🧮 algebra

1. **State the problem:** We need to find a function $f(n)$ that models the geometric sequence given by the terms $9, 3, 1, \frac{1}{3}, \frac{1}{9}$ for $n=1,2,3,4,5$ respectively

1. **State the problem:** Determine if the sequence $2, 12, 72, 432, \ldots$ is geometric and if so, find the common ratio. 2. **Recall the definition:** A sequence is geometric if

1. **State the problem:** We have a 3x3 magic square where every row, column, and diagonal sums to the same total. We need to find the values of $A$ and $B$ using the numbers provi

1. **State the problem:** Find the difference between the highest and lowest values in the list: $-4.3, -1.54, -6.819, -9.04, -12.3, -11$. 2. **Identify the highest and lowest valu

1. The problem is to expand the expression $ (a+b)^2 $. 2. The formula for the square of a binomial is:

1. **State the problem:** A painter uses 1.2 liters of paint to cover 1 square meter of wall. We need to find how many square meters he can cover with 12 liters of paint. 2. **Form

1. **State the problem:** An employee earns 175 for 15 hours of work at a constant hourly rate. We need to find how much the employee will earn in 18 hours. 2. **Formula:** Earning

1. **State the problem:** Find the values of $c$ such that the angle between vectors $\mathbf{u} = (1,2,1)$ and $\mathbf{v} = (1,0,c)$ is $60^\circ$. 2. **Formula used:** The cosin

1. **State the problem:** We have two types of pumps, large and small, filling a swimming pool. Two large and one small pump fill the pool in 4 hours. One large and three small pum

1. The problem asks to identify which statements about rational and irrational numbers are true. 2. Recall definitions:

1. **State the problem:** Solve the inequality $x + 12 > 17$ for $x$. 2. **Write the inequality:**

1. **Problem statement:** 6. b) If the school only has one pump, how long will it take to fill the pool? Given answer: 9.6 hrs.

1. The problem asks to determine the coordinates of the vertex of the parabola shown on the graph. 2. The vertex of a parabola given by the equation $y = ax^2 + bx + c$ is found us

1. **Problem Statement:** Determine the coordinates of the vertex of the parabola from the graph. 2. **Understanding the Vertex:** The vertex of a parabola in vertex form is given

1. **State the problem:** Solve the equation $w(w+4) = -8$ using the quadratic formula and express the solution set in exact simplest form. 2. **Rewrite the equation:** Expand and

1. **State the problem:** Solve the quadratic equation using the quadratic formula and express the solution set in exact simplest form. 2. **Recall the quadratic formula:** For a q

1. **State the problem:** Solve the equation $2(w+4) = -8$ for $w$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses.

1. **State the problem:** Solve for $x$ in the equation $$10^3 \cdot 10^x \cdot 10^2 = 10^5.$$\n\n2. **Recall the rule for multiplying powers with the same base:** When multiplying

1. **State the problem:** Solve the quadratic equation $$-2t^2 - 10t + 5 = 0$$ by completing the square and applying the square root property. 2. **Rewrite the equation:** First, d

1. **Problem statement:** We have a situation where $d$ represents the number of days of driving, and the expression $14 - 0.6d$ is given.

1. **State the problem:** Simplify the expression $6 - 2x + 5 + 4x$ and identify the error in Tyler's work. 2. **Tyler's error:** Tyler incorrectly grouped terms as $(6 - 2)x + (5