🧮 algebra

1. **State the problem:** We need to find which expression among F, G, H, and J is equivalent to $1000 + 196$. 2. **Calculate the sum:**

1. Let's evaluate each expression step-by-step. 2. Evaluate $25 - 3^4$:

1. **Stating the problems:** - Problem 1: Find the value equivalent to the expression shown (options: 19, -11, 7, -14).

1. **State the problem:** We need to find which expressions are equivalent to the given sums.

1. **State the problem:** Evaluate the numeric expression $$5^2 - 6(4^2 - 10) - 3$$ and find which value among (A) 19, (B) -11, (C) 7, (D) -14 is equivalent. 2. **Recall the order

1. **State the problem:** Evaluate the expression $5 - 2(3)^2 + 4$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition

1. **State the problem:** We want to find the amount Rosa saves out of 100 dollars, given a ratio table of dollars saved to dollars earned. 2. **Given data:**

1. **State the problem:** Vista pickleball team needs to win 3 out of 15 games. We want to find what percent this represents, which means finding an equivalent ratio with a denomin

1. **State the problem:** Factor the expression $$p^{12}q^{2} - p^{3}q^{6}$$. 2. **Identify the greatest common factor (GCF):**

1. **State the problem:** We need to write a linear function that represents the total cost $y$ of a charity gala based on the number of attendees $x$. 2. **Identify the components

1. **State the problem:** A florist needs 12 roses for each round table and 36 roses for a centerpiece. We want to write an equation for the total number of roses $y$ depending on

1. **Problem:** Simplify the expression $6^7 \cdot 6^9$ and verify if it equals $6^{16}$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $$a^m \cdot

1. **State the problem:** Solve the equation $$15y + 5y^3 + 3y^5 = 5x^3$$ for $y$ in terms of $x$. 2. **Rewrite the equation:**

1. The problem involves simplifying expressions with rational exponents and radicals. 2. Recall the key rule: $$a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$$ where $a$ is the

1. **State the problem:** Solve the equation $$(1 + \ln x)^2 = 0$$ for $x$. 2. **Understand the equation:** The square of a quantity equals zero only if the quantity itself is zero

1. **Stating the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$ using the laws of exponents. 2. **Formula and rules:**

1. **State the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$. 2. **Recall the laws of exponents and division:** When dividing powers with the same base, subtract the e

1. The problem involves applying the laws of exponents to simplify expressions. 2. Recall the key exponent rules:

1. **State the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$ using the laws of exponents. 2. **Recall the laws of exponents:**

1. Das Problem ist, ein Gleichungssystem mit der Methode des Gleichsetzens zu lösen. 2. Die Methode des Gleichsetzens besteht darin, beide Gleichungen nach derselben Variablen aufz

1. **Problem statement:** We have two wine packages with different numbers of bottles and total prices. We want to find the price of one bottle of red wine and one bottle of white