🧮 algebra

1. **State the problem:** Find the smallest value of $x$ that satisfies the quadratic equation $$x^2 - 3x = 0$$. 2. **Write the equation:** $$x^2 - 3x = 0$$.

1. **State the problem:** We need to graph and analyze the system of inequalities:

1. **State the problem:** We need to find the equation of a line that is perpendicular to the line given by $$-7x - 9y = -35$$ and passes through the point $$(-4, -7)$$. 2. **Rewri

1. **State the problem:** We are given a procedure to apply to numbers: multiply by $12$, add $8$, divide by $2$, then subtract $4$. We want to verify the results for given numbers

1. **State the problem:** We are given a procedure to apply to four numbers: multiply the number by 12, add 8, divide by 2, then subtract 4. We will find the result for each number

1. **State the problem:** We are given the function $$h(t) = -t^2 - 3t + 15$$ and we want to understand its properties. 2. **Identify the type of function:** This is a quadratic fu

1. **State the problem:** We are given the sequence $$27, -9, 3, -1$$ and need to identify a pattern to find the next number. 2. **Look for a pattern:** Observe the sequence:

1. **State the problem:** We need to find the value of the function $f(x) = -3x + 6$ at $x = -3$.

1. **State the problem:** We are given the expression $\left(4.5 m + \frac{7}{8}\right) - 9$ and Vance's attempt to use the associative property to rewrite it as $4.5 m \left(\frac

1. **State the problem:** We need to find the last operation performed when evaluating the expression $$(8 - 2x)^2 + 4$$ for $x = 3$. 2. **Substitute the value:** Replace $x$ with

1. **State the problem:** We want to find which expressions are equivalent to $$\frac{1}{3} + 8d + \frac{5}{7}$$. 2. **Recall the properties:** Addition is commutative and associat

1. **State the problem:** Determine if Maggie correctly applied the commutative property to the expression $$\frac{4}{5} + 6.9y - 8$$ by rewriting it as $$6.9y + 8 - \frac{4}{5}$$.

1. **State the problem:** We want to find which expressions are equivalent to $$8.9 x + 6.2 + 8.7$$. 2. **Recall the rules:** Equivalent expressions have the same terms combined in

1. **State the problem:** We need to find the first operation performed when evaluating the expression $5 + (9 \times -3) \div 2$ after substituting $x = 5$. 2. **Substitute the va

1. **State the problem:** We want to find which expression is equivalent to $$a + (c + 7)$$. 2. **Recall the associative property of addition:** It states that for any numbers $x,

1. **State the problem:** Determine if the piecewise function $$f(x) = \begin{cases} x^2 & \text{if } 0 < x \leq 5 \\ 5x & \text{if } 5 < x < 8 \\ 40 & \text{if } x \geq 8 \end{cas

1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} x^2 & \text{if } 0 < x \leq 5 \\ 5x & \text{if } 5 < x < 8 \\ 40 & \text{if } x \geq 8 \end{cases}$$

1. 题目要求求表达式 $\max\{x+\frac{1}{y}\} + \max\{y+\frac{3}{z}\} + \max\{z+\frac{5}{x}\}$ 的最小值，其中 $x,y,z$ 都是正实数。 2. 由于 $x,y,z$ 是正实数，且每个部分都是两个正项的和，我们可以分别对每一项使用不等式来求最小值。

1. **State the problem:** We are given a graph showing the percentage of charge $C$ in a phone battery over time $t$ (in hours). We need to determine which statements about the fun

1. **State the problem:** Solve the compound inequality $$x + 2 \geq 2$$ and $$x + 10 \leq 9$$. 2. **Solve the first inequality:**

1. **State the problem:** Solve the compound inequality $$x + 10 \geq 6$$ and $$7x - 1 \geq 6$$ and write the solution in interval notation. 2. **Solve the first inequality:**