🧮 algebra

1. **State the problem:** Old McDonald has 250 chickens and goats. The total number of feet is 760. We need to find how many chickens and goats there are. 2. **Understand and devis

1. **State the problem:** Calculate the value of the expression $2 \times 115 \div 360 \times \frac{22}{7} \times 25 \times 25$. 2. **Write the expression clearly:**

1. Masalah: Diberikan fungsi $f(x)$ dan translasi $T = (a, b)$ dengan $a > 0$ dan $b < 0$. Tentukan fungsi bayangan hasil translasi tersebut. 2. Translasi fungsi secara umum dapat

1. **Stating the problem:** Calculate the factorial of a number, for example, 5!. 2. **Formula:** The factorial of a positive integer $n$ is defined as:

1. **Problem Statement:** Check if 8836 is a perfect square using the Vedic Square Root method. 2. **Vedic Square Root Method Overview:**

1. Let's revisit how we found $x = 3$ as a root of the quadratic equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1

1. Let's solve a random algebra problem: Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. The formula to find roots of a quadratic equation $$ax^2 + bx + c = 0$$ i

1. The problem states: Solve the equation $$\log_4 x + \log_2 y = 5$$ given the conditions from the previous system. 2. Recall the change of base formula and properties of logarith

1. The problem is to express the equation $\frac{1}{x-2} - \frac{2}{x+5} = \frac{3}{x+1}$ in the form $ax^2 + bx + c = 0$. 2. To do this, we first find a common denominator for the

1. **State the problem:** We are given the exponential population model $$A=886.3e^{0.019t}$$ where $A$ is the population in millions and $t$ is the number of years after 2003. We

1. **State the problem:** Solve the logarithmic equation $$\log_3 (x + 5) = 4$$ and find the exact solution(s), rejecting any values not in the domain. 2. **Recall the definition a

1. **Problem:** Solve for $x$ in the equation $\log_2(x + 3) = 5$. 2. **Formula and rules:** Recall that $\log_b(a) = c$ means $b^c = a$. Here, $b=2$, $a = x+3$, and $c=5$.

1. The problem asks us to evaluate $\log_6 4^8$ without a calculator. 2. Recall the logarithm power rule: $\log_b (a^n) = n \log_b a$.

1. **State the problem:** Determine if the relation given by the set of ordered pairs \((2, 3), (-18, 9), (2, -9), (0, 15)\) is a function. 2. **Recall the definition of a function

1. **State the problem:** We are given a relation as a set of ordered pairs from the table: $$\{(12, -20), (-12, 4), (0, 20), (0, 4)\}$$

1. **State the problem:** We are given the set of ordered pairs \((16, -18), (1, 18), (16, 10), (1, 10)\) and asked whether this relation is a function. 2. **Recall the definition

1. The problem asks whether the given relation is a function. 2. A relation is a function if every input $x$ has exactly one output $y$.

1. **State the problem:** Determine if the relation consisting of the points (19, 18), (19, -8), and (-12, 18) is a function. 2. **Recall the definition of a function:** A relation

1. **State the problem:** Determine if the given relation is a function. 2. **Recall the definition of a function:** A relation is a function if every input (x-value) corresponds t

1. The problem asks whether the given relation \{(-3, 14), (20, 2), (20, 9)\} is a function. 2. A relation is a function if every input (x-value) corresponds to exactly one output

1. The problem is to use the quadratic formula to factor a quadratic expression. 2. Let's consider the quadratic equation $2x^2 - 4x - 6 = 0$.