🧮 algebra

1. **State the problem:** Solve the equation $4(x+1)=2x+4$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Simplify or factor the polynomial expression $$8y^8 + 21y^4 + 13$$. 2. **Identify the structure:** Notice that the polynomial is in terms of powers of $y^

1. **State the problem:** An investor has stock in two companies: Company A worth 5550 and Company B worth 1700 last year.

1. **State the problem:** Simplify the expression $$(q+2)(q-3)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method):

1. **State the problem:** Expand the expression $$(3t - 4)(2t - 3)$$. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$(a + b)(c + d) = ac + ad + b

1. **State the problem:** An investor has stocks in two companies, A and B. Last year, Company A's stock was worth 4230 and Company B's stock was worth 3130. Company A's stock incr

1. **State the problem:** We are given the height of a rocket as a function of time: $$y = -16x^2 + 235x + 67$$ where $y$ is the height in feet and $x$ is the time in seconds. We n

1. **State the problem:** We are given the profit function $$y = -x^2 + 84x - 630$$ where $y$ is the profit and $x$ is the selling price per widget. We need to find the maximum pro

1. The problem states that a cup of soda costs 4 dollars initially, and each refill costs 0.80 dollars. 2. We need to write an equation for the total amount spent, $y$, based on th

1. The problem asks us to construct an equation in slope-intercept form $y=mx+b$ to represent the total hours $e$ a customer uses their phone per day, based on the number of calls

1. **State the problem:** Simplify the expression $$- 5^2 - (-0.02 + 1.1) \times 4.3 + 2$$. 2. **Recall order of operations:** Calculate exponents first, then parentheses, then mul

1. **State the problem:** Add the terms $4\sqrt{5}$ and $3\sqrt{5}$.\n\n2. **Identify like terms:** Both terms have the same radical part $\sqrt{5}$, so they are like terms and can

1. **State the problem:** Simplify the expression $$\frac{\sqrt{80x^3}}{\sqrt{5x}}$$ using the quotient rule for square roots, assuming $x > 0$. 2. **Recall the quotient rule for s

1. **State the problem:** Solve the equation $9x + 16 = 4x - 19$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by

1. **State the problem:** We want to find what percentage 36 is of 150. 2. **Formula:** The percentage is given by the formula

1. **State the problem:** Solve the equation $$\frac{3x - 4}{4} = 5x - 1$$. 2. **Multiply both sides by 4** to eliminate the denominator:

1. The problem asks to find the value of $k$ where $k = \frac{f(6) - f(1)}{6 - 1}$ for the function $f(x) = 5x - 2$. 2. First, calculate $f(6)$ and $f(1)$:

1. **State the problem:** You receive 15% of the profit from a car wash. The total profit is 300. We need to find how much money you receive. 2. **Formula:** To find the amount you

1. **State the problem:** We need to find what percent of 12 is 3. 2. **Formula:** The percentage is found by the formula $$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole

1. The problem asks: 12 is what percent of 50? 2. To find what percent one number is of another, use the formula:

1. **State the problem:** We need to find the number $x$ such that 12% of $x$ equals 48. 2. **Write the equation:** 12% means 12 per 100, so we write: