🧮 algebra

1. The problem asks which graph represents a linear function increasing at a constant rate. 2. A linear function increasing at a constant rate has a positive slope and is a straigh

1. **State the problem:** Translate and solve the equation "4 less than 5 times a number equals 16". 2. **Write the algebraic equation:** Let the number be $x$. The phrase "5 times

1. **State the problem:** Zorna weighs 92 pounds, which is 6 pounds more than half of her father's weight. We want to find her father's weight. 2. **Set up the equation:** Let $x$

1. **State the problem:** Solve the equation $x - 10 + 7x = 15 + 3x$ for $x$. 2. **Combine like terms on each side:**

1. **State the problem:** We are given the sequence formula $a_n = 20n - 30$ and asked to find the term $a_{31}$. 2. **Formula used:** The formula for the $n$-th term of the sequen

1. **State the problem:** Find the maximum height of the rocket given by the height function $$h(t) = -16t^2 + 96t + 112$$ where $t$ is time in seconds. 2. **Formula and rules:** T

1. **State the problem:** We have an arithmetic sequence representing the number of toy rockets produced each hour for 8 hours. The first hour's production is 40 rockets, and the s

1. We are asked to find the equations of 5 parabolas in the form $$f(x) = a(x-p)^2 + q$$ where $$a$$ is one of $$\frac{10}{9}, -2, -\frac{1}{2}, \frac{1}{4}$$. 2. The form $$f(x) =

1. **State the problem:** Simplify and solve the expression $$\frac{(4x - 7)^2 \cdot (x - 3)(x - 2y)0}{x - 2y4}$$ given the vertical fraction and terms. 2. **Analyze the expression

1. **State the problem:** Determine if the y-intercept of Function A is greater than the y-intercept of Function B. 2. **Recall y-intercepts:** From previous calculations, Function

1. **State the problem:** We are given two functions, Function A (a linear function graphed) and Function B (given as a table of points). We need to determine which statement about

1. **Stel het probleem vast:** We hebben drie tweedegraadsfuncties (parabolen) met gegeven vertex (top) en oriëntatie (omhoog of omlaag). We moeten voor elke functie het domein, be

1. **State the problems:** - Problem 28: Simplify $$\frac{(2x^{9})^{3}(x^{2}y)^{-2}}{x^{3}y^{0}}$$

1. **State the problem:** Solve the quadratic equation $$x^2 - 8x = -15$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the equation $$\frac{1}{1 - x} + \frac{1}{1 + \sqrt{x}} = \frac{1}{1 - \sqrt{x}}$$ for $x$. 2. **Identify the domain:** Since $\sqrt{x}$ appears, $x

1. **Stating the problem:** We are given a piecewise linear graph with two line segments. The first segment has an open circle at $(-7,5)$ and passes through $(-10,-9)$. The second

1. Let's start by stating the problem: we want to find the value of $X$ such that $X=3$. 2. The equation is already given as $X=3$, which means $X$ is equal to 3.

1. **State the problem:** Solve the quadratic equation $$5x^2 - 13x - 6 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $

1. **State the problem:** Solve the equation $$\sqrt{2x + 5} + 2\sqrt{x + 6} = 5$$ for $x$. 2. **Isolate one of the square root terms:** Let's isolate $$\sqrt{2x + 5}$$:

1. **State the problem:** We need to find which quadratic function has solutions $x=8$ and $x=-5$. 2. **Recall the factored form of a quadratic:** If the roots are $r_1$ and $r_2$,

1. The problem is to simplify the expression $$(\sqrt{12} + \sqrt{z})(\sqrt{12} - \sqrt{z})$$ assuming all variables are positive. 2. This expression is a product of conjugates, wh