🧮 algebra

1. **State the problem:** Convert the decimal number 10.08 into a fraction. 2. **Understand the decimal:** The number 10.08 has two digits after the decimal point.

1. Problemet er at finde den afledte funktion $f'(x)$ for en given funktion $f(x)$.\n\n2. Den generelle regel for differentiation er, at hvis $f(x) = x^n$, så er $f'(x) = nx^{n-1}$

1. **Problem (a):** Tom's car has lost 18% of its value and is now worth 18450. 2. **Formula:** If the original value is $V$, then after losing 18%, the value is $V \times (1 - 0.1

1. The problem is to simplify the expression $\frac{ab - bc}{b}$. 2. We start by factoring the numerator:

1. **Problem statement:** Estimate powers of 2 using the approximation $2^{10} \approx 1000$. 2. **Recall the rule:** $2^{a+b} = 2^a \times 2^b$ and $2^{ka} = (2^a)^k$.

1. **Stating the problem:** We need to identify which dot pattern corresponds to blank 1 and blank 2 from the given options, then find the number sequence that matches the dot coun

1. **State the problem:** Matthew rides for $x$ km at 12 km/h. Zoe rides for $x+4$ km at 10 km/h. Their total riding time is 1.5 hours. Find $x$ and $x+4$. 2. **Recall the formula:

1. **State the problem:** We have a sequence of dot patterns arranged in 2 rows, with the number of dots in each row increasing by 1 each step. The first three terms show 3 dots pe

1. The problem asks to insert one pair of brackets in each expression so that the equation holds true. 2. For part a) $7 - 5 \times 4 + 8 = 16$, we want to find where to place brac

1. The problem is to find 7% of a number or value. 2. The formula to calculate a percentage of a number is:

1. **State the problem:** Solve the equation $3x a - 5y = 10 - 2$ and then solve the inequality $\frac{3x - 1}{3} < \frac{x + 7}{2}$. 2. **Solve the equation:**

1. The problem asks us to describe parts of the expression $4(8x + 5)$.\n\n2. The entire expression $4(8x + 5)$ is the product of two parts: the number 4 and the sum inside the par

1. **State the problem:** We need to factor the quadratic expression $10x^2 + 13x - 3$.

1. The problem states that Janelle saved up 265 and then bought a sweater for d dollars. 2. To find out how much money Janelle has left, we subtract the cost of the sweater from th

1. مسئله: دنباله \(a_n\) خطی است و تابع \(f(x) = k^x\) از نقاط \(A(a_1, a_r)\)، \(A(a_7, a_r)\) و \(B(a_7, a_6)\) عبور می‌کند. باید مقدار \(\frac{a_r}{a_7}\) را پیدا کنیم. 2. چون د

1. The problem asks us to represent the average depth of the ocean, which is 12,352 feet below the surface, as an integer. 2. Since the depth is below the surface, it is represente

1. The problem is to add two negative numbers: $-95 + (-47)$. 2. When adding negative numbers, you add their absolute values and keep the negative sign.

1. The problem states: 70% of what number is 10. 2. Let the unknown number be $x$.

1. **State the problem:** Solve for $b$ in the formula $$A = h \left( \frac{a + b}{2} \right)$$ given $A = 10$, $h = 4$, and $a = 3$. 2. **Write the formula:** The area $A$ of a tr

1. The problem is to solve a basic algebra question suitable for year 8 level. 2. Let's consider a simple example: Solve for $x$ in the equation $2x + 3 = 11$.

1. **Problem statement:** Factorise the expression given (assuming a general quadratic expression for demonstration, e.g., $x^2 + 5x + 6$). 2. **Formula and rules:** To factorise a