🧮 algebra

1. The problem asks us to determine which statement supports the claim that the function $f(x) = x^3 + x$ is an odd function and not an even function. 2. Recall the definitions:

1. **State the problem:** We have a linear function $P(t)$ modeling the price of a used car based on its age $t$ in years. Given $P(4) = 7300$ and $P(7) = 5500$, we want to find ho

1. The problem asks us to determine over which intervals the function $f$ is increasing based on its graph. 2. A function is increasing on an interval if, as $x$ moves from left to

1. **State the problem:** Simplify the expression $-\frac{1}{2}[x - 2(x-1)]$. 2. **Apply the distributive property inside the brackets:**

1. **State the problem:** Solve the equation $4^{x+2} + 4 = 2$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $4^x = 2 \cdot \sqrt{2}$ for $x$. 2. **Rewrite the bases:** Note that $4 = 2^2$ and $\sqrt{2} = 2^{\frac{1}{2}}$.

1. **State the problem:** We need to find the sum of the two polynomials $5x^2 + 3x - 7$ and $12x + 12$. 2. **Formula used:** To add polynomials, add the coefficients of like terms

1. **State the problem:** Find the zeros of the function $$f(x) = x^2 + 2x - 24$$. 2. **Recall the formula:** To find zeros, solve $$f(x) = 0$$, so:

1. **State the problem:** Simplify the expression $$\frac{\sqrt{2^3 \cdot 3 \cdot a^3 \cdot b^5}}{\sqrt[3]{2^3 \cdot 3 \cdot a^3 \cdot b^5}}$$. 2. **Recall the formulas:**

1. The problem is to find the explicit formula for the geometric sequence given: 12, 6, 3, 1.5, 0.75, ... 2. The general formula for a geometric sequence is:

1. The problem asks for the explicit formula for the number of seats in the nth row of the auditorium, given the sequence: 26, 32, 38, 44, 50, ... 2. This is an arithmetic sequence

1. **State the problem:** We need to find two points with integer coordinates on the graph of the function $$f(x) = -4^{x+5} + 6$$ and identify the asymptote. 2. **Identify the asy

1. **State the problem:** We have two sequences describing the number of stuffed frogs Janet and Patrick collect each month. We need to determine if each sequence is arithmetic or

1. **Stating the problem:** We have a point $P$ moving in the $Oxy$-plane with parametric equations: $$x(t) = \frac{1}{2} \sin(t), \quad y(t) = \sin\left(t + \frac{1}{3} \pi\right)

1. The problem asks for the common ratio $r$ of the geometric sequence $(42, 21, 10.5, 5.25, \ldots)$.\n\n2. The common ratio $r$ in a geometric sequence is found by dividing any t

1. The problem asks to identify two points on the graph of the function $f(x) = 2 \cdot 3^{x-2} - 2$ and determine if the asymptote is vertical or horizontal. 2. The function is an

1. **State the problem:** We need to classify each given sequence as either an arithmetic sequence or a geometric sequence. 2. **Recall definitions:**

1. The problem asks to find two points with integer coordinates on the graph of the function $f(x) = 3 \left(\frac{1}{2}\right)^x - 5$. 2. The function is an exponential decay func

1. **Stating the problem:** We have two sequences: (0, 6, 12, 18, 24, ...) and (1, 6, 36, 216, 1296, ...). We need to identify which is arithmetic, find its common difference, and

1. The problem is to solve the equation or expression given previously (user did not specify, so assuming continuation of a prior problem). 2. Since the user asked to "solve the re

1. The problem asks to match each function with the correct rule describing the sequence. 2. Let's analyze each function: