🧮 algebra

1. Stating the problem: Simplify the expression $$\frac{3x - 4}{5} + \frac{5x - 2}{5}$$. 2. Since both terms have the same denominator 5, we can combine the numerators over the com

1. El problema consiste en unir enunciados para completar frases sobre funciones y sus puntos de corte con los ejes. 2. Primero, recordemos que una función es una relación entre do

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}.$$\n\n2. **Use the given equalities:** We know $a - b = 2$ and

1. **State the problem:** Simplify the expression $$\frac{-14.2 m^2}{2m}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, s

1. **State the problem:** Find the slope $m$ of the line passing through the points $(11,14)$ and $(-18,3)$. 2. **Recall the slope formula:**

1. **State the problem:** Simplify the expression $$\frac{3y}{y^2 + 3y - 10} - \frac{5}{2y + 10}$$ and check if it equals $$\frac{5y - 5}{y^2 + 3y - 10}$$. 2. **Factor the denomina

1. The problem is to write a given expression or function as $f(x)$, which means expressing it as a function of $x$. 2. The general form of a function is $f(x) = \text{expression i

1. The problem asks to find the average rate of change of the function $f(x) = 7$ on the interval $[6, 8]$. 2. The formula for the average rate of change of a function $f$ on the i

1. **State the problem:** We need to find the missing values A, B, C, and D in the tables for the simultaneous equations: $$y + 9x = 0$$

1. **State the problem:** Simplify the expression $$\frac{3}{5} - \frac{2x - 1}{10} + \frac{3x - 2}{4}$$. 2. **Find a common denominator:** The denominators are 5, 10, and 4. The l

1. **State the problem:** We have two equations based on Alfie's and Lyra's operations with numbers $c$ and $d$:

1. **State the problem:** Simplify the expression $$\frac{x^{2} + 2x - 48}{x^{2} + x - 42} \div \frac{x^{2} + 2x - 15}{x^{2} + 15x + 56}$$ given the factorizations: $$x^{2} + 2x -

1. **State the problem:** We are given the equation of a line in slope-intercept form: $y = mx + c$. 2. **Identify the line from the graph:** The blue line passes through the origi

1. **Stating the problem:** We have a sequence of patterns made from matchsticks forming equilateral triangles. The number of matchsticks for the first six patterns is given as 3,

1. **State the problem:** We need to find the time spent per flyer for each person (Goran, Josh, Frank) and determine who worked the fastest. 2. **Formula:** Time spent per flyer i

1. The problem is to evaluate $49^{-\frac{3}{2}}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. The problem is to complete the factorization of the difference of squares expression $a^2 - b^2$. 2. The formula for the difference of squares is:

1. **State the problem:** Simplify the expression $12x + 30$ by factoring. 2. **Formula and rules:** To factor an expression, find the greatest common factor (GCF) of all terms and

1. The problem asks for the expression of the area of a rectangle with width $9 - d$ and height $3$. 2. The formula for the area $A$ of a rectangle is:

1. The problem asks for the y-intercept of the line given by the equation $$y + 15 = 12 - 2x$$. 2. The y-intercept is the point where the line crosses the y-axis. At this point, th

1. **State the problem:** Solve the linear equation $$4 - 3x = 6 - 5x$$. 2. **Write down the equation:** $$4 - 3x = 6 - 5x$$.