🧮 algebra

1. **State the problem:** We are given a table showing Avery's earnings $y$ for working $x$ hours. We need to find the rate of change, which represents how much Avery earns per hou

1. **State the problem:** Given the equation $$a \cos^{12} A + b \cos^{8} A + c \cos^{6} A - 1 = 0$$ and the condition $$\sin A + \sin^2 A = 1,$$ find the value of $$\frac{b+c}{a+b

1. The problem states the ratio of red cars to black cars is 79 : 51. 2. We want to express this ratio in the form $n : 1$, where $n$ is a decimal number.

1. **State the problem:** Solve for $m$ in the equation $$3(2m + 5) = 4m + 29$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. Problem: Add $\frac{5}{8} + \frac{1}{4}$ and simplify. Formula: To add fractions, use $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \n

1. The problem is to understand what a logarithm is and how to work with it. 2. A logarithm answers the question: to what power must we raise a base number to get another number? T

1. **State the problem:** We have a rectangle and a square with the same perimeter. The rectangle has length $x+10$ cm and height 4 cm. The square has side length $x+4$ cm. We need

1. The problem is to simplify the equation given by the user. 2. Since no specific equation was provided, simplification generally involves combining like terms, factoring, expandi

1. Problem 10: Calculate the highest temperature recorded at Scott Base. The problem states the highest temperature recorded is 63.8 °C.

1. **State the problem:** We want to simplify the expression $$(A+B+C)(A+B+C)(A+B+C)$$ using algebra. 2. **Formula and rules:** This expression is the cube of a trinomial, written

1. **State the problem:** We are given the function $f(x) = x^3 - 3x^2 - 9x - 5$ and need to find the $x$-intercepts and $y$-intercept. 2. **Recall definitions:**

1. **State the problem:** Simplify each rational expression and state its domain. 2. **Recall:** The domain excludes values making the denominator zero.

1. **State the problem:** Simplify the expression $$(ab^2 c)^3 (2a^2)^2$$ and compare it with the expression $$2a^5 (b^3 c^2)^2$$ to identify which option (A, B, C, or D) matches.

1. **State the problem:** We have a piecewise function defined as $$g(x) = \begin{cases} x & \text{if } x > 0 \\ -x + 1 & \text{if } x \leq 0 \end{cases}$$. We want to understand a

1. The problem is to find the equation of the line passing through the points (6, -4) and (8, 10). 2. We use the point-slope form of a line equation: $$y - y_1 = m(x - x_1)$$ where

1. **State the problem:** Simplify the expression $\frac{10 \times 256}{5 \times 256}$. 2. **Formula and rules:** When dividing fractions or products, common factors in numerator a

1. Exercise 1: Use the vertical line test to determine if each graph represents a function. 2. Formula and rule: The vertical line test says: if any vertical line intersects the gr

1. **State the problem:** Simplify the expression $\frac{10 \times 256}{5 \times 256}$. 2. **Recall the rule:** When the same non-zero factor appears in both numerator and denomina

1. **Exercise (1): Use vertical line test to verify if each graph is a function.** - The vertical line test states that if any vertical line intersects the graph more than once, th

1. The problem is to find the sum of a series or sequence. 2. To solve a sum, we first need to identify the type of series: arithmetic, geometric, or other.

1) Matrix operations and determinants 1. State the problem: Given matrices