🧮 algebra

1. **State the problem:** Solve the linear equation $2.25x + 70 = 193.75$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtrac

1. **State the problem:** A group of friends has 69.75 to spend on parking and admission to an amusement park. Parking costs 17.25, and each ticket costs 17.50. We want to find the

1. **State the problem:** Robert buys cheese and lemons, paying a total of 24.36. The cheese costs 5.31, and he buys 5 bags of lemons at the same price each. We need to find the co

1. The problem asks to write down the two inequalities describing the unshaded region on the graph. 2. The graph shows two lines:

1. **State the problem:** The lacrosse team raised 1775.50 to go to a tournament. They rented a bus for 901.50 and budgeted 46 per player for meals. We need to find the number of p

1. The problem involves understanding and interpreting inequalities involving $x$ and $y$. 2. Inequalities like $x - y < 4$ and $x - y > 4$ describe regions in the coordinate plane

1. **State the problem:** We need to write the two inequalities that describe the unshaded region on the coordinate plane. 2. **Identify the lines:**

1. **Problem 7:** The value of $y$ varies directly with $x$. Given $x=5$ and $y=-15$, find the constant of variation and the value of $y$ when $x=9$. 2. **Direct Variation Formula:

1. **State the problem:** We need to find the inequalities describing the unshaded region on the graph. 2. **Identify the lines:**

1. **Problem statement:** The value of $y$ varies directly with $x$. When $x=5$, $y=-15$. We need to find the constant of variation and then find $y$ when $x=9$. 2. **Formula for d

1. **Problem 2:** Find the equation in slope-intercept form of a line with slope $m=2$ passing through point $(3,4)$. 2. The slope-intercept form is given by the formula:

1. **Problem 1:** Find the equation representing the table and graph with points $(5,-2)$, $(6,-4)$, $(9,-10)$, $(11,-14)$, and $(12,-16)$. The graph shows a line with y-intercept

1. **Problem 1: Find the positive value of $x$ such that matrices $M$ and $N$ commute under multiplication.** Given matrices:

1. **State the problem:** We need to find the equation of the line that matches both the given table of values and the graph description. 2. **Analyze the table:** The table gives

1. **State the problem:** Convert the improper fraction $\frac{45}{8}$ into a mixed number. 2. **Formula and rules:** A mixed number consists of a whole number and a proper fractio

1. **Problem:** Given matrices \(M = \begin{bmatrix}4 & 8 \\ 2 & x\end{bmatrix}\) and \(N = \begin{bmatrix}x^2 & 4 \\ 1 & 4x\end{bmatrix}\), find the positive value of \(x\) such t

1. The problem asks to evaluate the expression $12.41E+\pi$. 2. Here, $E$ represents the scientific notation symbol for "times ten to the power of". So $12.41E+\pi$ means $12.41 \t

1. **State the problem:** Reduce each fraction to its lowest terms. 2. **Formula and rule:** To reduce a fraction $\frac{a}{b}$, find the greatest common divisor (GCD) of $a$ and $

1. **State the problem:** We are given a rectangle with perimeter 105 feet. The sides are labeled as $2f - 2$ and $\frac{3}{2}f + 9$. We need to write an equation for the perimeter

1. **State the problem:** Reduce each fraction to its lowest terms. 2. **Formula and rules:** To reduce a fraction $\frac{a}{b}$, find the greatest common divisor (GCD) of $a$ and

1. **State the problem:** Solve the system of linear equations: $$-x - y = -9$$