🧮 algebra

1. The problem asks what output will be displayed if the user inputs 0 for the area of a square. 2. The pseudocode is:

1. **State the problem:** We are given two points representing profits after certain years: (1, 3) and (4, 15), where $x$ is years in business and $y$ is profit in millions. We nee

1. **State the problem:** We are given two points $(86,113)$ and $(176,239)$ and need to find the linear equation relating $R$ and $C$ in the form $R = mC + b$.

1. **State the problem:** Calculate the value of the expression $$2^3 + 5(-2)^2$$. 2. **Recall the order of operations:** We first evaluate exponents, then multiplication, and fina

1. **State the problem:** Solve the equation $$2 - \frac{x + 3}{4} = \frac{x - 1}{8}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, multiply b

1. **State the problem:** We need to find the equation of the line passing through the points $(-1,0)$ and $(0,-4)$. 2. **Formula used:** The equation of a line can be found using

1. **State the problem:** Solve for $x$ given the function $f(x) = \frac{x^2 - 5}{x - 2}$ and $f(x) = 4$. 2. **Write the equation:**

1. **State the problem:** We are given a logarithmic function $$f(x) = -3 \log_{0.5}(x + 4) + 2$$ and a quadratic function $$g(x) = 5(x - 2)^2 + 7$$ which is said to be the inverse

1. Problem: Add the integers given in each expression. 2. Formula: For any two integers $a$ and $b$, addition is $a + b$.

1. **State the problem:** Simplify the expression $\frac{5x^2}{5x}$.\n\n2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} =

1. Problem: Add the integers given in the first expression: $(+73) + (+64)$. 2. Formula: Integer addition is straightforward: add the numbers if they have the same sign, subtract i

1. **State the problem:** Solve the quadratic equation $$5x^2 + 10x - 45 = 0$$ by completing the square. 2. **Divide the entire equation by 5** to simplify the coefficient of $$x^2

1. **Problem 1: List subsets of the set \{4, 5, 6\}** The subsets of a set include the empty set, single-element sets, two-element sets, and the full set itself.

1. **State the problem:** Solve the quadratic equation $x^2 + 6x - 14 = -2$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Simplify the expression $$w^{-\frac{1}{7}} \cdot w^{-\frac{12}{5}}$$ assuming all variables are positive. 2. **Recall the rule for multiplying powers with

1. **State the problem:** Simplify the expression $$x^{-\frac{17}{6}} \times x^{-\frac{11}{5}}$$ and write the answer in the form $$A$$ or $$\frac{A}{B}$$ where $$A$$ and $$B$$ are

1. **Problem 1: Solve $x^3 - 64 = 0$** This is a difference of cubes since $64 = 4^3$. The formula for difference of cubes is:

1. **State the problem:** Simplify the expression $10m^2 \cdot 3m^5$ without negative exponents. 2. **Recall the rule for multiplying powers with the same base:** When multiplying

1. **State the problem:** Simplify the expression $$\frac{6x^{10}y}{2x^{7}y^{3}}$$ using properties of exponents. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the inequality $$\frac{-x^2}{4x - 1} \geq \frac{2}{x - 9}$$ using an interval table. 2. **Rewrite the inequality:** Bring all terms to one side to c

1. The problem asks: Josie has 47 left in her checking account and writes a check for 55. What is her new balance? 2. Writing a check for 55 means subtracting 55 from her current b