🧮 algebra

1. **Problem Statement:** We are given that $q$ is inversely proportional to $p^3$, and when $p=4$, $q=4$. We want to find the relationship between $q$ and $p$, and use it to find

1. **State the problem:** Simplify the expression $$\frac{6}{x^2 - 3x - 28} - \frac{2}{2x^2 + 3x - 20}$$ to the form $$\frac{2(ax - b)}{(x - c)(x + d)(2x - 5)}$$ where $a, b, c, d$

1. **State the problem:** We want to find the average speed driving to Trigville and the average speed driving home given the distances and speeds. 2. **Set up the rational equatio

1. **State the problem:** Simplify or factor the expression $A^3 - A^2 - 8A + 8$. 2. **Recall the factoring formula:** For cubic polynomials, try factoring by grouping or use the f

1. **State the problem:** Factor the cubic polynomial $x^3 + x^2 - x - 1$. 2. **Recall the factoring method:** For cubic polynomials, try factoring by grouping or use the Rational

1. Diketahui fungsi $f(x) = 3x + 4$ dan $g(x) = 5 - 2x$. Kita diminta mencari nilai dari komposisi fungsi $(f \circ g \circ f)(x)$. 2. Komposisi fungsi $(f \circ g \circ f)(x)$ ber

1. **Problem:** Solve the simultaneous equations: y + x = 3

1. **Problem:** Define a complex number. A complex number is a number of the form $z = x + iy$, where $x$ and $y$ are real numbers and $i$ is the imaginary unit with the property $

1. The problem is to estimate the square root of 0.036 using a number line. 2. Recall that the square root of a number $x$ is a number $y$ such that $y^2 = x$.

1. The problem is to estimate the square root of 0.036. 2. Recall the formula for square root: if $x = a^2$, then $\sqrt{x} = a$.

1. Let's create practice problems based on the topics you shared: Squares and Square Roots, Non-Perfect Squares, and related concepts. 2. Problem 1: Find the square of 12.

1. **State the problem:** We are given a number trick with the following steps: - Choose a number $n$

1. The problem is to understand perfect and non-perfect squares. 2. A perfect square is a number that can be expressed as $n^2$ where $n$ is an integer. For example, $1, 4, 9, 16,

1. **Problem Statement:** Use inductive reasoning to make a conjecture about the addition of an even integer and an odd integer, then prove it deductively. 2. **Inductive Reasoning

1. Stating the problem: Solve the equation $$\sqrt{3}a - 5 + \sqrt{2}a + 3 + 1 = 0$$ for $a$. 2. Combine like terms: Group the terms involving $a$ and the constants separately.

1. **State the problem:** Find the maximum value of the function $$g(x) = -\left|(-x)^2 - l^2 + ml + z\right|$$ for real numbers $l$, $m$, and $z$. 2. **Rewrite the function:** Not

1. The problem is to solve question 12 in a shorter way. Since the original question is not provided, let's assume it involves solving a quadratic equation for demonstration. 2. Th

1. **Problem statement:** Solve the simultaneous equations. Since the user did not provide specific equations, let's consider a general example: $$\begin{cases} ax + by = c \\ dx +

1. **Problem:** Solve for $x$ and find the restricted values in the equation $$52x - 16(x-1) = 45(3x-2).$$ 2. **Formula and rules:** Use distributive property and combine like term

1. **State the problem:** Given the function $f(x) = \frac{x(x+1)(2x+1)}{6}$, find the value of $x$ such that $f(x) = 384$. 2. **Write the equation:**

1. **State the problem:** We are given the function $$f(x) = \frac{x(x+1)(2x+1)}{6}$$ and asked to evaluate it at $$x=100$$. 2. **Formula and explanation:** This function is a know