🧮 algebra

1. **State the problem:** Simplify the expression $$(5a^2 - 6 + 9)(2a - 3) - (2a^2 - 5a + 4)(5a + 1).$$ 2. **Simplify inside parentheses:**

1. Find the equation of the line passing through the points (2,7) and (5,−13). Step 1: State the problem.

1. **State the problem:** Find the domain and range of the piecewise function: $$q(x) = \begin{cases} \sqrt{x+3} & \text{if } -3 \leq x < 1 \\ |x-2|+1 & \text{if } 1 \leq x \leq 5

1. The problem is to solve a math question suitable for class 8. Since no specific problem was given, let's consider a common algebra problem: Solve for $x$ in the equation $2x + 3

1. **State the problem:** Simplify the expression $-8 - 3 + 8 + (-3)$. 2. **Rewrite the expression:** $-8 - 3 + 8 - 3$.

1. **State the problem:** Simplify the expression $1 - \left(-3\right) - 5$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. S

1. Stating the problem: Simplify the expression $5 + (-11) - (-11)$.\n\n2. Recall the rules: Adding a negative number is the same as subtracting the positive number, and subtractin

1. **State the problem:** Simplify the expression $-1 - 3 - (-9) + (-5)$. 2. **Recall the rules:** Subtracting a negative number is the same as adding its positive counterpart, so

1. **State the problem:** Simplify the expression $-5 - 15 + 4 + 15$. 2. **Combine like terms:** Group the negative and positive numbers separately.

1. Stating the problem: Simplify the expression $$\frac{16x^2 y - x^5 y^3}{x^2 y}$$. 2. Write the expression as a single fraction:

1. **State the problem:** Simplify the expression $6 + 2 - \left(-1\right) + \left(-8\right)$. 2. **Recall the rules:** Subtracting a negative number is the same as adding its posi

1. **State the problem:** Simplify the expression \(\frac{16x^2y - x^5 y^3}{x^2 y} - \frac{9d^6 e^5 - 15d^7 e^3 + 12 d^8 e^4}{3 d^3 e^2}\). 2. **Simplify the first fraction:**

1. **State the problem:** Simplify the expression $19 - 11 + (-17) + (-19) + 11$. 2. **Recall the rules:** Adding a negative number is the same as subtracting its positive counterp

1. **Problem statement:** Given a function $f(x)$ with domain $[0,8]$ and range $[-2,5]$, find the domain and range of the following functions: (a) $g(x) = f(x+2) - 3$

1. Bài toán yêu cầu tìm giá trị của tham số $m$ sao cho hai phương trình $$x^2 - x + m = 0 \quad (1)$$ và $$x^2 - mx - 1 = 0 \quad (2)$$ có nghiệm chung. 2. Giả sử $x = \alpha$ là

1. **Problem statement:** Given a function $f(x)$ with domain $[-2,5]$ and range $[1,4]$, find the domain and range of the following functions: (a) $g(x) = f(x-3) + 1$

1. **State the problem:** Given a function $f(x)$ with domain $[1,9]$ and range $[-3,6]$, find the domain and range of the function $g(x) = 3f(x)$.\n\n2. **Recall the domain and ra

1. **State the problem:** Given that $3+2i$ is a root of a polynomial equation with real coefficients, find the other root(s). 2. **Important rule:** For polynomials with real coef

1. **State the problem:** Factor the expression $2n^2 - 8$.

1. **State the problem:** We have a logistic growth model for the cat population given by $$P(t) = \frac{84}{1 + 11e^{-0.07t}}$$ where $t$ is time in weeks and $P(t)$ is the popula

1. **Problem statement:** The population of gnomes grows exponentially. Initial population $P_0=7$. After 3 years, population $P(3)=12$. We need to find: