🧮 algebra

1. The problem is to evaluate the expression $0^0$. 2. The expression $a^b$ means $a$ raised to the power of $b$.

1. The problem is to understand the Fibonacci sequence and find its terms. 2. The Fibonacci sequence is defined by the recurrence relation:

1. **State the problem:** We have two curves $C_1$ and $C_2$ with equations: $$C_1: y = 2x^3 + 10, \quad x > 0$$

1. **State the problem:** We have two curves: $$y = 2x^3 + 10$$ for curve C1 and $$y = 42x - 15x^2 - 7$$ for curve C2, both defined for $$x > 0$$.

1. **State the problem:** We need to find which has the steeper gradient: the submarine or the torpedo. 2. **Formula for gradient:** Gradient (slope) is calculated as the ratio of

1. **State the problem:** We need to determine which slope is steeper between Abdulla's rocky slope and Jonathen's grassy slope. 2. **Formula used:** The steepness of a slope can b

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 eq

1. **State the problem:** Simplify the expression $$2 - \frac{3}{x} - \frac{1}{x^2}$$ assuming all denominators are nonzero. 2. **Find a common denominator:** The denominators are

1. **State the problem:** We need to express the improper fractions $\frac{17}{4}$ and $\frac{22}{3}$ as mixed numbers and identify their whole number, numerator, and denominator p

1. **Problem Statement:** Find the next number in each of the given sequences. 2. **Sequence a:** $5, 11, 17, 23, 29, 35$

1. **State the problem:** We need to find an expression to determine the product of $-4$ and $3 \frac{1}{4}$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** We want to factor the polynomial $$12x^3 - 15x^2 + 2$$. 2. **Look for common factors:** Check if there is a greatest common factor (GCF) among the terms.

1. **State the problem:** Mr. Lee can complete the exhibit setup in $4$ days, and Jordan can do it in $6$ days. Mr. Lee works alone for $3$ days, then Jordan finishes the remaining

1. **Problem 1: Find the fraction exactly halfway between $\frac{1}{3}$ and $\frac{3}{7}$.\n\n2. To find the fraction halfway between two fractions, we calculate their average usin

1. **State the problem:** Ari buys three dozen eggs and five avocados weekly. We want to find how much less he paid this week with the discounted prices compared to regular prices.

1. **Stating the problem:** We are given a pattern of equations: $$1 + 4 = 5$$

1. **State the problem:** Liam has mangos and plantains in the ratio $39:50$. We want to find how many mangos he has if he has $400$ plantains. 2. **Understand the ratio:** The rat

1. The problem states that the bottom left expression should be $\frac{x}{2}(3.14)(10)$ instead of $\frac{x}{2110}$.\n\n2. Let's analyze the expression $\frac{x}{2}(3.14)(10)$. Thi

1. **State the problem:** We are given the equation $$\frac{x}{2110} = \frac{8.73}{360}$$ and need to solve for $x$.

1. **Problem Statement:** Simplify the given complex fraction or rational expression. 2. **Formula and Rules:** To simplify complex fractions, use the rule: $$\frac{\frac{a}{b}}{\f

1. **State the problem:** Solve for $y$ in the equation $$\sqrt{25 - 3y} = y + 1$$. 2. **Recall the domain restriction:** Since the expression under the square root must be non-neg