🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-64a^6} \cdot \sqrt{64a^6}}{-4a^3 - 2a^3}$$. 2. **Simplify the numerator:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-64a^6} \cdot \sqrt{64a^6}}{-4a^3 - 2a^3}$$. 2. **Simplify the numerator:**

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. Stating the problem: Simplify the expression $$\frac{\sqrt{\left(-13 p^{2} q\right)^{2}+\left(-12^{2} p^{4} q^{2}\right)}}{-5 p^{2} q}$$. 2. Simplify inside the square root:

1. The problem is to solve the equation 12. 2. Since 12 is a constant and not an equation, there is no variable to solve for.

1. The problem asks to describe the graph of the equation $y = 88$. 2. This is a horizontal line because the value of $y$ is constant and does not depend on $x$.

1. **Problem statement:** Simplify the expression $$2x^4 (x - 16)(x + 2)$$. 2. **Step 1: Expand the binomials**

1. Solve the system of linear equations: $$7x + \frac{5y}{8} = 26$$

1. **State the problem:** We want to find how many counters (dots) are in the 10th term of the given pattern. 2. **Analyze the pattern:**

1. The problem states that Rob thinks of a number with one decimal place that rounds to 6 when rounded to the nearest whole number. 2. To round to 6, the number must be at least 5.

1. Let's start by stating the problem: understanding quadratics as taught in Year 9 Pearson Maths. 2. A quadratic equation is any equation that can be written in the form $$y = ax^

1. The problem states that the frog's jump is modeled by the function $f(x) = -x^2 + 2x$, and we need to find the maximum height of the jump. 2. This function is a quadratic in the

1. The problem asks for the equation of a line perpendicular to the line given by $p(t) = 3t + 4$ and passing through the point $(3, 1)$. 2. The slope of the line $p(t)$ is the coe

1. The problem asks for the equation of a line passing through the point $(1,4)$ and parallel to the line $y = 2x + 1$. 2. Lines that are parallel have the same slope. The given li

1. **State the problem:** We need to find the value of $x$ for a linear function passing through points $(x, 2)$ and $(-4, 6)$ with slope $m=3$. 2. **Recall the slope formula:** Th

1. **Stating the problem:** We need to discuss the nature of solutions of systems of linear equations, specifically the types: consistent, inconsistent, independent, and dependent.

1. We are given the inverse function $$f^{-1}(x) = \frac{x - 8}{7}$$ and need to find the original function $$f(x)$$. 2. Recall that if $$y = f^{-1}(x)$$, then $$x = f(y)$$. So, we

1. Problem 1: Prove or disprove the inequality $x^3 + y^3 < (x + y)^3$. 2. The student expands $(x + y)^3$ correctly:

1. Problem: You saw a group of sheep with a total of 28 legs and 14 eyes. How many sheep are there? - Each sheep has 4 legs and 2 eyes.

1. The problem is to simplify the expression $3 - 6a - \frac{5}{2a}$. 2. First, identify the terms: $3$ is a constant, $-6a$ is a linear term in $a$, and $-\frac{5}{2a}$ is a ratio

1. Let's start by defining a **sequence**: it is an ordered list of numbers, where each number is called a term. 2. A **series** is the sum of the terms of a sequence.