🧮 algebra

1. **State the problem:** Find the area of a square with side length $\frac{2}{3}y$ cm. 2. **Formula for the area of a square:**

1. The problem asks who is correct about the first step in multiplying the expressions $\frac{7}{12} \left( \frac{1}{6}x - \frac{1}{3} + \frac{3}{4}x - \frac{5}{12} \right)$. Juan

1. **State the problem:** Simplify the expression $$2(5 + 3x) + (x + 10)$$. 2. **Use the distributive property:** Multiply 2 by each term inside the first parentheses.

1. **State the problem:** Solve for $x$ in the equation $3 - 14x = 17$. 2. **Isolate the term with $x$:** Subtract 3 from both sides to get the term with $x$ alone.

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -4]$ by using the line segment connecting the points where $x = -6

1. **Stating the problem:** Risolvi la disequazione $$\frac{x+6}{x-3} \geq 0$$. 2. **Formula and rules:** Per risolvere disequazioni frazionarie, analizziamo il segno del numerator

1. **State the problem:** Solve the equation $$45 + 2x = 5x - 9$$ and prove that $$x = 18$$. 2. **Formula and rules:** To solve linear equations, we use properties of equality such

1. **State the problem:** Given the equation $$\frac{1}{3}x - 6 = 10$$, prove that $$x = 48$$. 2. **Show the formula and rules:** To solve for $$x$$, we use the Multiplication Prop

1. **Stating the problem:** We have a 3×3 grid where each cell contains expressions involving logarithms base 10 of numbers formed by digits in red and blue boxes.

1. **State the problem:** We need to fill in the boxes with digits 0 to 9 (each digit used once per blue box and once per red box) to make the logarithmic expressions true and incr

1. **State the problem:** Factorise fully the expression $$8ax - 14bx + 4ay - 7by$$. 2. **Identify common factors:** Group terms to find common factors:

1. **Stating the problem:** Förenkla uttrycket $$3y(2y + 3) - y(y + 5)$$.

1. **State the problem:** We need to find the coordinates of another point on the line $h$ which has a slope of 4 and passes through the point $(20,12)$. 2. **Formula used:** The e

1. Problemet är att förenkla uttrycket $$3a(b - 2) - a(b + 3)$$. 2. Använd distributiva lagen: $$x(y + z) = xy + xz$$ för att multiplicera varje term.

1. The problem is to simplify the expression or equation given previously. 2. To simplify, we combine like terms, factor where possible, and reduce fractions.

1. **Problem statement:** We need to find the cost function $K(x)$ given the derivative(s) and initial conditions for each part.

1. **State the problem:** We need to fill in the boxes with digits 1 to 9 (each digit used once) to create logarithmic expressions that produce an integer, an irrational number, an

1. **State the problem:** Solve the equation $$\frac{1}{1 - e^x} = 5$$ for $$x$$. 2. **Rewrite the equation:** Multiply both sides by $$1 - e^x$$ to clear the denominator:

1. **State the problem:** We need to determine if the variables $x$ and $y$ are proportional based on the graph provided. 2. **Recall the definition of proportionality:** Two varia

1. The problem asks to rewrite the exponential equation $$3^{-4} = \frac{1}{81}$$ as a logarithmic equation. 2. Recall the definition of logarithms: If $$a^x = b$$, then $$\log_a(b

1. **State the problem:** Simplify the expression $$\frac{x^6 z^3}{x^2 z^5}$$. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n} = a^{m-n}$$.