🧮 algebra

1. **State the problem:** We need to find the value of $g(2) \cdot h(3)$ given the function $g(x) = 5x - x^2$. However, the function $h(x)$ is not provided, so we can only evaluate

1. **State the problem:** Factor the polynomial $$4x^2 + 12x + 9$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two binomials $$(mx + n)(px

1. **Problem Statement:** We are given a rational function $f(x)$ with vertical asymptotes at $x = -2$ and $x = 2$, and a horizontal asymptote at $y = 0$. We need to determine whic

1. Problemet handlar om att avgöra om bensinen räcker hela vägen under en bilresa. 2. Vi vet att tanken var full i början, vilket vi kan kalla 1 (hela tanken).

1. Problemet handlar om att förstå hur bråket $\frac{3}{4}$ kan representeras och hur man kan ställa upp det. 2. Ett bråk $\frac{a}{b}$ betyder att vi delar något i $b$ lika delar

1. Problemet handlar om att avgöra om bensinen räcker hela vägen under en bilresa. 2. Vi vet att tanken var full i början, vilket vi kan kalla 1 (hela tanken).

1. Problemet handlar om att avgöra om bensinen räcker hela vägen under en bilresa. 2. Vi vet att tanken var full i början, och efter \(\frac{4}{5}\) av resan finns \(\frac{1}{4}\)

1. **State the problem:** Find the slope of the line passing through the points $(-5, 3)$ and $(5, -3)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. **State the problem:** Solve the inequality $2(x - 1) < 6 - x$. 2. **Apply the distributive property:**

1. **Énoncé du problème :** Simplifiez l'expression $\frac{(8x^2 y^{-1})^2}{4x^{-3} y^5}$. 2. **Formule et règles importantes :**

1. The problem asks to draw lines with given gradients (slopes) on squared paper. 2. The gradient (or slope) of a line is the ratio of the vertical change (rise) to the horizontal

1. **State the problem:** We want to simplify and understand the expression $\left|1+\frac{1}{x}\right|$. 2. **Recall the absolute value definition:** The absolute value $|a|$ of a

1. **State the problem:** Solve the equation $1+\left|1+\frac{1}{x}\right|=4$ for $x$. 2. **Isolate the absolute value:** Subtract 1 from both sides:

1. **Problem statement:** Elisabeth's grandfather wants to rent a minibus to visit the zoo 70 km away. There are two offers: - Offer 1: 63 euros per day plus 0.50 euros per kilomet

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y + z = 6 \\ 2x - y + 3z = 9 \\ -x + 2y + 2z = 9 \end{cases}$$

1. **Problem statement:** Fill in the missing fractions or units in the given equations. 2. **Step (a):** Given $$\frac{19}{8} = 2 + \text{missing fraction}$$

1. The problem is to identify which inequality corresponds to the interval $(-\infty, -1)$ on a number line. 2. The interval $(-\infty, -1)$ means all numbers less than $-1$, but n

1. **Problem:** Find the x and y intercepts of the line passing through points (-4, -4) and (4, 4). 2. **Formula and rules:**

1. **State the problem:** We are given that pumpkins cost 5 each and tomatoes cost 3 each. The total sales amount to 98. We know 10 pumpkins were sold, and we need to find the numb

1. **State the problem:** We need to find the area of the region enclosed by the curve $y^2 = 4ax$ and the line $x = a$, where $a > 0$. 2. **Understand the curve:** The curve $y^2

1. **Stating the problem:** You want to understand how the expression $\frac{1}{0.7}$ becomes $\frac{1.4}{0.25}$ in the given steps. 2. **Recall the original equation:**