🧮 algebra

1. **State the problem:** Solve the equation $$2(2x-1)^4 - 3(2x-1)^2 + 1 = 0$$ for $x$. 2. **Introduce substitution:** Let $$y = (2x-1)^2$$. Then the equation becomes $$2y^2 - 3y +

1. **Problem:** Understand what equivalent fractions are. Equivalent fractions are different fractions that represent the same value or proportion of the whole.

1. **State the problem:** We need to find the value of $a$ for which the system of simultaneous equations has a unique solution. The system is:

1. **State the problem:** We need to find the value of $a$ for which the system of simultaneous equations has a unique solution: $$\begin{cases} x + y + z = 2 \\ x + 2y - 3z = 5 \\

1. **State the problem:** We have a quadratic curve $y = ax^2 + bx + c$ with a maximum point at $(-3, 14)$ and it passes through the point $(0, -4)$. We need to find $a$, $b$, and

1. The problem asks to find the answer to the expression inside the brackets using the fractions provided. 2. To solve expressions with fractions inside brackets, first simplify th

1. The problem is to find the value inside the bracket, but the expression or equation is not provided. 2. To solve for the value inside brackets, we need the full expression or eq

1. **Stating the problem:** We have a quadratic function $y=f(x)$ with a tangent line $y=-1$ to the curve. The vertex is at $(0,1)$ and the curve passes through $(2,-1)$ and $(-3,1

1. The problem is to understand why the profit calculation is $(50 - 40) + 2 = 12$ and why we add 2 instead of subtracting 2. 2. The formula for profit is generally: $$\text{Profit

1. Solve for $x$: $$2x + 3 = 7$$ 2. Find the roots of the quadratic equation: $$x^2 - 5x + 6 = 0$$

1. The problem appears to be identifying the missing numbers in the boxes in the sequence: \(\boxed{?} \rightarrow \boxed{?} \rightarrow \boxed{?} \rightarrow 46 \rightarrow 20 \ri

1. **State the problem:** We are given a matrix \(\begin{bmatrix} x & 3 & x \\ x & x-2 & ? \end{bmatrix}\) (assuming the matrix is square and the last element is missing or a typo,

1. Let's start by stating the problem: You have the expression $ (50 - 40) + 2 = 12 $ and you want to understand why we add 2 instead of subtracting 2. 2. The expression $ (50 - 40

1. **State the problem:** Solve the system of simultaneous equations using Cramer's rule: $$\begin{cases} x + y + z = 2 \\ x + 2y + z = 6 \\ 6x + 5y + 4z = 8 \end{cases}$$

1. 题目说明：计算表达式 $52.9\% \times 7.11\% + 47.91\% \times 1\%$ 的值。 2. 公式和规则：百分数转换为小数时，除以100，即 $a\% = \frac{a}{100}$。

1. The problem is to express the number $0.5891205$ in scientific notation and verify the given expression $5.891205 \times 10$. 2. Scientific notation expresses numbers as $a \tim

1. The period of a function is the length of the smallest interval over which the function repeats its values. 2. For trigonometric functions like sine and cosine, the standard per

1. The problem is to understand and analyze the function $f(x) = |x|$, which represents the absolute value of $x$. 2. The absolute value function is defined as:

1. **Problem Statement:** Find the turning point of the function $$f(x) = |x|$$. 2. **Understanding the function:** The absolute value function $$f(x) = |x|$$ outputs the distance

1. **Stating the problem:** Simplify the expression $$(-4)^3 \times (-4)^{-2}$$. 2. **Recall the exponent rules:**

1. **Problem Statement:** A hot air balloon rises at a steady rate of 15 meters per minute. We need to find its height after 6 minutes. 2. **Formula Used:** Height $h$ after time $