🧮 algebra

1. **State the problem:** Fully simplify the expression $$9d + 5n - 6d - 2n + 11 - 11 - 3d$$. 2. **Group like terms:** Group the terms with $$d$$, $$n$$, and the constants separate

1. **State the problem:** We need to write an expression for the perimeter of a triangle with two sides labeled $4y$ and one side labeled $3y$. 2. **Identify the sides:** The trian

1. The problem asks which statement is true about the polynomial function given its graph. 2. The graph has two real zeros at approximately $x = -2$ and $x = 2$.

1. Énoncé du problème : Nous devons réduire les expressions suivantes : X = -x + 3n - 5o

1. The problem is to simplify the expression $_x + 3x_5x$. 2. The expression likely means: $_x + 3x - 5x$ (assuming _ denotes a subtraction sign or misplacement).

1. **Problem Statement:** Solve the system of linear equations using (i) Cramer's rule and (ii) Gauss elimination, then sketch given functions and express the volume of an open box

1. First, let's clarify what it means to "satisfy i." Commonly, in mathematics, especially in complex numbers, the imaginary unit $i$ is defined by the property that $$i^2 = -1.$$

1. The problem is to determine if each point satisfies the inequality $x + 3y > 3$. Check each point:

1. **State the problem:** We are given the quadratic expression $$(x-2)(x+4)$$ and need to find its vertex and y-intercept without graphing. 2. **Expand the expression:** Use the d

1. The problem is to graph the equation $y = x + 4$. 2. This is a linear equation with a slope of 1 and a y-intercept at $(0, 4)$, meaning the line crosses the y-axis at 4.

1. The user asked for examples of graphic polynomial functions. 2. A polynomial function is a function of the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$$ where ea

1. Stating the problem: We need to solve $$(x-2)^2 = 9$$ using the factorization method. 2. Start by rewriting the equation: $$(x-2)^2 - 9 = 0$$.

1. The problem is to solve an equation or simplify an expression using the factorization method. 2. Factorization involves expressing the given expression as a product of its facto

1. The problem involves understanding and analyzing polynomial functions, which are expressions involving variables raised to whole number powers combined by addition, subtraction,

1. Problem: Convert Luca's walking speed from $5 \frac{14}{1}$ km/hr to m/s. Since $5 \frac{14}{1}$ is ambiguous, interpret as $5 \frac{14}{1} = 5+14=19$ km/hr.

1. The problem states that the square of $(x-2)$ equals 9. This can be written as the equation $$ (x-2)^2 = 9.$$ 2. To solve for $x$, first take the square root of both sides. Reme

1. Stating the problem: Simplify the expression $$\frac{\sqrt{3}}{3} \times \sqrt{2} - 2 \times \sqrt{3}$$. 2. Multiply the terms in the first part: $$\frac{\sqrt{3}}{3} \times \sq

1. The problem is to find the conjugate of the expression $$-3 + 8\sqrt{6}$$. 2. The conjugate of a binomial expression of the form $$a + b$$ is $$a - b$$.

1. **Problem Statement:** Given the polynomial $$P(x) = (x + 2)^2 (x + 3)^3 (x - 1)^4 (2x + 1),$$ Find the leading term, leading coefficient, degree, constant term, y-intercept, x-

1. The problem asks to find $\log_8 8^2$. 2. Recall that the log of a power, $\log_b (a^n)$, can be simplified using the power rule of logarithms:

1. Määritellään tehtävä: Laske positiivisten kokonaislukujen summa, jotka ovat pienempiä kuin annettu luku $n$. 2. Jos $n$ on esimerkiksi 5, pienemmät positiiviset kokonaisluvut ov