🧮 algebra

1. **State the problem:** We need to select all the squares from the given list of expressions and then order those squares from least to greatest. 2. **Identify squares:** A squar

1. **State the problem:** We have a polynomial $Q(x) = x^3 + cx^2 + dx + 12$.

1. **State the problem:** We have a polynomial $$Q(x) = x^3 + cx^2 + dx + 12$$.

1. The problem is to identify or work with the variables $a$, $b$, or $c$ as given. 2. Since the prompt is ambiguous, let's consider these as variables commonly used in algebra or

1. **State the problem:** We need to find the lowest integer value of $p$ such that the inequality $8p + 6 > 30 - 2p$ holds. 2. **Write the inequality:**

1. **State the problem:** Determine whether the function $f$ is even, odd, or neither based on its graph. 2. **Recall definitions:**

1. **Problem Statement:** We are given the function $$f(x) = k^2$$ and asked to find $$f(2)$$. 2. **Understanding the function:** The function is defined as $$f(x) = k^2$$, but the

1. **Problem 1:** Simplify and analyze $$x^{-\frac{5}{2}} + \frac{1}{x} + 5$$. 2. **Problem 2:** Simplify $$\left(x^{\frac{1}{2}} - 1\right)^2$$.

1. **State the problem:** We have a triangle with angles $x$, $y$, and $75^\circ$. We know that $x > 2y$ and want to find the possible values of $x$. 2. **Recall the triangle angle

1. **State the problem:** Solve the inequality $$x^2 - 10x + 24 \ge 0$$. 2. **Identify the type of problem:** This is a quadratic inequality.

1. **State the problem:** We want to express $\frac{1}{\sqrt[3]{13}}$ in the form $13^t$ and find the value of $t$. 2. **Recall the rules:** The cube root of 13 can be written as a

1. **State the problem:** Simplify the fraction $\frac{124}{5}$. 2. **Formula and rules:** To simplify a fraction, divide the numerator by the denominator to see if it can be expre

1. **State the problem:** Solve the equation $$\frac{14}{x^2-4} - \frac{12}{x+2} = \frac{6}{2-x}$$. 2. **Rewrite and analyze:** Note that $$x^2-4 = (x-2)(x+2)$$ and $$2-x = -(x-2)$

1. **State the problem:** We need to find the x-intercept and y-intercept of the given line. 2. **Recall definitions:**

1. **State the problem:** We need to find the x-intercept and y-intercept of a line given its graph. 2. **Recall definitions:**

1. **State the problem:** We need to find the x-intercept and y-intercept of the line shown in the graph. 2. **Recall definitions:**

1. **Problem Statement:** Find the x- and y-intercepts of the line given that it passes through the points where it crosses the axes. 2. **Recall:**

1. The problem asks us to graph the function $f(x) = 0$ by plotting points to determine the shape of the graph. 2. The function $f(x) = 0$ means that for every value of $x$, the ou

1. **State the problem:** Simplify the expression $$12x^3 - 12x^2$$. 2. **Identify common factors:** Both terms have a common factor of $$12x^2$$.

1. **State the problem:** Simplify or factor the expression $$35x^8 + 7x^2 - 14x$$. 2. **Identify the greatest common factor (GCF):** The coefficients are 35, 7, and -14. The GCF o

1. **State the problem:** We are given the linear equation $$1.5x + 4.5y = 18$$ and asked to find where the graph intersects the y-axis. 2. **Recall that the y-intercept occurs whe