🧮 algebra

1. **State the problem:** Solve the proportion $$\frac{11}{5} = \frac{10}{x}$$ for $x$ and round the answer to the nearest tenth. 2. **Use the cross-multiplication formula:** For p

1. **State the problem:** Solve the equation $$x - 5 = 2\sqrt{x} - 5$$ for $x$. 2. **Isolate the square root term:** Add 5 to both sides to simplify:

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the

1. **State the problem:** Simplify the factorial expression $$\frac{9! \times 8!}{11!}$$. 2. **Recall the factorial definition:** For any positive integer $n$, $n! = n \times (n-1)

1. **State the problem.** We are given the system of equations:

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** Solve the equation $$\frac{1}{5}(x - 5) = 7$$ for $x$. 2. **Formula and rules:** To solve for $x$, first eliminate the fraction by multiplying both sides

1. **Simplify** $16^{-\frac{3}{4}}$. Recall the rule: $a^{-m} = \frac{1}{a^m}$.

1. Simplify each expression step-by-step. **a. Simplify** $\sqrt{36x^4}$

1. **State the problem:** We need to match each exponential function to its corresponding graph based on their behavior and points. 2. **Recall the properties of exponential functi

1. **Problem 1:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula:** To isolate $x$, subtract 2 from both sides: $$x + 2 - 2 = 4 - 2$$

1. **State the problem:** Ling is driving at a constant speed of 55 miles per hour. We need to find how long it will take him to drive 275 miles. 2. **Formula used:** The relations

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** Solve the equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one sid

1. **State the problem:** We are given a table of miles and hours and need to find the unit rate in miles per hour. 2. **Formula:** The unit rate (miles per hour) is calculated by

1. **State the problem:** Solve $a^3+a^2=36$ for $a$. 2. **Use a standard factoring idea:** First move everything to one side:

1. **State the problem:** Solve the linear equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $$\frac{4b}{8}$$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common divi

1. **State the problem:** Solve the equation $$(3x+1)^2 - (2x-5)^2 = 504$$ for $x$. 2. **Recall the difference of squares formula:**