🧮 algebra

1. **Problem 1:** Yalina thinks of a number that rounds to 10 when rounded to the nearest whole number. 2. She says it is the largest number with 2 decimal places that rounds to 10

1. **State the problem:** We need to divide 24 into three parts $x$, $y$, and $z$ such that $x + y + z = 24$ and the product $P = x \cdot y^2 \cdot z^3$ is maximized. 2. **Express

1. The problem states that a shopkeeper bought an article for 400 and sold it for 480. We need to find the profit percentage. 2. First, calculate the profit by subtracting the cost

1. **State the problem:** Solve the inequality $$8 - (-1)w > 7$$ for $w$. 2. **Simplify the expression:** Note that subtracting a negative is the same as adding a positive, so:

1. **State the problem:** Solve the inequality $$-5 + -4r > 3$$ for $r$. 2. **Isolate the term with $r$:** Add 5 to both sides to move the constant term.

1. **State the problem:** We need to determine which fraction among $\frac{3}{5}$, $\frac{6}{13}$, $\frac{5}{9}$, and $\frac{4}{7}$ is the largest. 2. **Convert each fraction to a

1. **State the problem:** Simplify the expression $2(2x-1)(x+4)$. 2. **Apply the distributive property:** First, multiply the two binomials $(2x-1)(x+4)$.

1. **Find the slope of the line through (2, 3) and (5, 9).** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$.

1. **State the problem:** Solve the equation $$2(x - 1)^2 = (2x - 3)(x + 1)$$ for $x$. 2. **Expand both sides:**

1. The problem is to find the pattern or rule governing the sequence: 3, 5, 9, 17, 33. 2. Observe the differences between consecutive terms:

1. **State the problem:** We know 3 men can complete a work in 12 days.

1. The problem is to simplify the function $f(x) = x^2 + mx^2 - 5x - 7$. 2. Combine like terms: $x^2$ and $mx^2$ are like terms because both have $x^2$.

1. 問題描述： 請解下列方程式，並說明每一步的解題過程。

1. **State the problem:** We know 8 men can complete a work in 12 days. We need to find how many days 6 men will take to complete the same work. 2. **Understand the relationship:**

1. The problem is to convert the number 0.0348 into standard form. 2. Standard form (also called scientific notation) expresses a number as $a \times 10^n$ where $1 \leq a < 10$ an

1. **State the problem:** A man spends 40% of his income and saves the rest. His total income is 25000. 2. **Calculate the amount spent:**

1. The expression given is $1 - 2x$. 2. This is a linear expression in terms of $x$.

1. The problem is to express the number 1.276 x 10^{-3} in decimal form. 2. Recall that multiplying by 10^{-3} means moving the decimal point 3 places to the left.

1. Let's clarify the question: You are asking if, when you have a negative whole number, you should "rotate" it and remove the negative sign. 2. In mathematics, a negative whole nu

1. Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. Simplify the expression $$\frac{3x^2 - 12x}{6x}$$.

1. The expression given is $15c^{-8}$. 2. Recall that a negative exponent means the reciprocal: $a^{-n} = \frac{1}{a^n}$.