🧮 algebra

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:** $$4 - 3x = 6 - 5x$$.

1. Vamos resolver um problema fácil de álgebra: Resolver a equação $2x + 3 = 7$. 2. A fórmula básica para resolver equações lineares é isolar a variável $x$.

1. **State the problem:** We have a kite with four sides: two sides each of length $n$ cm and two sides each of length $n + 3$ cm. The perimeter is given as 102 cm. 2. **Formula fo

1. **State the problem:** Solve for $a$ in the equation $$\left(\frac{1}{9}\right)^{a+1} = 81^{8+a+1} \cdot 27^{2 - a}.$$\n\n2. **Rewrite bases as powers of 3:**\n- $9 = 3^2$, so $

1. **State the problem:** Solve the equation $$\left(\frac{1}{9}\right)^{a+1} = 81^{8+a+1} \cdot 27^{2-a}$$ for the variable $a$. 2. **Rewrite bases as powers of 3:**

1. The problem asks for the area of a square with side length $4x + 3$. 2. The formula for the area of a square is:

1. **State the problem:** A rectangular picture frame measures 20 cm by 30 cm. A mat of uniform width $x$ cm is placed inside the frame, creating a border. The area of the mat is e

1. **Problem statement:** We need to sketch a quartic polynomial function $y = f(x)$ such that $f(x) > 0$ when $x < -5$, $2 < x < 3$, and $x > 4$. We also need to write an inequali

1. **State the problem:** Lilly thinks of a number $k$. She triples it and then subtracts 8 to get 7. 2. **Write the equation:** Tripling $k$ means $3k$. Subtracting 8 gives $3k -

1. **State the problem:** We are given the expression $y = (a + b)(a - b)$ and need to find the value of $y$ when $a = 7.5$ and $b = 2.5$.

1. **State the problem:** We need to find the value of $y$ given the expression $y = (a + b)(a - b)$ when $a = 7.5$ and $b = 2.5$. 2. **Recall the formula:** The expression $(a + b

1. Add the polynomials. **a)** $(3x^2 - x + 2) + (4x^2 + 3x - 1)$