🧮 algebra

1. **State the problem:** Find the Highest Common Factor (HCF) of 144 and 96. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leavi

1. **State the problem:** We need to find the Highest Common Factor (HCF) of 144 and 96. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both wi

1. **State the problem:** Solve the equation $$x^{0.95} \times 760 = 18.5x$$ for $x$. 2. **Rewrite the equation:** We have $$760x^{0.95} = 18.5x$$.

1. Let's analyze the given expression: $\frac{42}{2} = \frac{21}{3} = 7$. 2. First, calculate each fraction separately.

1. **Stating the problem:** We want to understand what prime factorization is and how to find the prime factors of a number. 2. **Definition:** Prime factorization is expressing a

1. **Stating the problem:** (a) Alvin runs 5 km in two sessions. In the first session, his average speed is $x$ km/h. In the second session, his speed is reduced by 2 km/h, and he

1. Problem 30: A snail climbs a 10 m pole, climbing 5 m during the day and sliding down 4 m at night. How many days until it reaches the top? - Each full day (day + night) the snai

1. The problem is to solve the equation or expression given by the user, but since no specific equation or expression was provided, I cannot solve a particular problem. 2. To resol

1. **Problem 1:** Solve the equation $$\left\lceil 2\lfloor x \rfloor + \Delta + 2\right\rceil = 1$$. - Here, $\lfloor x \rfloor$ is the floor function (greatest integer less than

1. **Problem 1:** Solve the equation $[x] + x + [x] = 1$, where $[x]$ denotes the floor function (greatest integer less than or equal to $x$). 2. **Step 1:** Let $n = [x]$, then th

1. **State the problem:** We are given two functions: $$f(x) = 3x^2 - 5x + 7$$

1. **State the problem:** Simplify the expression $$(1+i)(2+3i)(4-3i)$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Recall the formula and rules:** When mult

1. **Problem Statement:** Ramu borrowed 1000 at 10% per annum simple interest for 3 years, but after the first year, the interest rate was revised to 12% per annum. We need to find

1. **State the problem:** A photograph measures 7 \(\frac{1}{2}\) cm (which is 7.5 cm) by 5 cm. It is enlarged so that the longer side becomes 24 cm. We need to find the length of

1. **State the problem:** We have a room with dimensions 30 ft long, 25 ft wide, and 14 ft high. There are 42 balloons inside the room, and we want to find how many cubic feet of s

1. **State the problem:** We need to find how many passengers, each weighing 50.5 kg, can fit in an elevator with a maximum load capacity of 605 kg. 2. **Formula used:** To find th

1. **Problem statement:** Determine whether the quadratic equation $x^2 + 4x + 4 = 0$ has distinct real roots, equal real roots, or no real roots. 2. **Formula used:** For a quadra

1. The problem is to understand the difference between $np$ and $n^p$ in mathematical expressions. 2. The expression $np$ means multiplication of $n$ and $p$, i.e., $n \times p$.

1. **Problem Statement:** Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula Used:** The quadratic formula for roots of $$ax^2 + bx + c = 0$$ is $$x = \fra

1. The problem is to convert the quadratic equations from standard form to vertex form. 2. The standard form of a quadratic equation is $$y = ax^2 + bx + c$$.

1. The problem is to understand and verify the logarithmic identity: $\log_a b = \frac{1}{\log_b a}$. 2. Recall the change of base formula for logarithms: $\log_a b = \frac{\log_c