🧮 algebra

1. **State the problem:** Solve the equation $e^{3x} = 12$ for $x$. 2. **Recall the formula and rules:** To solve equations involving exponentials, we use the natural logarithm $\l

1. The problem is to analyze the function $h(t) = -4.9t^2 + 30t + 55$, which models the height of an object over time $t$. 2. This is a quadratic function in the form $h(t) = at^2

1. **Problem Statement:** Evaluate expressions involving rational exponents and radicals such as $16^{3/4}$, $16^{-3/4}$, $8^{2/3}$, etc. 2. **Formula and Rules:**

1. **Problem:** Given functions $f(x) = 3x - 5$ and $g(x) = 7x + 2$, find each combined function and state any domain restrictions. 2. **Formula and rules:**

1. **State the problem:** Find the quadratic equation in factored form given two x-intercepts and a point on the graph. 2. **Recall the formula:** A quadratic with roots $r_1$ and

1. **State the problem:** Expand the function $y=2(x-3)^2+6$ to general form and find its range. 2. **Recall the formula:** The general form of a quadratic function is $y=ax^2+bx+c

1. **State the problem:** Write a quadratic function in factored form with x-intercepts $\left(-\frac{1}{4}, 0\right)$ and $(8, 0)$ that passes through the point $(0, 2)$. 2. **Rec

1. **State the problem:** A sea otter's position changes by $-73.5$ feet in 3 minutes. We need to find the average change in position per minute. 2. **Formula:** Average change per

1. The problem is to determine whether a given solution is extraneous or not. 2. An extraneous solution is a solution that emerges from the process of solving the equation but does

1. **State the problem:** Solve the equation $$\frac{4}{x} + 1 = \frac{5}{3}$$ for $x$. 2. **Isolate the fraction:** Subtract 1 from both sides:

1. **State the problem:** Vincent, Nari, and Lizbeth play a carnival game. Vincent's score is $-35$ points. Nari's score is $\frac{3}{7}$ of Vincent's score.

1. **State the problem:** Vincent, Nari, and Lizbeth play a carnival game. Vincent's score is $-35$ points. Nari's score is $\frac{3}{7}$ of Vincent's score. Lizbeth scores $\frac{

1. **State the problem:** We are given the number of crimes committed in 2011 and the percentage increase from 2011 to 2012 for three places. We need to find the number of crimes c

1. **State the problem:** A video has $4 \times 10^8$ views in total, and 3% of these views are from Italy. We need to find how many views come from Italy and express the answer in

1. Il problema chiede di risolvere l'espressione $$\left[\left(\frac{3}{4} - \frac{1}{2}\right)^2 \left(\frac{1}{2} - \frac{1}{4}\right)(-3)^2 - 1\right] + (-3)2 - 1$$. 2. Calcolia

1. **State the problem:** Calculate the value of $$4^2 - \left(\frac{2}{3}\right)^2 + \left(-\frac{3}{2}\right)^2 \times \frac{1}{3}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $x[x^2 + 3]$. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

1. The problem asks us to analyze the graph of Jason's height above the ground during a Ferris wheel ride over time and determine which statements about the function are correct. 2

1. **State the problem:** Factorise fully the quadratic expression $$6y^2 - 5y - 4$$. 2. **Recall the factoring formula:** For a quadratic $$ay^2 + by + c$$, we look for two number

1. **State the problem:** We are given a piecewise linear function with two segments intersecting at $x=0$. The left segment goes from $(-2,3)$ to $(0,-4)$ and the right segment go

1. **State the problem:** We need to find the equation that represents the water level $w$ after $d$ days based on the given data points: $(3, 96)$, $(6, 90)$, $(9, 84)$, $(12, 78)