🧮 algebra

1. **State the problem:** Solve the system of equations using Cramer's rule: $$\begin{cases} 15x - 4y - 7z = 14 \\ -4x + 6y - 2z = 34 \\ 4x - 3y - 2z + 12z = 1 \end{cases}$$

1. **Problem Statement:** A man buys 20 pens and 30 pencils for a total of 600.

1. The problem is to "make a solution," which is unclear, so I will interpret it as solving a simple algebraic equation for demonstration. 2. Let's solve the equation $2x + 3 = 7$.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$$ where $[x]$ is the greatest integer less than or equal to $x$ (floor functio

1. **State the problem:** Simplify the expression $$\left(\frac{100x^4 y^3}{4x^8 y^{-1}}\right)^{\frac{1}{2}}$$ completely and write the answer using positive exponents. 2. **Write

1. **Problem Statement:** We want to understand why the line $\log_8 y$ is a linear function of $\log_4 y$. 2. **Recall the change of base formula:** For any positive numbers $a,b,

1. **State the problem:** We are given that $\log_8 y$ is a linear function of $\log_4 x$ with vertical intercept 5 and horizontal intercept 3. We need to find which equation among

1. Masalah: Diberikan fungsi profit $P(x) = a(x-b)^2 + Q$ dengan vertex di titik $(b, Q) = (20, 40000)$ dan parabola membuka ke bawah. 2. Diketahui titik lain pada grafik adalah $x

1. **Soal 1: Menentukan nilai $x$ jika $y=200$ pada persamaan $y=5x+7$** Diketahui persamaan garis lurus:

1. **State the problem:** A carton of apples is shared equally among 10 people. Then 4 people give up their shares, and the remaining 6 people each receive 4 more apples than befor

1. **State the problem:** We need to divide the rational expression \( \frac{x^2 - 9x + 20}{3x^2 + 10x - 8} \) by \( \frac{x^2 - 8x + 16}{3x^2 + 13x - 10} \).

1. The problem asks which form of the quadratic function $h$ displays the zeros of the function. 2. The zeros of a quadratic function are the values of $x$ for which $h(x) = 0$.

1. **Problem statement:** Ardizha starts with a monthly salary of 6,000,000 in January 2025. Each year, his salary increases by 2% of the initial salary. We need to find his monthl

1. **State the problem:** We need to analyze the quadratic function $f(x) = x^2 - 6x + 5$ by finding its x-intercepts, y-intercept, vertex, and axis of symmetry. 2. **Formula and r

1. **Problem Statement:** Given the functions $f(x) = x^3 - x^2 + ax + b$ and $g(x) = x^2 - 2x - 8$, if $g(x)$ is a factor of $f(x)$, prove that $2a - 3b = 4$. 2. **Understanding t

1. **State the problem:** Solve for $i$ in the equation $5i = 1 - (1+i)^{-10}$. 2. **Rewrite the equation:**

1. Masalah yang dihadapi adalah pembagian angka 1957,00 dengan 0,9144 di Excel tidak berhasil. 2. Dalam Excel, tanda koma (,) biasanya digunakan sebagai pemisah ribuan atau desimal

1. **State the problem:** We need to add the fractions $\frac{5}{2}$ and $\frac{39}{4}$. 2. **Formula and rules:** To add fractions, they must have the same denominator. If not, fi

1. **State the problem:** Find the slope of the line given by the equation $x = -3$. 2. **Understand the line:** The equation $x = -3$ represents a vertical line where all points h

1. **Problem statement:** A rectangle has a perimeter of 74. The length ($l$) and width ($w$) are integers. We need to find the maximum possible area of this rectangle. 2. **Formul

1. The problem asks to find the percentage of questions Ruby answered correctly on her English test. 2. The formula to find percentage is: $$\text{Percentage} = \left(\frac{\text{N