🧮 algebra

1. Simplify each expression step-by-step. **a. Simplify** $\sqrt{36x^4}$

1. **State the problem:** We need to match each exponential function to its corresponding graph based on their behavior and points. 2. **Recall the properties of exponential functi

1. **Problem 1:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula:** To isolate $x$, subtract 2 from both sides: $$x + 2 - 2 = 4 - 2$$

1. **State the problem:** Ling is driving at a constant speed of 55 miles per hour. We need to find how long it will take him to drive 275 miles. 2. **Formula used:** The relations

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** Solve the equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one sid

1. **State the problem:** We are given a table of miles and hours and need to find the unit rate in miles per hour. 2. **Formula:** The unit rate (miles per hour) is calculated by

1. **State the problem:** Solve $a^3+a^2=36$ for $a$. 2. **Use a standard factoring idea:** First move everything to one side:

1. **State the problem:** Solve the linear equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $$\frac{4b}{8}$$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common divi

1. **State the problem:** Solve the equation $$(3x+1)^2 - (2x-5)^2 = 504$$ for $x$. 2. **Recall the difference of squares formula:**

1. **State the problem:** We analyze the monthly charges of three telecom companies (Any Talk, Easy Talk, Talk More) based on their usage time (minutes) from the graph. 2. **Initia

1. The problem is to identify the values of $a$, $b$, and $c$ in the quadratic equation $ax^2 + bx + c$ for each colored parabola based on their graph shapes and vertex positions.

1. The problem is to understand how the coefficients $a$, $b$, and $c$ in the quadratic equation $$ax^2 + bx + c$$ affect the shape and position of the parabola on the graph. 2. Th

1. **State the problem:** We are given four quadratic equations and need to find their horizontal intercepts and the x-coordinate of their vertex without graphing. 2. **Recall the

1. **Problem 12:** Given a line graph with a positive slope, how does changing the slope to 2 affect the graph? 2. The slope of a line determines its steepness and direction. A pos

1. **State the problem:** We need to fill in the table for the quadratic functions $y = x^2$, $y = 2x^2$, $y = \frac{1}{2}x^2$, and $y = -2x^2$ at given values of $x$. 2. **Recall

1. **State the problem:** John hired a car for 8 days and drove 850 kilometres. We need to find the total cost of hiring the car.

1. The problem is to simplify the expressions involving powers of 8 and 1. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$ where $a$ is the

1. The problem asks: When multiplying powers with the same base, you ________ the exponents. 2. The rule for multiplying powers with the same base is: