🧮 algebra

1. **Problem:** The opposite of a number is tripled and then decreased by 7. The result is 3 greater than twice the number. Find the number. Step 1: Let the number be $x$.

1. **Problem:** The opposite of a number is tripled and then decreased by 7. The result is 3 greater than twice the number. Find the number. Step 1: Let the number be $x$.

1. **State the problem:** Solve the equation $$4^{x+1} + 4^x = 320$$ for $x$. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the equation $$4^{x^2} = 8^x$$ for $x$. 2. **Rewrite the bases as powers of 2:**

1. (a) Express $16x^2 - 24x + 10$ in the form $(4x + a)^2 + b$. Start with the expression:

1. **State the problem:** We have the graph of $y=f(x)$ formed by lines AB and BC, and the graph of $y=g(x)$ formed by lines A'B' and B'C' which is obtained by applying two transfo

1. **State the problem:** Solve the system of linear equations using the elimination method: $$\begin{cases} 4x - y = 1 \\ 2x + 3y = 11 \end{cases}$$

1. **State the problem:** Mason owns 48 books in total. Hanna owns 6 times as many non-fiction books as Mason. We need to find how many books Hanna owns in total. 2. **Analyze Maso

1. We are given two systems of linear equations to solve for $x$ and $y$. 2. First system:

1. **State the problem:** Simplify the rational expression given by $$\frac{x^2 - 2x + 8}{1}$$ (assuming the expression is over 1 since no denominator was provided). 2. **Identify

1. **State the problem:** Simplify the rational expression \( \frac{4y(y - 3)(y + 4)}{y(y^2 - y - 6)} \). 2. **Factor the denominator:** The quadratic \( y^2 - y - 6 \) factors as

1. Let's start by understanding what a function is. A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output

1. **State the problem:** Let $p$ be the kilograms of cheese produced.

1. Aufgabe c ist nicht explizit im Text angegeben, aber basierend auf den gegebenen Informationen und den mathematischen Ausdrücken konzentrieren wir uns auf die Berechnung von $0,

1. **State the problem:** Find the values of $a$ such that the distance between the points $(1, a)$ and $(3, 5)$ is $\sqrt{8}$.\n\n2. **Formula used:** The distance $d$ between two

1. **State the problem:** We need to find the values of $a$ and $b$ such that the midpoint of the points $(a, 3)$ and $(7, b)$ is $(5, 4)$. 2. **Formula for midpoint:** The midpoin

1. **Problem statement:** We need to find a rule for the volume $V$ (in litres) of water in a flask as a function of time $t$ (in minutes), given that the flask is filled at a cons

1. **State the problem:** Find the vertex, y-intercept, and x-intercepts of the quadratic function $$y = 3x^2 - 12x + 9$$ using calculation. 2. **Vertex formula:** The vertex of a

1. **State the problem:** Find the vertex, y-intercept, and x-intercepts of the parabola given by the equation $$y = x^2 - 4$$. 2. **Vertex:** The vertex form of a parabola is $$y

1. مسئله: عبارت جبری $4y - y - 4$ را با استفاده از تجزیه به دست آورید. 2. ابتدا باید عبارات مشابه را با هم جمع کنیم. در اینجا $4y$ و $-y$ عبارات مشابه هستند.

1. مسئله را بیان می‌کنیم: عبارت جبری $$-3ab - 2b^3c + ab^2$$ را با استفاده از تجزیه به عوامل ساده‌تر کنیم. 2. ابتدا عبارت را به صورت کامل می‌نویسیم: