🧮 algebra

1. **State the problem:** We are given parametric equations $x(t) = t^2 - 2t$ and $y(t) = t + 1$ for $-2 \leq t \leq 4$. We need to sketch the curve, indicate the direction, and fi

1. **State the problem:** We are given parametric equations $x(t) = t^2 - 2t$ and $y(t) = t + 1$ for $-2 \leq t \leq 4$. We need to sketch the curve, indicate the direction, and fi

1. Дано выражение $\left(-\frac{1}{2}\right)^{-4}$. Нужно упростить его. 2. Правило степеней с отрицательным показателем: $a^{-n} = \frac{1}{a^n}$, где $a \neq 0$.

1. **Problem statement:** Find the equations of two lines passing through the point $(-2,4)$ that form triangles with the coordinate axes having an area of 9 square units. 2. **For

1. **Stating the problem:** We have three halls with chairs to be moved: Legon hall (350 chairs), Akuafo hall (100 chairs), and Volta hall (200 chairs). Only one-tenth of each supp

1. Identify whether the following numbers are rational or irrational: $\sqrt{16}$, $\pi$, $\frac{22}{7}$, $0.333\ldots$, $\sqrt{2}$. Explain your reasoning. 2. Compute the sum, dif

1. **State the problem:** We need to sketch the graph of the linear function $f(x) = -3x + 2$ using the slope and one point method. 2. **Recall the formula:** A linear function can

1. Let's start by stating the problem: We want to solve a more difficult algebraic equation or expression to practice. 2. A good way to increase difficulty is to include quadratic

1. **Problem Statement:** We need to sketch the graph of the linear function $f(x) = 2x - 4$ using the $x$-intercept and $y$-intercept.

1. **Problem 1: Solve the linear equation** Solve for $x$ in the equation $$3x - 7 = 2x + 5$$.

1. Let's start by understanding what linear equations and inequalities are. 2. A linear equation is an equation of the form $ax + b = 0$, where $a$ and $b$ are constants and $x$ is

1. **Problem:** Identify the relationships among the number systems: natural numbers ($\mathbb{N}$), whole numbers ($\mathbb{W}$), integers ($\mathbb{Z}$), and rational numbers ($\

1. The problem is to solve for $c$ without using vectors. 2. Since the problem statement is brief, let's assume it involves a common algebraic equation or geometric relation where

1. **State the problem:** You have 80000 birr and want to buy fuel at two different prices: 131.90 birr per liter and 129.31 birr per liter. We want to find how many liters you can

1. **Problem Statement:** A ship's cargo worth 100000 is partially lost to save the ship. Amanda's cargo is worth 20000, Barry's cargo is worth 200, and 50000 worth of cargo is los

1. **Problem statement:** Sketch the curve defined by the parametric equations $$x(t) = 2 \cos(t)$$ and $$y(t) = 3 \sin(t)$$ for $$0 \leq t \leq 2\pi$$. Indicate the direction of m

1. **State the problem:** Solve the equation $$\log_4 x^{\log_4 729} - \log_3 27^{\log_4 x} = 15.$$\n\n2. **Recall logarithm rules:**\n- Power rule: $$\log_a b^c = c \log_a b.$$\n-

1. **State the problem:** Simplify the expression $\sqrt{x}x^2 - 3x$. 2. **Recall the rules:**

1. Problem: Solve the equation $6 + X = 14$ and verify the solution. 2. Formula and rules: To find $X$ in an equation like $a + X = b$, subtract $a$ from both sides: $$X = b - a$$

1. The problem states that the point $(4, 10)$ lies on the curve $y = f(x)$, meaning when $x = 4$, $f(4) = 10$. 2. We need to find the coordinates of the corresponding point on the

1. **State the problem:** Find the inverse function $f^{-1}(x)$ for the function $f(x) = \sqrt{x - 1}$ where $x \geq 1$. 2. **Recall the definition of inverse functions:** The inve