🧮 algebra

1. **State the problem:** Calculate the product $1.827 \times 10 \times 9000 \times 6$ and express the answer in standard form. 2. **Calculate step-by-step:**

1. The problem states that a television originally costs 550 and the price is reduced by 4%. We need to find the new price after the reduction. 2. Calculate the amount of the reduc

1. **State the problem:** Trevor bought two items priced at 800 and 400 respectively, and he paid 12.5% VAT on the total price. We need to find the total amount Trevor paid includi

1. **State the problem:** We have a rectangular field with width 35 m. Around the field, 15 poles each 5 m wide are placed 7 m apart. We need to find the length of the field. 2. **

1. The problem asks to write the repeating decimal $0.146\overline{0}$ as a fraction in simplest form. 2. Note that $0.146\overline{0}$ means the decimal $0.146000\ldots$ where the

1. **State the problem:** Anna Lee has 3 bags of sweets with quantities 145, 206, and 167. 2. **Find the total number of sweets:**

1. The problem asks to work out the expressions and give each answer in standard form. (a) Evaluate $2 \times 1.10^8 \times 10^{101}$.

1. We are given the expression $$E = 2x + \frac{3x + 7}{x + 4}$$ with the domain $$x \in [1, 5[.$$\n\n2. The problem is to understand and simplify the expression for values of $$x$

1. We are given the expression $$E = 2x + \frac{3x + 7}{x + 4}$$ with the domain $$x \in [1, 5[.$$\n\n2. First, understand the problem: we want to simplify or analyze the expressio

1. **Problem Statement:** Find the gradient and equation of the line passing through points A(2,3) and B(9,4), then find the equation of a line parallel to it passing through C(4,5

1. **Problem:** Solve the equation $2x+3=11$. 2. **Goal:** Isolate $x$ by undoing operations in reverse order.

1. **State the problem:** Solve the equation $-x + \frac{3y}{2} = 10 - 2x$ for $y$ in terms of $x$. 2. **Rewrite the equation:**

1. **Problem 1:** Beth walks 4 km to the station at 6 km/h and wants to catch the 0924 bus. Find the latest time she can leave home. 2. Calculate the time taken to walk 4 km at 6 k

1. **State the problem:** We are given a linear relationship between $t$ and $\log_4 V$ for $t \geq 0$ with the line $l$ passing through $(0, \log_4 40000)$ and having gradient $-\

1. The problem states that all buses take the same time to travel from the station to the city centre. 2. We are given the departure times from the station: 09:24 and 11:06.

1. Problem: Convert each given linear equation to slope-intercept form $y = mx + b$ and interpret the slope and intercept. 2. For $11\ 2x = \frac{5x - 2y}{4}$:

1. **Problem statement:** (b) Express $ (2 + x)^{-1} $ in the form $ A(1 + Bx)^{-1} $ where $ A $ and $ B $ are rational numbers.

1. Given equation: $3x - 2y = 15$ Rewrite in slope-intercept form $y = mx + b$:

1. Stating the problem: Solve the equation $X + \frac{2y}{2} = -6$ for $X$ in terms of $y$. 2. Simplify the fraction: $\frac{2y}{2} = y$.

1. The problem asks for the equation of a line with gradient $\frac{2}{5}$ and y-intercept at $(0, -5)$ in the form $ax + by = c$ where $a$, $b$, and $c$ are integers in lowest ter

1. **Problem statement:** The value of a car $V$ is modeled by $V = ab^t$, where $a$ and $b$ are constants and $t$ is the number of years since purchase. The line $l$ shows the lin