🧮 algebra

1. The problem states that the relation $f$ is defined by $f:x-x^2-2$ where $x$ belongs to the set $\{-1,-2,0,2\}$. We need to find $f(x)$ for each $x$ in this set. 2. The formula

1. The problem is to simplify the expression $1 - (1 - 1) - 1$. 2. Start by evaluating the expression inside the parentheses: $1 - 1 = 0$.

1. The given function is $$G(x) = (7x + 3)^4 (5x - 2)(3x + 2)^4 (5x + 3)^4 (5x - 1).$$ 2. We are told the multiplicity of the zero $$-\frac{3}{5}$$ of $$G$$ is $$\frac{3}{7} m$$, a

1. Stating the problem: A farmer has a rectangular field with length $230$ m and breadth $160$ m, and he wants to fence it with 3 rounds of rope. 2. First, calculate the perimeter

1. نبدأ بقراءة المسألة: لدينا $ص = ٤٥ - ٣ع$ و $٤٢٧ = ص$ و $ع = \frac{١}{١ + ص^٢}$. المطلوب هو حساب $ع ع ع$. 2. نعوض قيمة $ص$ في المعادلة الثانية:

1. **نطرح المشكلة:** لدينا مصفوفة $J = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix} + 1 \cdot b + 2 \cdot c$ وهناك ثلاث مصفوفات معطاة كخيارات. 2. **نستنتج المطلوب:** المطلوب إيجاد قي

1. Let's clarify the concept of putting an expression "in y." Usually, when dealing with a function or equation, we write it in the form $y = f(x)$ to explicitly indicate the outpu

1. The problem is to solve the equation $$(\lg x)^2 - 5 \lg x + 6 = 0.$$\n2. Let us use a substitution to simplify the problem. Set $$y = \lg x.$$ Then the equation becomes $$y^2 -

1. Stating the problem: Solve the equation $x^2 - x^1 = 31$ for $x$. 2. Rewrite the equation: $x^2 - x = 31$.

1. To derive or understand a formula, first clearly state what you want to find or solve for. 2. Identify the known variables and constants relevant to the situation.

1. Stated problem: Solve for $c$ in the equation $$\frac{1 - e^{-470c}}{1 - e^{-1000c}} = 0.5.$$\n\n2. Multiply both sides by the denominator to clear the fraction:\n$$1 - e^{-470c

1. **Problem 1: Find the percentage discount given the original price and the discount price.** The original price is K30 and the discount price is K24.

1. Find the common ratio of the geometric sequence: 3, 6, 12, 24, 48, ... - The common ratio $r$ is found by dividing any term by its previous term.

1. **State the problem:** We are given the equation $$x^2 - 3y = 31$$ and asked to analyze it. 2. **Rewrite the equation to express y in terms of x:**

1. The equation $y = mx + c$ is the equation of a straight line in slope-intercept form. 2. Here, $m$ represents the slope of the line, which indicates how steep the line is.

1. **Problem 32:** Find the equation of the linear relationship between sales $x$ and selling expense $y$ when sales increase from 100 to 400 and expense from 75 to 150. 2. **Calcu

1. **Problem:** Given $f(x) = x^2 + 3x - 7$, find $f(-2)$, $f(0)$, $f(4)$, $f(3x)$, and $f(2y)$. Step 1: Calculate $f(-2)$. Substitute $-2$ into $f(x)$:

1. **State the problem:** Factor the quadratic expression $$12q^2 + 17q + 6$$. 2. **Multiply the coefficient of** $$q^2$$ *and* the constant: $$12 \times 6 = 72$$.

1. Solve $|-x| = 3,4$. Since $|-x| = |x|$, the equation $|x| = 3$ has solutions $x = 3$ and $x = -3$.

1. Stating the problem: Solve the equation $y = 2x + y$. Step 1: Subtract $y$ from both sides to isolate terms.

1. Diberikan fungsi linear $y = 2x + 4$. Kita diminta menentukan fungsi bayangan setelah dilakukan translasi. 2. Translasi a: Geser 3 satuan ke atas dan 3 satuan ke kiri.