🧮 algebra

1. **State the problem:** Solve the inequality $$\left(\frac{2}{3}\right)^{5x+2} > \left(\frac{3}{2}\right)^{2x}$$. 2. **Rewrite the right side with a common base:** Note that $$\f

1. **State the problem:** Solve the inequality $$4^{x + 2} < 8^{2x}$$ using properties of exponential inequalities. 2. **Rewrite bases with the same base:** Note that $$4 = 2^2$$ a

1. **State the problem:** Solve the inequality $$4^{2x + 7} \leq 32^{2x - 3}$$. 2. **Rewrite bases as powers of 2:**

1. State the problem: Solve the inequality $$\left(\frac{2}{5}\right)^{5x-1} \geq \frac{25}{4}$$. 2. Rewrite the right side with base $$\frac{2}{5}$$:

1. Problem: Find the percent increase in oil price when it changed from ₱30.00 to ₱31.35 per liter. 2. Calculate the increase in price:

1. To explain why the numbers 4 and 2 appear in step 5, we need to look at the problem context where these values come from. 2. Usually, 4 and 2 could be coefficients or constants

1. Problem 12: Find the sum to infinity of the series $$3 - 2 + \frac{4}{3} - \frac{8}{9} + ...$$ 2. Identify the pattern in the series:

1. The problem asks us to graph the function where the output is the greatest integer less than or equal to $\frac{1}{3}x$. 2. This function is written as $y=\left\lfloor \frac{1}{

1. Let's clarify the problem: finding the interval refers to determining the domain or range of a function or solving inequalities to find values where certain conditions hold true

1. Soal a: Diberikan fungsi komposisi \((g \circ f)(3)\). Untuk menyelesaikannya, kita perlu mengetahui fungsi \(f(x)\) dan \(g(x)\). Namun soal ini belum menyediakan fungsi ekspli

1. Problem: Find the value of the infinite series starting with $3 - 2 + \frac{4}{3} - \frac{8}{9} + ...$ corresponding to the given multiple-choice answers. Step 1: Observe the pa

1. The problem states the equation $1.73 = 4$. 2. We observe that this is a false statement since the decimal number $1.73$ does not equal the integer $4$.

1. Problem 1: $\dfrac{x^2}{16} - \dfrac{y^2}{25} = 1$ - This is a hyperbola centered at the origin with transverse axis on the x-axis.

1. The first function given is $f(x) = \sqrt{7x - 10} - 1$. 2. The second function given is $m(x) = \sqrt[3]{8x - 1} - 4$.

1. The problem is to plot the graph of the highest integer step function, also known as the ceiling function. 2. The ceiling function, denoted as $y=\lceil x \rceil$, maps any real

1. Problem 3: Solve the system of inequalities $$4x + 8y \leq 640;

1. **State the problem:** We are given several matrices A, B, C, D, and E and asked to find their order (dimensions).

1. State the problem: Simplify the expression $6^2 - \left[\frac{2 + 2 \times 3^2}{10}\right]$. 2. Evaluate the exponents first:

1. The problem is to graph the function $y=(-2x+1)^3-6$. 2. This is a cubic function with a transformation. The base cubic function is $y=x^3$.

1. **State the problem:** Paul uses some number of trays A, B, and C to bake a total of 378 donuts. Tray A has 9 donuts, Tray B has 3 donuts, and Tray C has 6 donuts.

1. Diketahui fungsi $f(x) = x + 3$ dan $g(x) = 3x - 5$. Tentukan: 1.a. Cari invers fungsi $f^{-1}(x)$ dan $g^{-1}(x)$.