🧮 algebra

1. **State the problem:** A machine costs 45000 and has a salvage value of 4350 after 6 years. The depreciation is computed using a constant percentage rate on the declining book v

1. **State the problem:** Solve for $c$ in the equation $7c = 4c - 13 + c + 36$. 2. **Combine like terms on the right side:**

1. The problem asks for the value of $c$, but no equation or context is provided. 2. To find $c$, we need an equation or relationship involving $c$.

1. **State the problem:** Solve the equation $32c + 5 = 24c + (c + 32)$ for $c$. 2. **Expand and simplify:** First, expand the right side:

1. **State the problem:** Solve for $s$ in the equation $(19s - 18) + (33s - 36) = 32s$. 2. **Combine like terms on the left side:**

1. Problem: Calculate $\log_3 x$ for given expressions of $x$ with $a,b,c>0$ and base 3. 2. Recall logarithm rules:

1. **Problem statement:** Simplify and expand the expression $5(u+5)(u-5)(u+2)$. 2. **Recall the difference of squares formula:**

1. **State the problem:** Expand the expression $2(x-4)(x+4)$. 2. **Recall the formula:** The product of two binomials of the form $(a-b)(a+b)$ is a difference of squares:

1. Problem 15 asks to find $\log_2 x$ for various expressions of $x$ where $a,b,c>0$. 2. Recall the logarithm properties:

1. **State the problem:** Multiply the polynomials $\left(5x^2 + 2x + 8\right)\left(7x - 6\right)$. 2. **Recall the distributive property:** To multiply two polynomials, multiply e

1. **State the problem:** We are given a rectangular box with dimensions Length = $3x + 4$, Width = $3x$, and Height = $3x - 1$. The volume is given by $3x(3x + 4)(3x - 1)$. We nee

1. The problem is to simplify the expression $\frac{2\sqrt{3} - 3\sqrt{2}}{6}$.\n\n2. The formula used here is to simplify fractions by dividing numerator and denominator by common

1. The problem is to solve the equation $$\sqrt{x^2} = \sqrt{80}$$ for $x$. 2. Recall that $$\sqrt{x^2} = |x|$$, which means the square root of $x^2$ is the absolute value of $x$.

1. **State the problem:** Calculate the sum of the fractions $$\frac{1}{2} + \frac{1}{4} + \frac{1}{14}$$. 2. **Formula and rules:** To add fractions, find a common denominator, th

1. **State the problem:** Simplify the expression $$y = \sqrt[4]{x^5} - \frac{1}{\sqrt{x}}$$. 2. **Recall the rules:**

1. **State the problem:** Kyle invests money in a simple savings fund where the amount increases at a constant rate. We know the amount after 3 years is 16500 and after 6 years is

1. **State the problem:** We need to graph the solution to the system of inequalities: $$-5x + 2y \leq 2$$

1. The problem is to analyze the system of inequalities: $$-5x + 2y \leq 2$$

1. **State the problem:** We are given a function with vertical asymptotes at $x = -3$ and $x = 2$. We want to find a possible expression for the function $y$ that matches these ch

1. **State the problem:** Simplify the expression $-4\sqrt{100} + 10\sqrt{16}$. 2. **Recall the square root values:**

1. **State the problem:** Simplify the expression $$\left(\sqrt[4]{10v}\right)^5$$. 2. **Recall the rule for radicals and exponents:** The fourth root of a number is the same as ra