🧮 algebra

1. Soal: Cari limit dari $$\lim_{y \to -2} \left(\frac{4y^3 + 8y}{y + 4}\right)^{1/3}$$. 2. Gunakan Teorema Limit Biasa: Jika fungsi-fungsi di dalamnya kontinu pada titik limit, ma

1. Problem 8a: Solve $\log_{10} x = 2$. Formula: $\log_b a = c \implies a = b^c$.

1. The problem is to convert the fraction $\frac{1}{4}$ to a decimal. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator.

1. **Problem:** Show that the function $f(x) = x^2 - \cos x$ is an odd function. 2. **Definition:** A function $f$ is odd if $f(-x) = -f(x)$ for all $x$.

1. **Problem:** Determine if the ISBN number 978-1-4116-8691-5 is valid. 2. **Formula and rules:** ISBN-13 validation uses the formula:

1. **State the problem:** We need to write the equation of the ellipse given by $$9x^2 + 4y^2 = 36$$ in standard form. 2. **Recall the standard form of an ellipse:** The standard f

1. The problem is to create the graph of a function of the form $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general formula for an exponential function is:

1. **Problem Statement:** We have a company's cost function $C = 2x + 100$ and revenue function $R = 5x$. We need to graph both functions and find the break-even point.

1. **Stating the problem:** We are given the equation $$9x^2 + 4y^2 = 36$$ and asked to identify which of the given options matches this equation when rewritten in the standard for

1. **Problem Statement:** Complete the table for the function $f(x) = -2x^2 + 5x + 3$ for the domain $-2 \leq x \leq 5$ and determine the two roots of the quadratic equation.

1. **State the problem:** Solve for $X$ in an equation (the equation is not provided, so we assume a general approach). 2. **General formula and rules:** To solve for $X$, isolate

1. The problem is to solve the quadratic equation $x^2 - 4x - 42 = 0$ using the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to complete the table for the function $$f(x) = -2x^2 + 5x + 3$$ for the domain $$-2 \leq x \leq 5$$. 2. **Recall the function:** $$f(x) = -2x^2 +

1. The problem is to solve the given question step-by-step clearly and understandably. 2. Since the user did not specify a particular math problem, I will demonstrate a general app

1. The problem asks to expand the expression $2\log_4(X+4)$.\n\n2. Recall the logarithm power rule: $a\log_b(c) = \log_b(c^a)$. This means we can rewrite the coefficient 2 as an ex

1. The problem is to simplify the fraction $\frac{3}{6}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD).

1. Problem: Reduce the fraction $\frac{2}{4}$ to its lowest terms. 2. Formula: To reduce a fraction to its lowest terms, divide the numerator and denominator by their greatest comm

1. **Problem Statement:** Prove that the product $n(n+1)(n+2)$ is divisible by 3 for all integers $n > 1$ using the principle of mathematical induction. 2. **Induction Principle:**

1. The problem is to solve the inequality $\frac{m}{5} \geq 7$. 2. To isolate $m$, multiply both sides of the inequality by 5. Since 5 is positive, the inequality direction remains

1. **State the problem:** Simplify the expression $$\frac{\left(\frac{1}{2}\right)^x \cdot 8^x}{4^x}$$. 2. **Recall the laws of exponents:**

1. Masalah: Jumlah umur kakak dan dua kali umur adik adalah 27 tahun, dan selisih umur kakak dan adik adalah 3 tahun. Jika umur kakak adalah $x$ tahun dan umur adik adalah $y$ tahu