🧮 algebra

1. **Stating the problem:** Find the least common multiple (LCM) of the numbers given by their prime factorizations: - $2^2 \times 3$

1. **State the problem:** Solve the equation $3(x+5) + 4(x+5) = 25$ for $x$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the coefficients.

1. **Stating the problem:** Empat petugas dapat mengetik enam dokumen dalam waktu tujuh hari. Berapa lama waktu yang dibutuhkan tujuh petugas untuk mengetik 12 dokumen jika kecepat

1. **State the problem:** We are given the system of equations:

1. **Problem Statement:** Solve the system of linear equations using Gaussian elimination: $$\begin{cases} w - x + 3y - 3z = 3 \\ -5w + 2x - 5y + 4z = -5 \\ -3w - 4x + 7y + 2z = 7

1. **Problem 3:** Solve $$\frac{(x - 3)(x + 5)(x - 7)}{|x - 4|(x + 6)} \leq 0$$ 2. **Step 1:** Identify critical points where numerator or denominator is zero or undefined:

1. **Problem 1: For the function $f(x) = 2x + 5$** a) The domain of $f(x)$ is all real numbers because it is a linear function with no restrictions. So, domain: $(-\infty, \infty)$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} w - x + 3y - 3z = 3 \\ -5w + 2x - 5y + 4z = -5 \\ -3w - 4x + 7y + 2z = 7 \\ 2w + 3x + y - 11z = 1 \e

1. Solve $\frac{x(3 - 4x)(x + 1)}{2x - 5} < 0$. - Factor and find critical points: $x=0$, $x=\frac{3}{4}$, $x=-1$, $x=\frac{5}{2}$ (denominator zero).

1. **State the problem:** Calculate the value of $$(1.874)^{\frac{1}{5}} - 1$$. 2. **Recall the formula:** The expression involves the fifth root of 1.874, which can be written as

1. **State the problem:** Solve the system of equations: $$x^2 + y^2 + z^2 = 14$$

1. The problem asks us to predict the cost of the electricity bill after 15 days using the trend line equation. 2. The given trend line equation is $$y = 3x + 5$$ where $x$ is the

1. **State the problem:** Solve the quadratic equation $$x^2 + 5x = 12$$ and give solutions correct to 3 significant figures. 2. **Rewrite the equation in standard form:** Move all

1. **State the problem:** We need to find the equation of a line perpendicular to the line given by $$y = -\frac{1}{2}x - 1$$ that passes through the point $(-2, 4)$. The answer sh

1. **State the problem:** Find the equation of the line perpendicular to $y = \frac{1}{2}x - 9$ that passes through the point $(3, 2)$. 2. **Recall the formula:** The point-slope f

1. **State the problem:** Find the equation of the line perpendicular to $$y = -\frac{1}{8}x + 4$$ that passes through the point $$(2, 3)$$ in point-slope form. 2. **Recall the poi

1. **State the problem:** Find the equation of the line perpendicular to $y = \frac{1}{2}x + 8$ that passes through the point $(5, 3)$. 2. **Recall the formula:** The point-slope f

1. The problem asks for the equation of a line perpendicular to $y=\frac{1}{6}x+7$ that passes through the point $(2,6)$, expressed in point-slope form. 2. Recall the point-slope f

1. **Problem statement:** Calculate the values of $x = \sqrt{9 - 4\sqrt{5}}$ and $y = \sqrt{9 + 4\sqrt{5}}$, then evaluate and compare the expression $(9 + \sqrt{5})^2 - (9 - \sqrt

1. **Problem Statement:** Identify the key features and equation of the exponential function passing through points (0,4) and (1,20) with horizontal asymptote $y=0$. 2. **General F

1. **Problem statement:** Calculate the value of the piecewise function $$Z = \begin{cases} \sqrt{x^2 + 2x - 1 - 3y + 2y^3}, & x > y \\ |2x^3 + 4y^2| - 3x^4, & x < y \\ \sqrt[3]{4y