🧮 algebra

1. The problem states that the nth term of a sequence is given by the formula $T(n) = 8n + 9$. 2. We are asked to find the 5th term of this sequence, which means we need to find $T

1. **State the problem:** Find the first three terms of the sequence defined by the formula $a_n = 20 - 3n$. 2. **Formula:** The general term of the sequence is given by $a_n = 20

1. **State the problem:** Find the intercepts and extrema of the function $y = x^2 + 1$. 2. **Formula and rules:**

1. **State the problem:** Simplify the expression $$-3y + -y - 7y + -8y + 3y$$. 2. **Combine like terms:** All terms are multiples of $y$, so we add their coefficients.

1. **State the problem:** Simplify the expression $$6t^2 + (-10t^2) + (-4t^2) + (-10t^2) + 8t^2 + (-8t^2)$$. 2. **Combine like terms:** Since all terms are multiples of $t^2$, we c

1. **State the problem:** Two trains start 342 miles apart and travel toward each other. One train travels at 105 mph and the other at 85 mph. We need to find the time $t$ in hours

1. **State the problem:** Two trains leave the station at the same time, one heading east at 95 mph and the other west at 75 mph. We need to find the time $t$ in hours when they ar

1. **State the problem:** Simplify the expression $$\frac{9x^2 - 3x - 2}{2x - 6} \cdot \frac{x - 3}{9x^2 - 4}$$. 2. **Factor all polynomials where possible:**

1. **Problem statement:** Multiply and simplify the expression \(\frac{x^2 + 5x + 6}{4x - 12} \times \frac{x - 3}{x^2 + 2x - 3}\). 2. **Recall the formula and rules:** When multipl

1. The problem is to find the overall average percentage when you have 90% in 3 classes and 65% in 1 class. 2. The formula for the average percentage is:

1. **State the problem:** Jo has a mobile phone plan with a monthly charge of 16.

1. **State the problem:** Solve the equation $2x + 3 = 7$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse oper

1. **State the problem:** You have four classes, each worth 25% of your overall grade. You scored 85% in three classes and 50% in one class. We need to find your overall mark. 2. *

1. **State the problem:** Solve the rational equation $$\frac{1}{x} - \frac{x}{x-1} = -\frac{3x}{x-1}$$ for all values of $x$. 2. **Identify the common denominator:** The denominat

1. **State the problem:** Simplify fully the expression $\sqrt{3} (\sqrt{27} + \sqrt{3})$. 2. **Recall the properties of square roots:**

1. Stating the problem: Calculate the values of the following expressions using logarithm properties. 2. Recall important logarithm properties:

1. **State the problem:** We need to classify each system of linear equations (A, B, C) as consistent independent, consistent dependent, or inconsistent, and find the solution if i

1. **State the problem:** We are given three systems of linear equations (System A, B, and C) and need to classify each as consistent dependent, consistent independent, or inconsis

1. **State the problem:** Simplify the expression $5\sqrt{8} + \sqrt{18}$. 2. **Recall the rule:** To simplify expressions with square roots, factor the radicand (the number inside

1. **State the problem:** Classify each system of linear equations as consistent dependent, consistent independent, or inconsistent, and find the solution if it exists. ---

1. The problem involves simplifying algebraic expressions given in rectangular boxes. 2. We start with the first expression: $9 - f + 5$.