🧮 algebra

1. The problem asks to analyze the conditions when $x,y$ are positive and when $x,y$ are real integers. 2. For the case when $x,y$ are positive, we consider $x>0$ and $y>0$.

1. The problem is to understand how the total number of pairs is calculated when given points (-7,0) and (7,0). 2. Each point represents a pair of coordinates in the form $(x,y)$.

1. The problem states: Find the number of unordered pairs $(x,y)$ such that $x^2 - y^2 = 49$. 2. Rewrite the equation using the difference of squares factorization:

1. The problem is to find the square root of 49. 2. Recall that the square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. Vi starter med å skrive oppgaven: Løs likningen $$4x + (3x + 1) = 6 - 2(x + 1)$$. 2. Først fjerner vi parentesene på begge sider. På venstre side er det bare en parentes uten fo

1. The problem asks for the number of unordered pairs $(x,y)$ such that $x^2 - y^2 = 81$. 2. First, rewrite the equation using the difference of squares factorization:

1. **State the problem:** We have a 1-pound mixture of two types of rice costing 10 and 30 per pound respectively. The average cost of the mixture is 24 per pound. We need to find

1. **State the problem:** We have a polynomial $$f(x) = 2x^3 + ax^2 + bx - 6$$ and we know the remainders when divided by $$x-1$$ and $$x+4$$ are 12 and -18 respectively. We need t

1. The problem states that $x-1$ is a factor of the polynomial $f(x) = x^3 + kx^2 + 3x + 10$. We need to find the value of $k$ and then factorize the polynomial completely. 2. Sinc

1. **State the problem:** We are given that the polynomial $f[x] = 6 - x - x^2$ is a factor of $g[x] = ax^3 + 5x^2 + bx - 18$. We need to find the constants $a$ and $b$, and then f

1. **State the problem:** We have a polynomial $$f(x) = 4x^3 - 4x^2 - x - k$$ where $$k$$ is a constant. Given that $$x-1$$ is a factor of $$f(x)$$, we need to find the value of $$

1. **State the problem:** We are given that $x^2 - x - 6$ is a factor of the polynomial $f(x) = 3x^3 + px^2 + qx - 6$. We need to find the constants $p$ and $q$ and then find the z

1. **State the problem:** Solve the equation $e^{2x} = \frac{1}{2}$ for $x$. 2. **Rewrite the equation:** We have $e^{2x} = \frac{1}{2}$.

1. The problem involves understanding the polyline graph connecting the points with values 20, 10, 40, 46, and 38. 2. The polyline starts at 20, moves up to 10, then horizontally t

1. **State the problem:** Simplify the expression $$\frac{1}{7}+\frac{2}{3}+(\binom{1}{2}-2)x^2$$. 2. **Evaluate the binomial coefficient:** Recall that $$\binom{n}{k} = 0$$ if $$k

1. **Problem 8:** Describe the transformations for each graph from $y=f(x)$. - a) $y=f(x+4)$ shifts the graph of $f(x)$ 4 units to the left.

1. **State the problem:** Given the equations $x^2 = b - ax$ and $x^3(x^3 + c) = d$, find which values of $c$ and $d$ satisfy these conditions. 2. **Rewrite the first equation:** F

1. Problem 8: Describe the transformations for each graph based on $y=f(x)$. a) $f(x+4)$ shifts the graph of $f(x)$ 4 units to the left.

1. **Problem 8:** Describe transformations of the graph $y = f(x)$ for each case. a) $f(x + 4)$ shifts the graph of $f(x)$ **4 units to the left**.

1) Développer et réduire : - Pour $A = -2(2x - 3)$ :

1. The problem is to evaluate the expression $25 - 25 \div 5 \times 5$. 2. According to the order of operations (PEMDAS/BODMAS), division and multiplication are performed before su