🧮 algebra

1. **Problem:** Simplify the expression $$-3\Big[\frac{1}{2}(4a - 6b + 2c) - \frac{1}{3}(33 - 9b + 6c)\Big] + (a - b - c)$$. 2. **Distribute inside the brackets:**

1. **Problem 1: Identify the true statement about exponential functions.** - Exponential functions have the general form $$f(x) = a^x$$ where $$a$$ is a positive constant base (not

1. Let's state the problem: A student spends $\frac{1}{4}$ of his money on a book and $\frac{1}{3}$ on a shirt. We need to find the remainder (the fraction of money left).

1. Stating the problem: Solve the equation $$e^{2s+5} = 1$$ for $$s$$. 2. Recall that the exponential function $$e^x = 1$$ if and only if $$x = 0$$.

1. We are asked to find the value of the exponent in the expression $ (5^4)(5^{-10}) $. 2. Recall the exponent multiplication rule: When multiplying like bases, add the exponents.

1. Let's classify the equation $2^2 (400^{x+1}) = 80$. An exponential function has the form $f(x) = a^x$, and an exponential equation involves expressions with variables in the exp

1. We are given the equation $$8^{2p+1} = 8^{5p+3}$$ and asked to find the value of $p$. 2. Since the bases are the same (base 8) and the equation is equal, the exponents must be e

1. Problem 25: In a bag of oranges, the ratio of good ones to bad ones is 5:4. The number of bad oranges is 36. Find the total number of oranges. Step 1: Let the common ratio facto

1. The problem states that the number of bacteria $B$ is given by the formula $$B = 50 \cdot 10^{d/2}$$ where $d$ is the number of days. 2. We want to find the number of days $d$ w

1. Simplify the expression $$\frac{3}{x} + \frac{5}{y}$$ by finding common denominators or write as is. 2. Combine $$\frac{3}{8p^2 r} + \frac{5}{4p^2 r}$$:

1. **Problem Statement:** We are given the function describing the amount of medication in Carlos's bloodstream over time: $$M(t) = 20 \cdot e^{-0.8t}$$. We want to find the time $

1. **State the problem:** Find the domain and range of the function $f(X) = \frac{1}{X} - 2$. 2. **Find the domain:** The function involves division by $X$. Division by zero is und

1. To find the domain and range, we need the function or expression first. 2. The domain is the set of all input values ($x$) for which the function is defined.

1. The problem is to understand and analyze the function given by $$f(x)=\frac{1}{x-2}$$. 2. This function is a rational function where the numerator is 1 and the denominator is $x

1. Given the function $f(x) = \sqrt{x-3}$, we need to find its domain and range. 2. **Domain:** Since the expression inside the square root must be non-negative (\geq 0) for the fu

1. **Problem:** Write the permutation cycle of vertices for a cube rotated $90^\circ$ around an axis through opposite faces. 2. **Step 1:** Identify the four corners around the axi

1. \( -8(8a - 3) = -64a + 24 \) after distribution. 2. Simplify \( 3(x + 3x^2) - 5(x^2 - 3x) = 3x + 9x^2 - 5x^2 + 15x = 3x + 9x^2 - 5x^2 + 15x = 18x + 4x^2 \).

1. Let's create a question involving solving a quadratic equation. Problem: Solve for $x$ in the quadratic equation $$x^2 - 5x + 6 = 0$$.

1. State the problem: Solve the system of equations: $$-4x - y = -2$$

1. **Problem Statement:** We have a café charging customers based on the number of drinks ordered where $d$ is the number of drinks and $B(d)$ is the total bill. The function $B(d)

1. Stating the problem: Calculate the values of each given algebraic expression step-by-step. 2. For expression $E= \frac{5}{18} \times (-3) \times \frac{12}{20}$: