🧮 algebra

1. **State the problem:** We are given the first four terms of a geometric progression (GP): 1250, 250, 50, 10. We need to find:

1. **State the problem:** Calculate the value of $-45 - (-30)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. So, $a - (-b)

1. **Problem statement:** We have three sequences and three expressions. We need to associate each sequence with its correct general term (term of order $n$). 2. **Sequences given:

1. Stwierdzenie problemu: Sprawdzimy, czy podane przekształcenia wyrażeń algebraicznych są poprawne. 2. Dane wyrażenia to:

1. **Problem:** Simplify the expression $$\frac{4}{3}$$. 2. **Formula and rules:** This is a simple fraction already in simplest form.

1. Simplify $\frac{8^8}{8^4}$. Use the rule $\frac{a^m}{a^n} = a^{m-n}$.

1. The problem asks us to translate the graph of the parent function $y = x^3$ to the graph of $y = (x + 1)^3 - 4$. 2. The parent function is $y = x^3$, which is a cubic curve pass

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.