🧮 algebra

1. **State the problem:** Find the x-intercepts of the function $$g(x) = -2|x + 1| + 4$$. The x-intercepts occur where $$g(x) = 0$$. 2. **Set the function equal to zero:**

1. **Problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equation is in the

1. **Problem Statement:** We have three pyramids of boxes with fractions in the bottom and middle rows, and empty boxes in the middle and top rows. The goal is to find the missing

1. **State the problem:** We want to find out how many years it will take to complete 4000 hours of watch time if you generate 3 hours per day.

1. **State the problem:** YouTube requires 4000 hours of watch time to be eligible for ads. If you generate 3 hours of watch time per day, we need to find out how many days it will

1. **State the problem:** Find the slope of the line passing through the points $(0,0)$ and $(10,-7)$. 2. **Formula for slope:** The slope $m$ of a line passing through points $(x_

1. **State the problem:** Find the highest common factor (HCF) of $18$ and $9$. 2. **Formula and rules:** The HCF of two numbers is the greatest number that divides both numbers ex

1. **State the problem:** We need to find the time in minutes after midday when trains on both routes will stop at the station simultaneously again. 2. **Identify the key informati

1. The problem gives three functions: $$g(x)=3^{x-2}$$, $$h(x)=2\cdot 3^x$$, and $$i(x)=2^{x-3}-2$$. We are asked to understand or analyze these exponential functions. 2. Exponenti

1. **Stating the problem:** Madhna purchased a toy cycle for $1260$ and sold it for $1200$. We need to find her loss and the loss percentage.

1. Vamos entender o problema: temos que $\text{black mamba} = 2$ e $\text{black mamba} - \text{white mamba} = -5$. Queremos encontrar o valor de $\text{grey mamba}^{\text{black mam

1. The problem is to understand the expression $\binom{\pi}{}$, which appears to be an incomplete binomial coefficient. 2. The binomial coefficient $\binom{n}{k}$ is defined for in

1. The problem is to understand the expression $\frac{ }{ }$, which represents a fraction with an empty numerator and denominator. 2. A fraction is generally written as $\frac{a}{b

1. El problema es encontrar el valor de $x$ dado que no se proporciona ninguna ecuaci\u00f3n o contexto adicional. 2. Para resolver para $x$, necesitamos una ecuaci\u00f3n o una ex

1. **State the problem:** We need to find how many digits the number $12^{10} \times 6^{-8}$ has. 2. **Recall the formula for the number of digits:** The number of digits of a posi

1. **Planteamiento del problema:** Queremos encontrar el dominio y el rango de la función $$F(x)=\frac{x-3}{x+2}$$.

1. **Problem:** A car travels $180$ miles in $3$ hours. Find the unit rate in miles per hour. 2. **Formula:** Unit rate = $\frac{\text{total distance}}{\text{total time}}$

1. The problem is to calculate $2^2$. 2. The expression $a^b$ means $a$ multiplied by itself $b$ times.

1. **Stating the problem:** We want to understand what a parametric equation is. 2. **Definition:** A parametric equation expresses the coordinates of the points that make up a geo

1. **State the problem:** We need to identify which equation is already set up for direct use of the zero-factor property and then solve it. 2. **Recall the zero-factor property:**

1. We are given a list of equations involving $x$ and need to solve the first one: $$x^2 = 25$$ 2. The formula to solve equations of the form $$x^2 = a$$ is $$x = \pm \sqrt{a}$$, w