🧮 algebra

1. **Problem:** Solve the equation $$x^2 - 4x + 3 = 0$$ 2. **Formula:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a=1$$, $$b=-4$$, and $$c=3$$.

1. **State the problem:** Solve the equation $$\frac{7}{10}v + 1 = \frac{83}{15} - v$$ for $v$. 2. **Write down the equation:** $$\frac{7}{10}v + 1 = \frac{83}{15} - v$$

1. **Problem Statement:** Given data points for $x$ and $y$, fit a quadratic model $y = b_0 + b_1 x + b_2 x^2$ using the least squares method.

1. **State the problem:** A store buys a skateboard for 70 and applies a 15% markup. We need to find the selling price. 2. **Formula:** Selling Price = Cost Price + Markup

1. **State the problem:** We have a backpack originally priced at 30 and it is discounted by 40%. We need to find the sale price.

1. **Problem:** How many triangular tiles are there in the FIFTH figure of the sequence? 2. **Understanding the pattern:** The problem states the sequence of triangular tiles incre

1. **Problem:** How many triangular tiles are there in the FIFTH figure of the sequence? 2. **Understanding the pattern:** The sequence shows triangular tiles increasing in a patte

1. **Problem:** Given that $9x^{2} + 6xy + 4y^{2}$ is a factor of $27x^{3} - 8y^{3}$, find the other factor. 2. **Step 1: Recognize the form of the expression.**

1. **State the problem:** We have 7 numbers with a mean of 4. Six of the numbers are 2, 3, 1, 2, 7, and 8. We need to find: a) The seventh number.

1. **Problem statement:** Given the ordered numbers $x, (x+1), 5, (2x+1), (y+2), 7, 8,$ and $(3x+2)$, the mean is 6.5 and the median is 7. Find $x$ and $y$. 2. **Mean formula:** Th

1. **State the problem:** Find the function $f(x)$ given by the expression. 2. **Given:**

1. **State the problem:** We are given the linear equation $Y = -1x + 9$ and asked to find the answer, which typically means expressing it in a simplified or standard form or findi

1. **State the problem:** We need to identify the graphs of the functions

1. **State the problem:** Solve the logarithmic equation $$\log_5 (x - 18) - \log_5 x = \log_5 7$$ for $x$. 2. **Recall the logarithm subtraction rule:** For logarithms with the sa

1. **Stating the problem:** Calculate the value of the sum $$\sum_{n=1}^{25} (9n - 8)$$. 2. **Formula and rules:** The sum of a sequence $$\sum_{n=1}^N a_n$$ where $$a_n$$ is an ar

1. **State the problem:** Simplify the expression $Y - b - by - 1$. 2. **Identify like terms:** The terms are $Y$, $-b$, $-by$, and $-1$. Note that $Y$ and $y$ are different variab

1. Masalah: Cari nilai $x$ yang memenuhi persamaan linear $3x + 5 = 20$. 2. Formula yang digunakan adalah persamaan linear asas: $ax + b = c$.

1. **State the problem:** Solve the equation $x + 10 = 6$ for $x$. 2. **Formula and rule:** To isolate $x$, subtract 10 from both sides of the equation. This uses the rule that if

1. **State the problem:** Solve the equation $$\frac{2}{3}w - \frac{2}{3} = 0$$ for $w$. 2. **Write down the equation:** $$\frac{2}{3}w - \frac{2}{3} = 0$$

1. Problemi ifadə edək: Kiçik bir qalstuk dükanı hər qalstuku 3.50-ə satır. Gündəlik xərc funksiyası $C(x) = 0.0006x^3 - 0.03x^2 + 2x + 20$ olaraq verilib, burada $x$ satılan qalst

1. Énonçons le problème : Résoudre la partie A de l'épreuve demandée. 2. Comme le détail de la partie A n'est pas précisé, je vais supposer qu'il s'agit d'un problème algébrique cl