🧮 algebra

1. **State the problem:** We need to find the average rate of change in the number of students at the university from 1989 to 2014. 2. **Identify the given values:**

1. **State the problem:** Find the maximum and minimum points of the function $$f(x) = x^3 + 3x^2 - 4x$$ and describe its graph. 2. **Find the derivative:** To find critical points

1. **State the problem:** Find the polynomial function with zeros at $-3$, $1$, and $2$. 2. **Recall the fact:** If a polynomial has zeros at $a$, $b$, and $c$, then the polynomial

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square, which can be written as $x \times x$.

1. Tentukan determinan dari matriks-matriks berikut. **a.** Matriks $\begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square, which can be written as $x \times x$.

1. **State the problem:** We are given the parametric equations $x = 3 \cos t$ and $y = 4 \sin t$ and need to find the Cartesian equation relating $x$ and $y$ without the parameter

1. **State the problem:** We have three functions and need to identify their graphs based on given points and equations. 2. **Function 1:** Given points are $x = -2, -1, 0, 1$ and

1. **State the problem:** We have three functions with given information and need to identify their graphs. 2. **Function 1:** It is an exponential function with points:

1. **State the problem:** We are given a function $g$ as a set of points and a linear function $h(x) = 6x + 13$. We need to find the inverse values and compositions as follows: 2.

1. Diberikan persamaan eksponensial: $$6^{2x-1} - 1 = 6^{x-1}$$ 2. Tambahkan 1 ke kedua sisi agar lebih mudah: $$6^{2x-1} = 6^{x-1} + 1$$

1. The problem is to solve the inequality relation $y \le x + 2$. 2. This inequality means that for any value of $x$, the value of $y$ must be less than or equal to $x + 2$.

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square, which means it can be written as the product of $x$ and $x$.

1. The problem is to factor the expression $x^2 - 4$. 2. Recognize that $x^2 - 4$ is a difference of squares since $4 = 2^2$.

1. The problem is to simplify the expression $Y \lex + 2$. 2. It appears there might be a typo or unclear notation in the expression, as $\lex$ is not a standard mathematical opera

1. The problem is to simplify the expression $Y \lex + 2$. 2. However, the expression contains a term $\lex$ which is not a standard mathematical symbol or variable. Assuming it is

1. The problem involves a sequence of monthly deposits starting at 500000 and increasing by 100000 each month. 2. We identify the sequence as an arithmetic sequence with first term

1. Stating the problem: Solve the inequality $$3a^2 + 15a < 2(a + 5)$$. 2. Expand the right side: $$2(a + 5) = 2a + 10$$.

1. The problem asks us to find a polynomial function with zeros at $-3$, $1$, and $2$. 2. Recall that if a polynomial has zeros at $r_1$, $r_2$, and $r_3$, then it can be written a

1. **State the problem:** We have three painters: Alice, Bob, and Charlie, with rates $A$, $B$, and $C$ houses per hour respectively. 2. **Given information:**

1. The problem is to solve the inequality $-285 < -15r$ for $r$. 2. To isolate $r$, divide both sides of the inequality by $-15$. Remember, dividing by a negative number reverses t