🧮 algebra

1. The problem states that Dexter is converting the improper fraction $\frac{32}{3}$ and claims it equals $3 \frac{2}{3}$. We need to check if this is correct. 2. Recall that an im

1. **State the problem:** Benjamin invests money in a bank account with compound interest. After 2 years, the amount is 658.20, and after 5 years, it is 710.89. We need to find the

1. **State the problem:** Factorise the quadratic expression $3x^2 + 5x - 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that mu

1. **State the problem:** Factorise the quadratic expression $10x^2 + 19x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that m

1. The user mentioned a sum in a photo but did not provide the actual sum or any details. 2. To assist, I need the explicit sum or problem statement.

1. **Stating the problem:** We have 60 vehicles in total. 28 are cars and the rest are vans. Among the cars, 7 are second-hand, and among the vans, 5 are new. We need to find the v

1. **State the problem:** We need to find the values of $m$ (slope) and $c$ (y-intercept) for the line $R$ given by the equation $y = mx + c$. 2. **Identify given points:** The lin

1. **State the problem:** Find the equation of the straight line passing through the points $(-4, 2)$ and $(0, 10)$ in the form $y = mx + c$. 2. **Formula used:** The equation of a

1. **State the problem:** We have a metal block with mass 68.7 kg. Each cubic centimeter (cm³) of this metal has a mass of 8.1 g. The block is melted and recast into cylinders with

1. **State the problem:** Find the equation of the line $\ell$ in the $xy$-plane that passes through the point $(3,4)$ and makes an angle of $70^\circ$ with the positive $x$-axis.

1. **State the problem:** Simplify the expression $$\frac{2 \log_x \sqrt{y} + \log_x y}{2 \log_{x^2} y}$$ where $x > 1$ and $y > 0$. 2. **Recall logarithm rules:**

1. The problem is to factor the quadratic expression $w^2 + 3w - 28$. 2. The general form of a quadratic expression is $ax^2 + bx + c$.

1. The problem is to understand and apply the change of base formula for logarithms. 2. The change of base formula states that for any positive numbers $a$, $b$, and $c$ (with $a \

1. **Problem:** Find the decomposition of the rational fraction $$\frac{x^2}{(1-x)(1+x^2)^2}$$ into partial fractions. 2. **Formula and rules:** For partial fraction decomposition,

1. Planteamos el problema: queremos generar una lista de 305 valores de $X$ para la función $$Y = X^2 - 4.38X + 7.5$$ de modo que los valores de $Y$ estén entre 2.7 y 7.5. 2. Prime

1. Let's clarify the terms: The **domain** of a function is the set of all possible input values, usually represented by $x$. 2. The **image set** (or range) is the set of all poss

1. We are given the function $$y=3x^7+2x^6-8x^5+6x^4-3x^3+3x^2+4x-5$$ and asked to analyze or work with it. 2. This is a polynomial function of degree 7. Polynomial functions are s

1. The problem is to analyze the two linear functions: $$y = x + 4$$ and $$y = x - 4$$. 2. These are both linear equations in slope-intercept form $$y = mx + b$$, where $$m$$ is th

1. **State the problem:** We are given the linear function $y = x + 4$ and want to understand its properties. 2. **Formula and explanation:** This is a linear equation in slope-int

1. **State the problem:** We are given the function $f(x) = \sqrt{x} - 6$ and want to understand its behavior and graph it. 2. **Recall the domain of the square root function:** Th

1. **State the problem:** Solve the equation $3x + 2 = \frac{2x + 13}{3}$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the denominat