, the seventh grade raised 22%, and the eighth

1. **State the problem:** We have a sequence starting with terms -12, -9, -6, ... and we need to find the value of $x$ given that the ratio of the 8th term to the 6th term is $\fra