🧮 algebra

1. **State the problem:** We are given two odd functions $f$ and $g$ with values at positive $x$ given in a table. We need to find the value of the composition $(f \circ g)(-1)$, w

1. The problem asks for the turning point of the quadratic function $f(x) = x^2 - 3x + 4$ after three transformations: reflection in the x-axis, horizontal shift 2 units right, and

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n} = 10$$ and find the value of $n$. 2. **Write the formula and rules:** The expression is a fraction wher

1. **State the problem:** Find the value of the expression $$8 + 6 \div 2(3)^2 - 5$$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** We need to write an equation for the cost $y$ to rent a kayak, which is proportional to the number of hours $x$ rented. 2. **Understand the proportionalit

1. **Problem Statement:** Find the domain, even or odd degree, leading coefficient, number of turning points, least possible degree, number of real zeroes, y-intercept, end behavio

1. **State the problem:** Factor the quadratic expression $6x^2 - 7x - 3$. 2. **Recall the factoring method:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Solve the system of linear equations using Gaussian elimination: $$\begin{cases} 2x_1 + 4x_2 + 5x_3 = 7 \\ x_1 + 3x_2 + x_3 = 10 \\ 3x_1 + 5x_2 + 3x_3 = 2

1. **State the problem:** Simplify or understand the expression $$(x^3 + 2x)^{37}$$. 2. **Formula and rules:** This is a binomial expression raised to a power. The binomial theorem

1. **State the problem:** Factor the cubic polynomial $$x^3 - 6x^2 - 7x$$. 2. **Recall the factoring formula and rules:**

1. Pernyataan masalah: Diberikan relasi rekursif non homogen $$a_{n-1} = 2a_n + 4^n$$ dengan syarat awal $$a_1 = 3$$, dan diminta menyelesaikannya menggunakan fungsi pembangkit. 2.

1. The problem is to simplify or evaluate the expression $3x - 1$. 2. This is a linear algebraic expression where $3x$ means 3 times the variable $x$, and then subtract 1.

1. **State the problem:** Simplify the expression $3x - 1$ or evaluate it for a given value of $x$. 2. **Understand the expression:** The expression $3x - 1$ is a linear algebraic

1. The problem states the identity $a^2 - b^2 = (a - b)(a + b)$. 2. This is a difference of squares formula, which says that the difference between two squares can be factored into

1. The problem asks for the end behavior of the polynomial function $$p(x) = 4x^8 - 6x^7 + 3x^3 - 10.$$\n\n2. To determine end behavior, focus on the leading term of the polynomial

1. **State the problem:** Solve the quadratic equation $$-6x^{2} + 17x - 5 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^{2} + bx + c = 0$$ is

1. **Problem Statement:** Simplify the expression $9x^5 y^2 x - 2x^{-2} y^{-2}$. 2. **Recall the laws of exponents:**

1. **State the problem:** Simplify the expression $9x^5 y^2 \times (-2x)^{-2} y^{-2}$. 2. **Recall the rules:**

1. **State the problem:** We are given the simultaneous equations:

1. **State the problem:** Simplify the expression $9 x^{5} y^{2} x - 2 x^{-2} y^{-2}$. 2. **Rewrite the expression:** Combine like bases with exponents where possible.

1. The problem is to find the equation of a line with a given gradient (slope) of $-2$. 2. The general formula for the equation of a line in slope-intercept form is: