🧮 algebra

1. The problem asks to determine if each table represents a linear relation using first differences. 2. For table a), list the y-values: 0, 1, 8, 27, 64.

1. **State the problem:** Find the percent equivalent of the fraction $\frac{1}{400}$.\n\n2. **Formula:** To convert a fraction to a percent, multiply the fraction by 100:\n$$\text

1. **State the problem:** Determine if the functions $f(x) = (x-1)(x-2)$ and $g(x) = \frac{x-1}{x-2}$ are linearly independent. 2. **Recall the definition:** Two functions $f$ and

1. The problem asks: What is the percent? 2. Percent means "per hundred" and is a way to express a number as a fraction of 100.

1. The problem is to find the decimal fraction of $\frac{1}{400}$. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator:

1. **State the problem:** Solve the quadratic equation $$3x^2 = -4 + 8x$$ for $x$. 2. **Rewrite the equation in standard form:** Move all terms to one side to get $$3x^2 - 8x + 4 =

1. **State the problem:** Solve the quadratic equation $3x^2 = -4 + 8x$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. The problem is to simplify the expression _X_x. 2. Since _X_x is not a standard algebraic or mathematical expression, we interpret it as a variable or symbol.

1. **بيان المسألة:** لدينا الدالة $$f(x) = x^2 - 2x + 1$$ معرفة على المجال $$\mathbb{R} \setminus \{-1\}$$ ونريد دراسة نهاياتها، مشتقتها، سلوكها، وحساب المساحات المحصورة بين منحنى

1. **بيان المسألة:** نحن ندرس الدالة $$f(x) = \frac{x^2 - 2x^2 - x + 2}{(x-1)^2}$$ معرفة على المجال $$[-1,4]$$.

1. **Problem statement:** Determine the slope of each line given the descriptions. 2. **Recall the slope formula:** For two points $(x_1,y_1)$ and $(x_2,y_2)$, the slope $m$ is giv

1. **State the problem:** Juno starts with 150 in their bank account and spends 10 each week. We want to find how many weeks it takes for Juno to have 520 in the account. 2. **Anal

1. **Problem statement:** Given points $A(2,3)$ and $B(-1,-4)$, find the distance $|AB|$. 2. **Formula for distance between two points:**

1. The problem is to simplify the expression $-\left|-x\right|$. 2. Recall that the absolute value function $|a|$ returns the non-negative value of $a$, so $|-x| = |x|$ because abs

1. **Problem:** Simplify the expression $2a^2b + 3ab - a^2b + 2ab$. 2. **Step 1:** Group like terms. Terms with $a^2b$ are $2a^2b$ and $-a^2b$. Terms with $ab$ are $3ab$ and $2ab$.

1. **State the problem:** Find the solution or roots of the quadratic function $f(x) = x^2 - 3x - 7$. 2. **Formula used:** To find the roots of a quadratic equation $ax^2 + bx + c

1. The problem is to understand why $\frac{8}{5} \div 3$ equals $\frac{8}{15}$.\n\n2. When dividing fractions or numbers, remember the rule: dividing by a number is the same as mul

1. **State the problem:** We are given the sum of the first $n$ terms of a sequence as $S_n = n^2 + 3n$. We need to find the terms of the sequence and check if it forms an arithmet

1. **State the problem:** We are given the sum of the first $n$ terms of a sequence as $S_n = n^2 + 3n$. We need to find the terms of the sequence and check if it forms an arithmet

1. The problem is to write an expression or equation all together in steps without dividing it into separate parts. 2. To do this, we first identify the full expression or equation

1. **State the problem:** We need to find the graphical representation of the two lines given by the equations: $$-8x + 6y = -22$$