🧮 algebra

1. The problem asks to identify the graph of the inequality $y < -x - 3$ in the standard $(x, y)$ coordinate plane. 2. The boundary line for this inequality is $y = -x - 3$. This i

1. **State the problem:** We are given the vertices and foci of a conic section and need to identify and analyze it.

1. **State the problem:** Simplify the expression $$\left(\frac{125}{64}\right)^{\frac{2}{3}}$$ and find which of the given options matches the result. 2. **Recall the exponent rul

1. **State the problem:** A town has a population of 8,000 and grows at 2% every year. We want to find the population after 14 years, rounded to the nearest whole number. 2. **Form

1. **State the problem:** Graph the inequality $x \geq -3 \cdot 2$ for three different sets: integers ($\mathbb{Z}$), natural numbers ($\mathbb{N}$), and real numbers ($\mathbb{R}$

1. **State the problem:** Solve the simultaneous equations: $$x + 2y = 1$$

1. **State the problem:** We have a budget of $9600 for a product launch event. Various expenses reduce this budget, and we want to determine if the event cost was more than $200 u

1. **State the problem:** We need to find the greatest and smallest expenses from the given budget decreases for a product launch event. 2. **List the expenses:** Venue (-2400), Ca

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