🧮 algebra

1. **State the problem:** We need to find $g(f(5))$ given the functions $f(x) = x^3 - 8x$ and $g(x) = \sqrt{2x}$. 2. **Find $f(5)$:** Substitute $x = 5$ into $f(x)$:

1. **State the problem:** Jordan needs to mix whole wheat flour and bread flour in the ratio $1 : 2$ to get a total of $4 \frac{1}{2}$ cups of flour. 2. **Convert mixed number to i

1. **State the problem:** We want to find the group size $x$ (where $44 \leq x \leq 66$) that maximizes the total income for the ship owners. 2. **Define variables:** Let $x$ be th

1. **State the problem:** We need to determine if the linear equation $$-8 - 8(4n - 3) = -8(-n - 3) + 6$$ has one solution, no solution, or infinitely many solutions (all real numb

1. **State the problem:** Find the equation of the straight line in the form $y = mx + c$ given it crosses the y-axis at $(0, 12)$ and the x-axis at $(-1, 0)$. 2. **Recall the form

1. **State the problem:** Find the equation of the line in the form $y = mx + c$ given it crosses the y-axis at $(0, 25)$ and the x-axis at approximately $(8.33, 0)$. 2. **Recall t

1. **State the problem:** We have two sequences defined as: $$W_0 = 1$$

1. The problem asks to identify the three components of the algebraic expression $$3x - 2$$. 2. The components are:

1. **State the problem:** We have the function $$f(x) = \frac{2x+1}{2x-1}$$ with domain $$x < \frac{1}{2}$$.

1. The problem asks us to find all values of $x$ such that $f(x) = -5$. 2. From the given information, the function $f(x)$ is represented by a blue parabola-like graph.

1. **State the problem:** We need to graph the linear equation $$-4x - 5y = 40$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$, w

1. **State the problem:** We need to graph the linear equation $$3x + 5y = 30$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$:

1. **State the problem:** We need to graph the linear equation $$-5x + 3y = -15$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ w

1. **State the problem:** We need to graph the linear equation $$5x + 6y = 30$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$:

1. **State the problem:** We have 4 schools sending students to a language course. One school sent French and German students in the ratio $1:3$, with $21$ German students. The oth

1. **State the problem:** Find the equation of the line passing through the points $(-1,1)$ and $(-3,-5)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ a

1. **State the problem:** We need to multiply $6.1 \times 10^{8}$ by $8.5 \times 10^{2}$ and express the result in the form $a \times 10^{b}$. 2. **Recall the multiplication rule f

1. **State the problem:** We need to determine which graph correctly represents the equation $$y = 2x - 3$$. 2. **Recall the form and properties:** The equation is in slope-interce

1. **State the problem:** We have two functions $f(x) = x - 8$ and $g(x) = \sqrt{x + 9}$. We need to find the domains of $f$, $g$, $f+g$, $f-g$, $fg$, $ff$, $\frac{f}{g}$, and $\fr

1. **State the problem:** We have a network of one-way roads with flow rates represented by variables $x,y,z,u,v$ and constants. The flow in equals flow out at each intersection. 2

1. **State the problem:** We have a network of one-way roads with flow rates represented by variables $x,y,z,u,v$ in cars per hour. The flow into each intersection equals the flow