🧮 algebra

1. **State the problem:** We are given the function $$f(x) = 9x^2 + 4(2x+1)(x-2)^2$$ and asked to (i) express it in partial fractions and (ii) show that for sufficiently small $$x$

1. **Problem statement:** We are given a set of numbers: $x$, $(x+1)$, $5$, $(2x+1)$, $(y+2)$, $7$, $8$, and $(3x+2)$. The mean of these numbers is $6.5$, and the median is $7$. We

1. Let's start by understanding what you need help with in math. Since you mentioned you're bad at math, we'll begin with a simple problem to build your confidence. 2. Suppose we w

1. **Problem statement:** We are given the ordered numbers: $x$, $(x + 1)$, $5$, $(2x + 1)$, $(y + 2)$, $7$, $8$, and $(3x + 2)$. The mean of these numbers is 6.5, and the median i

1. El problema es resolver la ecuación cuadrática $$x^2 - 5x + 6 = 0$$. 2. La fórmula general para resolver ecuaciones cuadráticas es $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ don

1. **State the problem:** Use the distributive property to remove the parentheses in the expression $$2c^5(6c^2 - 4)$$ and simplify the result. 2. **Recall the distributive propert

1. **State the problem:** Simplify the expression $$(4x^2 + 1) - (2x^2 - 6x + 3)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to

1. **State the problem:** A car originally costs $29500. It depreciates $1680 in the first year and $475 each subsequent year. We want to find how many years it takes for the car's

1. **Stating the problem:** We are given a system of three equations representing distances in 3D space:

1. **Énoncé du problème :** Nous avons une inéquation qui modélise le salaire annuel de Louis en fonction du nombre d'heures travaillées par semaine $H$ et du nombre de semaines tr

1. **Énoncé du problème :** a) Traduire la situation en une inéquation.

1. Énoncé du problème : Louis gagne 9,50 par heure et veut savoir s'il gagne plus que le salaire moyen annuel de 35 781 en 2005. 2. Formule et hypothèses : Pour comparer, on doit c

1. The problem is to understand and apply the formula for the minimum value of a quadratic function. 2. The quadratic function is generally written as $f(x) = ax^2 + bx + c$ where

1. **Problem:** Determine the condition on $\alpha$ such that the quadratic equation $6x^2 - 11x + \alpha = 0$ has rational roots. 2. **Formula:** For a quadratic equation $ax^2 +

1. **Stating the problem:** We are given a table of values for $x$, $y_1$, and $y_2$. The goal is to analyze or interpret the data for $y_1$ and $y_2$ as functions of $x$.

1. The problem involves finding the missing values in percentage problems. 2. For the first problem, we know 5% of some number equals 79.8. We use the formula for percentage:

1. **State the problem:** Simplify the expression $$\left(\frac{\sqrt{2}-1}{2}\right)^{-1} - \left(\frac{1}{\sqrt{2}+1}\right)$$. 2. **Recall the rule for negative exponents:** For

1. Problema: Avem 14 exerciții de adunare cu un termen necunoscut, de forma $a + \_\_\_ = b$. Trebuie să găsim termenul necunoscut pentru fiecare. 2. Formula folosită: Pentru o ecu

1. **Stating the problem:** Simplify the expression $$N = \frac{\sqrt[3]{a^{3} \sqrt{a^{2} \sqrt{a^{5} \sqrt{a^{6}}}}}}{\sqrt[3]{\sqrt{a^{22}}}}$$. 2. **Rewrite nested radicals as

1. The problem involves calculating the missing value in a percentage proportion setup where two known values and a percentage are given, or vice versa. 2. The general formula for

1. The problem involves calculating the percentage values of given numbers. 2. The formula to calculate a percentage of a number is: