🧮 algebra

1. 문제: 일차함수 $y = ax - 3a$의 그래프와 $x$축, $y$축으로 둘러싸인 도형의 넓이가 9일 때, 상수 $a$의 값을 구하시오. (단, $a > 0$) 2. 공식 및 규칙:

1. **Stating the problem:** Solve the system of linear equations given by: $$1x + 6y = 372$$

1. The problem is to simplify the expression $2,5\sqrt{2}$. 2. First, note that the comma in $2,5$ is a decimal separator, so this is $2.5\sqrt{2}$.

1. The problem is to simplify the expression $\frac{5}{\sqrt{2}}$. 2. To simplify a fraction with a square root in the denominator, we multiply numerator and denominator by the con

1. **State the problem:** Solve the equation $-2(4 + 3y) = -2(4)$ for $y$. 2. **Apply the distributive property:**

1. The problem asks to solve the system of three linear equations with three variables: $$\begin{cases} 2x + 3y - z = 7 \\ x + y + z = 8 \\ x + y - z = 0 \end{cases}$$

1. Problem: Given functions $f(x) = 4x - 1$, $g(x) = x^2 - 5$, and $h(x) = 3^x$, find: 1.i. $g(x - 2)$ in simplest form.

1. **State the problem:** Solve for $a$ in the equation $$55 = 25 + \left(\frac{5}{11}\right)^a.$$\n\n2. **Isolate the exponential term:** Subtract 25 from both sides to get $$55 -

1. **State the problem:** Simplify or analyze the expression $$\frac{7x-4}{x+9}$$. 2. **Formula and rules:** This is a rational expression where the numerator is $7x-4$ and the den

1. **State the problem:** Callie was billed 416.48 for car repairs and will pay in 4 equal monthly installments. We want to find the net change in her bank account after each month

1. **Problem statement:** Jack and Jon have a hot dog eating contest. After the first 2 minutes, Jack has eaten 8 hot dogs and Jon has eaten 7 hot dogs. From that point, Jack eats

1. **State the problem:** Expand the expression $ (7x-4)(x+9) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Find the highest common factor (HCF) of 8, 12, and 20 using their factor trees. 2. **Write the prime factorization from the factor trees:**

1. **State the problem:** Simplify the expression $2(x+3) + 1$. 2. **Use the distributive property:** Multiply $2$ by each term inside the parentheses.

1. The problem asks: What does the y-intercept of the line tell you about the situation? 2. The y-intercept of a line on a graph is the point where the line crosses the y-axis. Thi

1. **State the problem:** Simplify the expression $4(-7)-2$. 2. **Apply the multiplication rule:** Multiply 4 by -7.

1. El problema consiste en verificar si las divisiones de monomios dadas son correctas. 2. Recordemos que para dividir monomios:

1. The problem involves solving the equation derived from the proportion and percentage expressions given: $$\frac{80}{x} = \frac{100}{100} \div \frac{25}{100} = \frac{36}{x} \time

1. **State the problem:** A kickball game lasted 11 innings, and 3 pitchers on one team pitched the same amount of innings. We need to find how long each pitcher pitched. 2. **Set

1. **State the problem:** Find the nth term of the sequence 0, -5, -10, -15. 2. **Identify the pattern:** The sequence decreases by 5 each time.

1. The problem involves analyzing the relationship between given $x$ and $y$ values from multiple tables. 2. We start by examining the first table: $x = [-120, -110, -100, -95, -90