🧮 algebra

1. **State the problem:** Find the value of $\left(3x^{2}y^{-5}\right)^{3}$. 2. **Recall the exponent rules:** When raising a product to a power, raise each factor to that power:

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **State the problem:** We need to find how many hours it takes for the moisture content to reduce from 42% to 14% if it decreases by 7% per hour. 2. **Formula and explanation:**

1. **State the problem:** We know 752 tickets were sold with the ratio of adult to children tickets as 3:1. We need to find the number of adult and children tickets sold. 2. **Use

1. **State the problem:** Find the left and right x-intercepts, the axis of symmetry, and the vertex of the quadratic function $$y = -(x + 1)(x - 5)$$. 2. **Find the x-intercepts:*

1. **Simplify each expression and leave in fraction and exponent form with positive exponents.** ---

1. **State the problem:** We need to graph the quadratic function $$y = -\frac{1}{2}(x - 3)^2 + 5$$ and understand its shape and key features. 2. **Formula and important rules:** T

1. **State the problem:** We are given the quadratic function $y = -x^2 - 2x + 4$ and need to find the vertex, axis of symmetry, direction the parabola opens, domain, and range. 2.

1. **State the problem:** Find the axis of symmetry, vertex, y-intercept, and x-intercepts of the parabola given by the equation $y = 3x^2 + 12x + 9$. 2. **Axis of symmetry formula

1. The problem asks to identify which inequality corresponds to a graph of a downward-opening parabola with x-intercepts near $x=2$ and $x=4$, vertex near $(3,5)$, and shading belo

1. **Stating the problem:** We want to find a quadratic function $f(x) = ax^2 + bx + c$ that fits the given temperature data over time without using the second difference formula.

1. **State the problem:** We analyze the parabola given by the equation $y = (x + 2)^2 + 3$. 2. **Identify the vertex:** The vertex form of a parabola is $y = a(x - h)^2 + k$, wher

1. **Stating the problem:** We are given a table of water temperatures over time and asked to find a quadratic function $f(x) = ax^2 + bx + c$ that models the temperature, where $x

1. The problem asks to identify the two inequalities that form the system graphed. 2. The graph shows a dashed upward-opening parabola with vertex at (1,0) and a solid decreasing l

1. **Problem statement:** We have a theatre seating arrangement where row 1 has 28 seats, and each subsequent row has one more seat than the previous row.

1. **State the problem:** Solve the quadratic equation $2x^2 - 10 = 26$ for $x$. 2. **Write the formula and rules:** To solve quadratic equations, we isolate the $x^2$ term and the

1. **State the problem:** Solve the inequality $$t - 1(t - 6)(t + 1) < 0$$. 2. **Rewrite the inequality:** The expression is ambiguous, so we interpret it as $$t - 1 \cdot (t - 6)(

1. The problem asks to find the coordinate point that represents the solution to a system of linear equations graphed on a coordinate plane. 2. The solution to a system of linear e

1. **State the problem:** Find the value of $z$ that satisfies the equation $$\frac{1}{4}(2 - z) + \frac{3}{2} = 3(z - 2).$$ 2. **Write the equation:** $$\frac{1}{4}(2 - z) + \frac