🧮 algebra

1. **Problem statement:** A jet ski rental charges a flat rate of 75 plus 60 per hour. You want to spend no more than 200. How many hours can you rent the jet ski and stay under bu

1. The problem is to solve a typical first-year IPE (Integrated Professional Education) algebra question, for example, solving a linear equation. 2. Consider the equation $3x + 5 =

1. **State the problem:** Evaluate the expression $8 \div 2(2 + 2)$. 2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication and division from

1. **Problem:** Rewrite the expression $x^{-3}$ with positive exponents only. 2. **Formula and rule:** Negative exponents mean the reciprocal of the base raised to the positive exp

1. State the problem: If $a - b = b - c = 2$, what is the value of the expression $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$. 2. Formula and rules: Use the identity $a - c = (a -

1. Problem: The third, fifth, and seventeenth terms of an arithmetic progression (AP) are in geometric progression (GP). Find the common ratio of the GP. 2. Let the first term of t

1. **State the problem:** We have a cubic curve given by the equation $$y = x^3 + ax + b$$ and it has a stationary point at $$(1, 13)$$. We need to find the values of $a$ and $b$.

1. Diberikan fungsi $f(x) = 2x - 3$ dan $g(x) = \frac{1}{3x + 1}$. Kita diminta menentukan invers dari komposisi fungsi $(f \circ g)^{-1}(x)$.\n\n2. Komposisi fungsi $f \circ g$ be

1. **State the problem:** Find the coordinates of the turning point of the curve given by the function $$y = \frac{x^2}{2} + 8x$$. 2. **Recall the formula and rules:** The turning

1. Let's consider a challenging algebra problem: Solve for $x$ in the equation $$\frac{2x^2 - 3x + 1}{x - 1} = 4x - 5.$$\n\n2. The problem requires solving a rational equation wher

1. Let's start with a simple problem: Find the 5th term of the arithmetic sequence where the first term $a_1=3$ and the common difference $d=4$. 2. The formula for the $n$th term o

1. **State the problem:** Amoebae double every hour. Starting with 1 amoeba, find how many amoebae there will be after 7 hours. 2. **Formula used:** The number of amoebae after $t$

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equati

Let's solve this step by step! 🎉 1. Imagine you have $x + \frac{1}{x} = 99$.

1. **Stating the problem:** Solve the equation for $x$: $Q4 A$ (assuming this means a specific algebraic problem, but since no explicit equation is given, please provide the exact

1. **State the problem:** Simplify or analyze the expression $12xx^2 + 5x + 8$. 2. **Rewrite the expression:** Note that $xx^2$ means $x \cdot x^2 = x^3$.

1. **State the problem:** Solve the simultaneous equations using substitution: $$7x - 2y = 27$$

1. **State the problem:** Solve the simultaneous equations: $$6(2x - 1 + y) + 5 = -13$$

1. **State the problem:** Solve the simultaneous equations: $$2^x = 4^{7 - 2y}$$

1. **State the problem:** Solve the system of linear equations: $$4.6t + 8.1u = 104$$

1. **Problem Statement:** Find the value of $\alpha^3 + \beta^3$ where $\alpha, \beta$ are roots of the quadratic equation $$3x^2 - 2x + 4 = 0.$$