🧮 algebra

1. The problem is to calculate the expression $\frac{15}{9} - 1 \frac{5}{18}$.\n\n2. Convert the mixed number $1 \frac{5}{18}$ to an improper fraction.\n\n$$1 \frac{5}{18} = \frac{

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x = 28$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. Stating the problem: A notary receives 3000 for each property deed and 2000 for each incorporation minute. He made a total of 22 operations (deeds and minutes) with a total inco

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. We start by factoring the quadratic expression. We look for two numbers that multiply to 6 and add to -5.

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides:

1. The problem asks: What percent is 60 of 80? 2. To find what percent one number is of another, use the formula:

1. The problem is to convert the fraction $\frac{5}{40}$ into a decimal. 2. To convert a fraction to a decimal, divide the numerator by the denominator.

1. **Problem:** Which of the following numbers is not a real number? Options: (a) $\frac{22}{7}$, (b) $\sqrt{25}$, (c) $\sqrt{-25}$, (d) 25

1. **Write down the order of each matrix:** 1.a) Matrix \( A = \begin{pmatrix} -3 & 4 & 2 \\ 1 & 5 & -1 \end{pmatrix} \) has 2 rows and 3 columns.

1. Simplify the expression \(\frac{5x+5}{3(2x-1)} - \frac{6-2x}{2(1-2x)}\). 2. Note that \(1-2x = -(2x-1)\), so rewrite the second denominator:

1. **Problem statement:** Simplify the expressions: (a) $\frac{4a + 13}{5} - \frac{2a + 3}{3}$

1. Stating the problem: Simplify the expression $$\frac{-3a^2 \times 4a^{-1} b^{-1}}{12 (ab)^{-2}}$$. 2. Simplify the numerator: Multiply the coefficients and the variables separat

1. State the problem: Solve the equation $2x + 10 = 23$ for $x$. 2. Subtract 10 from both sides to isolate the term with $x$:

1. **Problem 19:** Given the data set 2, 4, 5, 8, 11, determine the mean, median, mode, range, variance, and standard deviation. 2. **Mean:** The mean is the average of the data po

1. The problem states that $y$ is inversely proportional to $x$, which means we can write the relationship as: $$y \propto \frac{1}{x}$$

1. The problem is to solve the equation $2x + 10 = 25$ for $x$. 2. Start by isolating the term with $x$ on one side. Subtract 10 from both sides:

1. The problem states that $d = \frac{2.8}{h}$ and asks for the value of $d$ when $h = 0.07$. 2. Substitute $h = 0.07$ into the formula:

1. Stating the problem: Simplify the expression $$\frac{-3a^2 \times 4 \times b^{-1}}{12 (ab)^{-2}}$$. 2. Simplify the numerator: Multiply the constants and variables.

1. **State the problem:** We have two types of printers: old and new.

1. **State the problem:** We want to solve the equation $$4(x-3)-3(x-5)=3(x+1)$$ and understand why the solution is $$x=0$$. 2. **Expand each term:**