🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2y^2 - 10y \cdot y + 5}{y^2 + 10y + 25} \times 6y$$. 2. **Rewrite the expression clearly:**

1. **State the problem:** Leah has 50 gold beads and makes 5 identical bracelets using all the beads. We need to find how many beads are used in each bracelet. 2. **Formula used:**

1. **State the problem:** Denise read for 2 hours and finished 1 chapter at school. Using the graph, we want to find how many chapters Denise finished today in total. 2. **Analyze

1. **State the problem:** We are given data points representing the total number of hot dogs sold at different times during a game. Pablo sells 20 hot dogs in the second half of th

1. **Problem:** Write the slope-intercept form $y=mx+b$ of the line passing through the given point with the given slope using point-slope form. 2. **Formula:** Point-slope form is

1. **State the problem:** Ms. Finley has 5 boxes of granola bars. Each day, she packs 1 granola bar in each of her 2 children's lunches. We need to find how many school days the gr

1. **State the problem:** Simplify the expression $$\frac{(5p^2)(p-4)}{10p(p-9)}$$. 2. **Write the expression clearly:** $$\frac{5p^2(p-4)}{10p(p-9)}$$.

1. 题目说明：已知分段函数 $$f(x)=\begin{cases}3x+5,&x>0\\3x-1,&x<0\\23,&x=0\end{cases}$$

1. **State the problem:** Solve the equation $3(4x+6)=6(3x-10)$ for $x$. 2. **Use the distributive property:** Multiply the numbers outside the parentheses by each term inside.

1. **State the problem:** Solve the quadratic equation $$x^2 + 4x + 2 = 0$$ by completing the square. 2. **Recall the formula and method:** To complete the square for an equation o

1. The problem is to plot the mixed numbers $-1 \frac{1}{2}$ and $2 \frac{1}{4}$ on a number line ranging from $-3$ to $3$. 2. First, convert the mixed numbers to improper fraction

1. The problem is to find the value of $4^n$ for a given $n$. 2. The expression $4^n$ means 4 raised to the power of $n$, which is multiplying 4 by itself $n$ times.

1. Problem: Simplify each expression involving square roots and radicals. 2. Recall the rule: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ and simplify square roots by factoring

1. **State the problem:** Solve the equation $$\frac{1}{x} = 3 - 2x$$ using the null factor law. 2. **Rewrite the equation:** Multiply both sides by $x$ (assuming $x \neq 0$) to el

1. The problem is to find the function and analyze its properties. 2. We start by defining the function as $y = a^x$ where $a > 0$ and $a \neq 1$.

1. **State the problem:** Solve the equation using the null factor law. 2. **Explain the null factor law:** The null factor law states that if a product of factors equals zero, the

1. **State the problem:** Factorize the quadratic expression $2x^2 + 3x - 20$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that mu

1. **Stating the problem:** We are given the function $$y = -x^2 + 8x - 10$$ and asked to determine the correct range condition from the options: a. $$y \leq 6$$, b. $$y \geq 6$$,

1. **Stating the problem:** We are given a function defined as $f(x) = 3, \frac{3}{x+2}$. This looks like two separate expressions, so we need to clarify and analyze each part. 2.

1. **State the problem:** We are given the function $f(x) = 3$ and need to understand its properties. 2. **Formula and explanation:** This is a constant function, meaning for every

1. **State the problem:** We have two equations: a horizontal line $y = -1.5$ and a quadratic function $y = x^2 + 8x + a$, where $a$ is a positive constant. We want to find the val