🧮 algebra

1. **State the problem:** We are given an arithmetic sequence where the sum of the first 10 terms is $120$ and the sum of the first 20 terms is $840$. We need to find the sum of th

1. **State the problem:** Liz reads 30 pages on the first day and increases the number of pages by 5 each subsequent day. We want to find how many days it will take her to read a t

1. **State the problem:** You have 1 gagandilan troop every 5 minutes. You want to find out how many hours it will take to have 10,000 troops. 2. **Understand the rate:** The rate

1. **State the problem:** Simplify the expression $$\frac{\sqrt{223109}}{101}$$. 2. **Recall the formula:** To simplify a fraction with a square root in the numerator, check if the

1. **State the problem:** We need to find the value of $p$ such that in the expansion of $$\left(3x + \frac{p}{x}\right)^8$$ the coefficients of the terms with $x^4$ and $x^6$ are

1. **State the problem:** We are given the function $$f(x) = \sqrt[3]{x + 10}$$ and asked to find its inverse function $$f^{-1}(x)$$. 2. **Recall the definition of inverse function

1. Problem 1: Find the number of customers at lunch given ratios and difference. 2. Let the number of customers at breakfast, lunch, and dinner be $B$, $L$, and $D$ respectively.

1. **State the problem:** We have a total of 75 trees divided into small, medium, and large categories. 2. **Define variables:** Let $S$ be the number of small trees, $M$ the numbe

1. **State the problem:** Daniel shares 430 between charities A, B, and C. The ratio of A to B is 5:2, and the ratio of A to C is 4:3. We need to find how much C receives. 2. **Exp

1. **State the problem:** We need to factor the quadratic expression $$-3x^2 + 15x + 108$$.

1. **State the problem:** We are given the total area of the garden as $$2x^2 + 5x + 4$$ and the area of the corn as $$x^2 - 3x + 2$$. We need to find the area of the pumpkins, den

1. **State the problem:** We have a 5000 m race consisting of $12 \frac{1}{2}$ laps, each lap being 400 m. Kara finishes in 17.5 minutes, Hannah in 15.3 minutes, and Hannah passes

1. **State the problem:** Determine the end behavior of the function $$f(x) = 120x^4 - 2112x + 44x^5 - 1152 + 4x^6 - 1280x^2 - 160x^3$$. 2. **Identify the leading term:** The end b

1. **State the problem:** We need to evaluate the expressions $(-3)^3$ and $(-6)^2$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$3(3w - 8) = 21$$ for $w$. 2. **Apply the distributive property:** Multiply $3$ by each term inside the parentheses:

1. **State the problem:** We need to determine which of the expressions $-(60/6)$, $-60/6$, and $-60/-6$ are equal to 10. 2. **Recall the order of operations and division rules:**

1. **State the problem:** We need to determine which of the expressions $-\frac{15}{5}$, $-15/5$, and $-15/-5$ are equal to 3. 2. **Recall the division and negative sign rules:**

1. **State the problem:** Two trains start from the same station but at different times and speeds. The first train leaves at 2:00 p.m. traveling at 45 km/hr. The second train leav

1. **State the problem:** We want to find the time $x$ when the object hits the ground, which means when the height $h(x)$ is zero. 2. **Write the equation:** The height is given b

1. **State the problem:** We want to find the lowest altitude Guillermo reaches, given the altitude function $$g(x) = \frac{1}{20} x(x - 100)$$ where $x$ is the time in seconds aft

1. **State the problem:** Solve the compound inequality $$x + 8 < 0 \text{ or } 3x > -21$$. 2. **Solve each inequality separately:**