🧮 algebra

1. The problem is to understand the properties of rational exponents and how they relate to integral exponents. 2. The properties of rational exponents are similar to those of inte

1. **Stating the problem:** We want to understand the properties of rational exponents and see some examples. 2. **Definition:** A rational exponent is an exponent that is a fracti

1. The problem states that the graph of $\ln y$ against $\ln x$ is a straight line with a point $(7,9)$ and a vertical intercept of 5. 2. For a straight line graph of $\ln y$ versu

1. **State the problem:** Simplify and rewrite the function $y = -3\left(\frac{1}{2}x^2 - 2\right) + \frac{15}{2}$. 2. **Apply the distributive property:** Multiply $-3$ by each te

1. **Problem statement:** Two vehicles start at the same time from towns A and B, 160 km apart, traveling towards each other. The lorry travels at 45 km/h from A to B, and the car

1. **State the problem:** Solve the equation $$\sqrt{x-8} - \sqrt{2x-2} + 3 = 0$$ for $x$. 2. **Isolate one of the square roots:** Move terms to isolate one radical:

1. **Problem:** Solve the equation $\sqrt{x-8} - \sqrt{2x-2} + 3 = 0$. 2. **Step 1:** Isolate one square root term:

1. **State the problem:** Factorize the expression $$4x^2 - 12y + 9$$. 2. **Identify the type of expression:** This looks like a quadratic expression in terms of $x$ and a constant

1. **State the problem:** A store has 3 types of accessories: scarves, ties, and belts. Scarves are 20%, ties are 60%, and belts are 40 items. Half of the ties are replaced with sc

1. **State the problem:** Veronica has a bank account with an initial deposit of 200 and an annual interest rate of $m\%$ compounded annually. The amount after $t$ years is given b

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 + x + 1$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solut

1. **Énoncé du problème :** Soit la suite $(U_n)$ définie par $U_0 = 1$ et $U_{n+1} = \frac{30}{2(3 - U_n)}$.

1. **State the problem:** Jason plans to complete a journey in 1.5 hours (which is 90 minutes). He drives at an average speed of 48 km/h and takes 50 minutes to complete half of hi

1. **State the problem:** We have two 3x3 grids where each row, column, and diagonal must sum to the same total. Each of the given numbers can be used exactly 3 times in its respec

1. **Problem statement:** We have a rectangular metal sheet with length twice its width. Squares of side 60 cm are cut from each corner to form an open rectangular tank. The tank's

1. **State the problem:** Simplify the expression $$-\frac{2}{9} + 2 \frac{1}{2} \div \left(-\frac{2}{5}\right)$$. 2. **Convert mixed number to improper fraction:**

1. The problem is to explain the meaning and use of the variable $b$ in algebraic expressions or equations. 2. In algebra, $b$ often represents a constant term or a coefficient in

1. **Stating the problem:** We have two lorries transporting sand: a 7-tonne lorry making $x$ trips and a 14-tonne lorry making $y$ trips. The total sand transported is 133 tonnes,

1. The problem is to calculate $2 - \frac{2}{9}$.\n\n2. To subtract a fraction from a whole number, convert the whole number to a fraction with the same denominator. Here, $2 = \fr

1. **Stating the problem:** A transporter uses two lorries, one 7-tonne and one 14-tonne, to transport 133 tonnes of sand. The 7-tonne lorry makes $x$ trips, the 14-tonne lorry mak

1. Form linear equations for the given problems: (i) The perimeter of a rectangle is given by the formula $$P = 2(x + y)$$ where $x$ is length and $y$ is breadth.