🧮 algebra

1. **State the problem:** Find the sum of the arithmetic series (A.S) 25 + 21 + 17 + ... + (-23). 2. **Identify the first term ($a_1$), common difference ($d$), and last term ($a_n

1. The problem is to find the sum of the arithmetic sequence: 1, -2, -5, -8, ..., -236. 2. Identify the first term $a_1 = 1$ and the common difference $d = -2 - 1 = -3$.

1. **State the problem:** We are given an arithmetic progression (A.P.) with first term $U_1 = -26$, common difference $d = 2$, and the sum of the first $n$ terms $S_n = 324$. We n

1. **State the problem:** We are given an arithmetic progression (A.P.) with first term $A_1 = -17$, fifth term $A_5 = 2$, and the sum of all terms is 40. We need to find the total

1. The problem states that the store made a $900 sale in the first month and plans to increase sales by $600 each month for 11 months. 2. We need to find the total sales during the

1. Problem: Find $\cos \frac{\pi}{2}$.\nStep 1: Recall that $\cos \frac{\pi}{2} = 0$.\nAnswer: (a) 0\n\n2. Problem: Determine the quadrant for angles between $\frac{3\pi}{2}$ and $

1. **State the problem:** We need to find the rate of simple interest given the principal amount, the amount after 4 years, and the time period. 2. **Identify the known values:**

1. **State the problem:** We are given the equation $\sqrt{k - x} = 58 - x$ where $k$ is a constant. The equation has exactly one real solution. We need to find the minimum possibl

1. **Simplify powers and expressions:** - Simplify expressions like $3^5 \cdot 3^{-9}$ and $(m^2)^{-6}$.

1. State the problem: Solve for $x$ in the equation $$2^{3x-1} + 4 = 36$$. 2. Isolate the exponential term by subtracting 4 from both sides:

1. **State the problem:** Simplify the expression $$\frac{2y^2 - 3xy - 2x^2}{4y^2 - x^2}$$. 2. **Factor the numerator:**

1. Let's denote Mrs. Achieng's salary as $S$. 2. She spends $\frac{1}{5}$ of her salary on rent, so the amount spent on rent is $\frac{1}{5}S$.

1. **State the problem:** We need to express $x$ in terms of $y$ from the equation $$3x - 2y + 3 = 0.$$\n\n2. **Isolate the term with $x$:** Move the terms involving $y$ and consta

1. **State the problem:** Solve the system of equations: $$2x + y = 7$$

1. The problem states that in a code, CAT = DBU. 2. We need to find the code for DOG based on the same pattern.

1. Let's start by defining what we mean by "good x" and "good y." Typically, these terms refer to variables or quantities that have a positive or beneficial relationship in a given

1. Problem 6: Given \(g(x) = x^3\) and \(F(x) = \frac{1}{x - 4}\), evaluate \(F(g(x))\) and find its domain. 2. To find \(F(g(x))\), substitute \(g(x)\) into \(F(x)\):

1. The problem asks to find the value of the expression $10 - a$ when $a = 3$. 2. Substitute $a = 3$ into the expression:

1. The problem is to graph the function $f(x) = 5x^4 - 13$. 2. This is a polynomial function of degree 4, which means it is a quartic function.

1. The problem asks us to find the value of $10 - a$ when $a = 3$. 2. Substitute $a = 3$ into the expression: $10 - 3$.

1. **State the problem:** We are given that the sum of two alternate numbers is 16, and we need to find these numbers. 2. **Define variables:** Let the first number be $x$. Since t