🧮 algebra

1. **State the problem:** We need to find a two-digit number whose digits sum to 9, and nine times this number equals twice the number formed by reversing its digits. 2. **Define v

1. **State the problem:** We are given the quadratic equation $$3x^2 - 10x - 8 = 0$$ with roots $$\alpha$$ and $$\beta$$, where $$\alpha > \beta$$. We need to find the value of $$\

1. **State the problem:** Simplify the expression $\alpha\beta^2 + \alpha^2\beta$. 2. **Identify common factors:** Both terms contain $\alpha$ and $\beta$.

1. **State the problem:** Given the quadratic equation $$2y^2 - 5y - 3 = 0$$ with roots $$\alpha$$ and $$\beta$$, find the value of $$\alpha + \beta$$. 2. **Recall the formula:** F

1. Задача: Рассмотрим переменную $X$, которая всегда разрезается на две части, то есть $X$ делится на две половины. 2. Условие: $Y$ забрал 13 из половины $X$, то есть из $\frac{X}{

1. **State the problem:** Simplify the expression $5(27 \div 34)2$. 2. **Recall the order of operations:** Perform division and multiplication from left to right.

1. The problem is to verify the equality $\frac{1}{x} = x^{-1}$. 2. Recall the rule of exponents: for any nonzero number $x$ and integer $n$, $x^{-n} = \frac{1}{x^n}$.

1. **Problem statement:** Classify the system of linear equations based on the graph and find the solution. 2. **Recall:**

1. Énoncé du problème : Calculer l'expression $$\frac{5}{3} - \frac{3}{x} \times \frac{1}{2}$$ et déterminer sa valeur. 2. Formule et règles importantes : Pour soustraire ou additi

1. **Problem Statement:** Given the quadratic equation $ky^2 + ry + d = 0$ with roots $\alpha$ and $\beta$, show that $\alpha + \beta = -\frac{r}{k}$ and $\alpha \beta = \frac{d}{k

1. The problem asks to solve exercise 3, but since no specific details are given, I will assume it is a typical algebraic equation to solve. 2. The general approach to solving an e

1. The problem states the equation $1=5$. 2. This is a contradiction because the number 1 is not equal to 5.

1. The problem states that \(\alpha\) and \(\beta\) are the roots of a quadratic equation. We need to find relationships involving these roots. 2. For a quadratic equation of the f

1. **Problem Statement:** Solve the linear equation involving fractions, for example, $$\frac{2x}{3} + \frac{1}{4} = \frac{5x}{6} - \frac{1}{2}$$. 2. **Formula and Rules:** To solv

1. **State the problem:** Solve the quadratic equation $2x^2 - x + 5 = 0$. 2. **Formula used:** The quadratic formula for $ax^2 + bx + c = 0$ is

1. The problem is incomplete as given: "Let a->" does not specify what is asked or what expression is involved. 2. To assist you properly, please provide the full problem statement

1. The problem is incomplete as given: \left[\; is an opening bracket without a closing part or expression inside. 2. To solve or simplify expressions involving brackets, we need t

1. Nyatakan masalah: Fungsi kuadratik diberikan oleh $$f(x) = p(x + q)^2 + r$$ dengan pemalar $p$, $q$, dan $r$. Fungsi ini mempunyai nilai minimum $-4$ dan paksi simetri $x = 3$.

1. **State the problem:** Given $a+b=10$ and $ab=21$, find $(a-b)^2$. 2. **Recall the formula:** We know that $(a-b)^2 = (a+b)^2 - 4ab$.

1. **Nyatakan masalah:** Diberi fungsi kuadratik $$f(x) = 3(x + p)^2 + 2$$ dengan titik minimum pada $$(1, q)$$. Kita perlu cari nilai $p$, nilai $q$, dan persamaan paksi simetri.

1. **State the problem:** We are given an arithmetic progression (A.P.) with the first few terms 72, 68, 64, 60, … and we need to find which term is zero. 2. **Recall the formula f