🧮 algebra

1. **State the problem:** We need to solve the system of equations using substitution: $$y = 3x + 5$$

1. **State the problem:** Determine the symmetry of the graph of the equation $$y = x^2 + 6$$ without graphing. 2. **Recall symmetry rules:**

1. **State the problem:** We need to find the equation of a line passing through the point $(5, -4)$ and perpendicular to the line $y = \frac{1}{5} x + 4$.

1. **State the problem:** We need to determine if the function $$f(x) = x^5 + x$$ is even, odd, or neither, and then identify the symmetry of its graph. 2. **Recall definitions:**

1. **State the problem:** We are given the function $f(x) = x + 14$ and asked to find its inverse function $f^{-1}(x)$. 2. **Find the inverse function:**

1. **State the problem:** We have a list $S = \{1, 2, x, x+1, x+1, 15\}$ with $2 \leq x \leq 14$. The mean of $S$ is one more than the median of $S$. We need to find the value of $

1. **State the problem:** We need to find which expressions are equivalent to $$4(-4z - 6) + 4z$$. 2. **Simplify the original expression:**

1. **State the problem:** We need to find which expressions are equivalent to $$2(7m + 7) + 9$$. 2. **Start by simplifying the original expression:**

1. **State the problem:** We want to find how many minutes it takes to download a $16$-megabyte song at a speed of $56$ kilobits per second, given that $1$ megabyte equals $8000$ k

1. **State the problem:** Expand and simplify the expression $$(t - 2)(t + 5)(t - 4)$$. 2. **Use the distributive property (FOIL) step-by-step:** First, multiply the first two bino

1. **State the problem:** Find the slope of the line passing through points $(-6, -9)$ and $(6, -7)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$

1. **State the problem:** Find the slope of the line passing through the points $(-2, -10)$ and $(10, 0)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y

1. **Stating the problem:** We are given four fundamental fraction operations and equivalences involving fractions $\frac{a}{b}$ and $\frac{c}{d}$. 2. **Addition of fractions:** Th

1. **State the problem:** Kamilah picks a total of $16$ vegetables, which are radishes and carrots. The number of radishes is $3$ times the number of carrots. 2. **Define variables

1. **Problem:** Identify local minima and maxima, absolute extrema of $f$ from the graph. 2. **Given:** Graph starts near $(-6, -3)$, local minimum near $(-4, -5)$, local maximum n

1. **State the problem:** Kai picks a total of $9$ vegetables consisting of green peppers and tomatoes. The number of green peppers is $2$ times the number of tomatoes.

1. **State the problem:** We are given two sequences: \(I = 0, 3, 6, x, 8, 12\) and \(r = 5, 8, 12, 17, 24, y\). We need to find the arithmetic rule for each sequence and then find

1. **State the problem:** We need to find the focus and directrix of the parabola given by the equation $$(x - 5)^2 = 8(y - 1)$$. 2. **Identify the form:** This equation is in the

1. **State the problem:** We need to find the midpoint of the interval $40 < x \leq 50$. 2. **Recall the formula for midpoint:** The midpoint $M$ of an interval $[a, b]$ is given b

1. **State the problem:** Find the vertex of the quadratic function $$p(x) = (x + 2)^2 - 5$$. 2. **Recall the vertex form of a quadratic:** A quadratic function in vertex form is $

1. **State the problem:** Find the x-intercepts of the function $$g(x) = -2|x + 1| + 4$$. The x-intercepts occur where $$g(x) = 0$$. 2. **Set the function equal to zero:**