🧮 algebra

1. **State the problem:** We are given a linear function $f(x)$ and its graph, and we want to find which equation form $f(x)$ could have, given that $c$ and $d$ are positive consta

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **Problem statement:** Find the real values of $X$ and $Y$ that satisfy the equation $$X(X+i) + Y(Y - i) + i = 13.$$ 2. **Rewrite the equation:** Expand the terms:

1. **State the problem:** Evaluate the expression $16.66 - \left(\frac{1}{4} + 3.15\right)^3$. 2. **Identify the formula and rules:** We need to first simplify inside the parenthes

1. The problem is to solve the equation for $x$: $2x + 3 = 11$. 2. The formula used here is to isolate $x$ by performing inverse operations. Important rules: whatever you do to one

1. **State the problem:** Evaluate the expression $$\frac{1}{\sqrt{2}} + \pi$$ using the approximations $$\sqrt{2} = 1.414$$ and $$\pi = 3.141$$ up to three decimal places. 2. **Re

1. **State the problem:** Simplify and evaluate the expression $$\left( \frac{12^{\frac{1}{5}}}{27^{\frac{1}{5}}} \right)^{\frac{5}{2}}$$. 2. **Recall the exponent rules:**

1. **State the problem:** Calculate the value of the expression $15.66 - \left[\frac{1}{4} + 3.15\right]^2$. 2. **Recall the order of operations:** First, solve inside the brackets

1. The problem is to define what a real root is in mathematics. 2. A real root of an equation is a solution that is a real number. For example, if we have a polynomial equation $f(

1. **State the problem:** We need to express the fraction $$\frac{5 - \sqrt{3}}{2 + \sqrt{3}}$$ in the form $$x + y\sqrt{3}$$ where $x$ and $y$ are rational numbers. 2. **Formula a

1. **Problem statement:** Given the function $k(x) = |x - 3| - |x + 5|$, we need to write it as a simplified piecewise function by considering three intervals. 2. **Intervals to co

1. Diberikan sistem persamaan: $$3x + 2y = \log_4 \left(18^{\frac{5}{4}}\right)$$

1. المشكلة: حل المعادلة $x^2 - 5x + 6 = 0$. 2. الصيغة المستخدمة: معادلة من الدرجة الثانية على الشكل $ax^2 + bx + c = 0$، حيث $a=1$, $b=-5$, و $c=6$.

1. لنبدأ بتعريف الدالة العددية: الدالة العددية هي علاقة تربط كل عنصر من مجموعة تسمى المجال (domain) بعنصر واحد فقط من مجموعة أخرى تسمى المدى (range). 2. الصيغة العامة للدالة العددي

1. **Problem statement:** Given the continuous function $f:\mathbb{R} \to \mathbb{R}$ satisfying $$f(x) - 2f(1-x) = 3x - 3 - e^{-x} + 2e^{x-1}$$

1. Stating the problem: Solve for $x$ in the equation $$478394(x+5) = 32678132468$$ and then evaluate the expression $$543728973482904 \div 3409244873 + 54378929 \times 438294 + 47

1. Masalah: Selesaikan persamaan $4x = 4$ untuk mencari nilai $x$. 2. Gunakan aturan dasar aljabar: untuk mengisolasi $x$, bagi kedua sisi persamaan dengan 4.

1. The problem asks to find the value of $4 \log 8 + 4 \log 32$. 2. Recall the logarithm property: $a \log b = \log b^a$.

1. **State the problem:** Simplify the expression $4 \log 8 + 4 \log 32$. 2. **Recall the logarithm property:** $a \log b = \log b^a$ and $\log x + \log y = \log (xy)$.

1. Diketahui persamaan logaritma: $\log_2(x) + \log_2(x - 2) = 5$. 2. Gunakan sifat logaritma bahwa $\log_a(m) + \log_a(n) = \log_a(m \cdot n)$, sehingga:

1. Diketahui persamaan \(\log_2(x) + \log_2(x - 2) = 5\). Kita diminta mencari nilai \(x\).\n\n2. Gunakan sifat logaritma: \(\log_a(m) + \log_a(n) = \log_a(m \times n)\). Jadi, \(\