🧮 algebra

1. **State the problem:** We are given the quadratic function $$y = x^2 - 13x + 42$$ and need to analyze it, including finding its roots and graph features. 2. **Formula and rules:

1. **State the problem:** Find the factors of 81. 2. **Definition:** Factors of a number are integers that divide the number exactly without leaving a remainder.

1. **State the problem:** Solve for $g$ in the equation $$-3(g - 12.8) = -19.8$$. 2. **Use the distributive property:** Multiply $-3$ by each term inside the parentheses:

1. Solve the inequality $5 + 13 < 11$. Step 1: Combine like terms on the left side: $5 + 13 = 18$.

1. **State the problem:** Solve for $v$ in the equation $$-3v + -5.13 = -1.92$$. 2. **Rewrite the equation:** The equation can be written as $$-3v - 5.13 = -1.92$$.

1. **State the problem:** Solve for $s$ in the equation $$4s - (-10) = 18$$. 2. **Rewrite the equation:** Note that subtracting a negative is the same as adding a positive, so $$4s

1. **State the problem:** Solve the linear equation $$2z - 4.7 = -1.7$$ for the variable $z$. 2. **Formula and rules:** To solve for $z$, isolate $z$ on one side of the equation by

1. **State the problem:** Solve the two-step equation $$\frac{y}{-2} + (-3) = -0.1$$ for $y$. 2. **Understand the equation:** The equation has two operations on $y$: division by $-

1. **Problem Statement:** We are given an exponential function of the form $y = c^x$ and need to determine when the function is increasing for $x < 0$. 2. **Recall the behavior of

1. **State the problem:** We need to create a table of values for the function $$y=\left(\frac{2}{5}\right)^x$$ and understand its behavior. 2. **Formula and explanation:** The fun

1. **State the problem:** We need to sketch the function $$y=\left(\frac{3}{4}\right)^x$$ using a table of values.

1. **State the problem:** We have four expressions: $\frac{1}{x}$, $2x^4$, $\frac{x}{4}$, and $\sqrt{x}$. We want to find which inequality comparing two of these expressions is fal

1. The problem is to graph the six linear equations given: $$y = -x + 9$$

1. **Problem Statement:** We are given four expressions: $z^2$, $\sqrt{5}z$, $\frac{z}{4}$, and $\frac{1}{z}$. We need to determine which inequality comparing two of these expressi

1. **State the problem:** We have four expressions: $5z^3$, $\frac{3}{z}$, $\sqrt{z}$, and $\frac{z}{5}$. We want to find which inequality comparing two of these expressions is tru

1. The problem asks to find the value of $D$ in the given equation. However, the equation itself was not provided in your message. 2. To solve for $D$, we need the full equation or

1. The problem is to find the square root of 145. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find the square root of 330. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find the square root of 220. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find the square root of 38. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** We need to calculate $$\frac{1.2 \times 10^{15}}{3 \times 10^{9}}$$ and express the answer in standard form. 2. **Recall the rule for division of numbers