🧮 algebra

1. **State the problem:** Simplify or factor the quadratic expression $$x^2 - 5x + 6$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look f

1. **State the problem:** Simplify the expression $$2x^2 + 8x \times 2$$. 2. **Recall the order of operations:** Multiplication must be done before addition.

1. **State the problem:** Arelli bought a bike for $80 and sold it for 20% less. We need to find the selling price. 2. **Formula used:** To find the selling price after a percentag

1. **State the problem:** We have a pond shaped like a prism with dimensions length $= 2$ m, width $= 1$ m, and height $= 1.3$ m.

1. **State the problem:** We are given the ratio of purple cars to red cars as $89 : 53$. 2. **Goal:** Write this ratio in the form $n : 1$, where $n$ is a decimal rounded to 2 dec

1. **State the problem:** We need to evaluate the cube root of the expression $$\sqrt[3]{\frac{((24\times3600)^2 \times 6.67\times10^{-11} \times 5.97\times10^{24})}{4\pi^2}}.$$ 2.

1. **State the problem:** Solve the equation $$3d - 21(2d - 4) = -45(4d - 4)$$ for $d$. 2. **Distribute the constants inside the parentheses:**

1. Simplify $\sqrt{81} + 2\sqrt{5} + \sqrt{63} + \sqrt{45}$. 2. For $f(x) = x^2 + 4x - 2$:

1. Simplify $\sqrt{81} + 2\sqrt{5} + \sqrt{63} + \sqrt{45}$. 2. For $f(x) = x^2 + 4x - 2$:

1. The problem is to understand the graph described: a square or rectangular coordinate frame with a single rising diagonal line from lower-left to upper-right. 2. This line inters

1. **Problem Statement:** We need to find the linear equation that matches a graph described as a straight line with a positive slope, crossing the y-axis at about $-3$, and rising

1. Спочатку сформулюємо задачу, яку ви раніше надсилали (будь ласка, уточніть, якщо потрібно інше). 2. Припустимо, задача пов'язана з розв'язанням рівняння або системи рівнянь. Вик

1. Сформулюємо задачу: Розв'яжи рівняння $$3x + 7 = 22$$ самостійно. 2. Формула для розв'язання лінійного рівняння виду $$ax + b = c$$: $$x = \frac{c - b}{a}$$.

1. The problem is to understand why the coefficient $a$ in a quadratic function $y = ax^2 + bx + c$ determines the direction of the parabola. 2. The formula for a quadratic functio

1. **State the problem:** We need to find the equation of a parabola describing the height $h$ of a rocket above water as a function of time $t$. The parabola opens downward, has v

1. **Problem:** Write each number as a product of prime numbers. 2. **Prime factorization:**

1. **State the problem:** Solve the equation $i + 3 = 2$ for $i$. 2. **Isolate the variable:** To find $i$, subtract 3 from both sides of the equation.

1. **Probleemstelling:** We hebben de functie $f(x) = \log_5 x$ en na een verschuiving ontstaat de functie $g(x)$. We moeten het functievorschrift van $g(x)$ bepalen.

1. **Problem statement:** We have a number grid with rows of 9 numbers each. A cross shape covers five numbers: the top left corner number $n$, the top right corner, the center, th

1. **Problem Statement:** We are given the function $$f(x) = \log_2 x$$ and asked to:

1. **State the problem:** We are given the system of equations: