🧮 algebra

1. **State the problem:** Find the square root of 1919282872737. 2. **Recall the formula:** The square root of a number $x$ is a value $y$ such that $$y^2 = x.$$

1. **State the problem:** We have a train with adults and children at Station X, Y, and Z with given ratios and changes. We want to find:

1. The problem is to evaluate the expression $$2^^5$$, which represents tetration, a power tower of 2's of height 5. 2. Tetration is defined as repeated exponentiation. For example

1. The problem is to evaluate the expression $$2^^2$$, which represents tetration, a power tower of 2s of height 2. 2. Tetration $$a^^n$$ means $$a$$ raised to the power of $$a$$ r

1. **State the problem:** Simplify the ratio $9 : 81$. 2. **Formula and rules:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).

1. **Problem 11:** Find the missing number in the proportion $$6/\boxed{x} = 12/32$$ given $$96 = 12/32$$. Since $$12/32$$ is a fraction, the equality $$96 = 12/32$$ is likely a ty

1. **Problem statement:** Fill in the missing numbers (boxes) in the equivalent fractions for problems 12, 13, and 14. 2. **Recall the rule for equivalent fractions:** Two fraction

1. **State the problem:** We have five symbols representing numbers: ❄️, 🌎, ⚡, 🔥, 🌱, ☀️, and 🌀. We are given five equations involving these symbols and need to find the values of e

1. (a) (i) Calculate the exact value of $$(5.8^2 + 1.02) \times 2.5$$. Step 1: Calculate $5.8^2$.

1. **State the problem:** We are given the ratio of 12-year-olds to 13-year-olds as $5:3$ and the total number of students as $24$. We need to find how many students are 13 years o

1. **State the problem:** We need to find the equation of a line that passes through the point $(6, -4)$ and is perpendicular to the line given by the equation $$6 = 4y + 3x$$. 2.

1. **State the problem:** Find the equation of the line passing through points $(3,-5)$ and $(-2,7)$. 2. **Formula used:** The point-slope form of a line is:

1. **State the problem:** Simplify the expression $$\frac{2x-3x}{4y} \cdot \frac{y}{x^2-9}$$. 2. **Combine and simplify the numerator in the first fraction:**

1. **State the problem:** Solve the quadratic equation $$2x^2 - 4x + 5 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \sq

1. **State the problem:** Solve the equation $$\frac{3x}{2x-1} - \frac{2}{5-x} = 7.$$\n\n2. **Find a common denominator:** The denominators are $2x-1$ and $5-x$. The common denomin

1. **State the problem:** Solve for $x$ in the equation $0.06x = 1691$. 2. **Formula and rules:** To isolate $x$, divide both sides of the equation by $0.06$.

1. **State the problem:** Solve the equation $$8 = 45y$$ for the variable $$y$$. 2. **Formula and rules:** To isolate $$y$$, divide both sides of the equation by $$45$$.

1. **State the problem:** Solve the equation $$\frac{2}{3}r = 4$$ for the variable $r$. 2. **Formula and rules:** To isolate $r$, multiply both sides of the equation by the recipro

1. **State the problem:** Solve the equation $$12r=30$$ for the variable $$r$$. 2. **Formula and rules:** To isolate $$r$$, divide both sides of the equation by $$12$$. Remember, d

1. **State the problem:** Solve the equation $$-72 = 18v$$ for the variable $$v$$. 2. **Formula and rules:** To isolate $$v$$, divide both sides of the equation by the coefficient

1. **State the problem:** Solve the equation $$-3y=0$$ for the variable $y$. 2. **Formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation. Since $