🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2 \frac{1}{3} + \frac{5}{2} - 1}{12 - 11 \frac{3}{4}}$$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Jasmine takes 120 steps in 4 minutes, each step is 8 dm long. We need to find out how long it will take Jasmine to walk 60 meters. 2. **Convert step lengt

1. The **range** of a function is the set of all possible output values (or $y$-values) that the function can produce. 2. More simply, when you input all the allowed $x$-values (th

1. **Forme canonique** pour une fonction polynôme du second degré $f(x)=ax^2+bx+c$ est donnée par $$f(x)=a\left(x-\frac{-b}{2a}\right)^2 - \frac{\Delta}{4a}$$

1. Probleemstelling: We bekijken het tekenverloop van een derdegraads veeltermfunctie $f(x)$ rond haar nulpunten $x_1$, $x_2$ en $x_3$. 2. Eigenschappen:

1. Stating the problem: Calculate the value of $\frac{7}{3} + \frac{5}{2} - 1$ divided by $12 - \frac{47}{4}$. 2. Convert all mixed numbers and whole numbers to improper fractions:

1. Let's first understand the expression given: $a\Lambda 3 * 3ab$. 2. The symbol $\Lambda$ is typically the logical AND in logic or can be a typo. Assuming it represents multiplic

1. Let's analyze the given expression, which appears to involve the fraction $-\frac{1}{2}$, the number 2 below it, and the number 1 crossed out. 2. Since the number 1 is crossed o

1. **Problem 5a:** Express $$\frac{2x^2 + 7x - 6}{(x + 5)(x - 4)}$$ in partial fractions. Step 1: Divide numerator by denominator if possible. Here, degree numerator = degree denom

1. The problem asks to evaluate the expression $\left(\frac{1}{4}\right)^{-\frac{1}{2}}$. 2. Recall that for any expression $a^b$, when $b$ is negative, $a^b = \frac{1}{a^{-b}}$.

1. **Stating the problem:** The question asks to solve the last problem involving $ \pi$ (pi) and specifically wants the answer expressed using $\pi$ rather than a decimal approxim

1. We are given a quadratic function and asked to analyze its characteristics and solve it if needed. 2. Assume the problem is to find the roots of $y = ax^2 + bx + c$ and analyze

1. Let's state the problem: We want to find the power $n$ such that $2^n = 32$. 2. We know that 32 can be expressed as a power of 2: $32 = 2^5$.

1. We are asked to simplify the expression $\frac{1}{4}(2^n - 2^{n+2})$. 2. Start by factoring out the common term $2^n$ inside the parentheses:

1. The problem asks us to find the value of the expression $\frac{2 + 2 + 2 + 2}{4}$. 2. First, calculate the sum inside the numerator: $2 + 2 + 2 + 2 = 8$.

1. Stated problem: Solve the equation $$ (x + 3) \times \frac{2}{3} \times (4 - x) \times \frac{4}{9} = \frac{27}{8} $$ for $x$. 2. Simplify the left side by combining the fraction

1. State the problem: Simplify the given expression for $S_n$: $$S_n=3\left[1-\left(\frac{1}{3}\right)^{n}+\frac{1}{2\cdot 3}\right]$$ 2. Simplify the term inside the brackets step

1. The problem appears incomplete because no equation or expression is given to find solutions for. 2. To help you, please provide the full equation or problem statement you want t

1. The problem is to calculate $2 \times 10^{100} - 2 \times 10^{98}$ and express the answer in standard form. 2. First, factor out the common factor $2 \times 10^{98}$ from both t

1. **Stating the Problem:** We want to find out which petrol option offers better value for money and then calculate the cost of 30 litres from the cheaper option. 2. **Calculate p

1. **State the problem:** We want to write down the inequalities defining the feasible region, identify the corner points of this region, and then find the maximum and minimum valu