🧮 algebra

1. **State the problem:** We are given the quadratic equation $$x^2 + f(1)x + f(1) + f(2) = 0$$ and need to prove that $$f(1)^2 \geq 4 f(1) f(2)$$. 2. **Recall the discriminant con

1. **State the problem:** Find the equation of the line passing through the points $(-4, 5)$ and $(-1, -4)$.\n\n2. **Calculate the slope $m$:** The slope formula is $$m = \frac{y_2

1. **State the problem:** Solve the equation $$2^{3x-1} = 5(3^{1-x})$$ and express the answer in the form $$\frac{\ln a}{\ln b}$$ where $$a$$ and $$b$$ are integers. 2. **Rewrite t

1. **State the problem:** Simplify the expressions for $B$, $C$, and $D$, and solve the equations $x^2 = \frac{16}{25}$ and $3x^2 - 108 = 0$. 2. **Simplify $B = \sqrt{486} - 2\sqrt

1. The problem asks for the number of days in September when Kofi had no less than 900. 2. "No less than 900" means Kofi had at least 900, or $\geq 900$.

1. **State the problem:** Kofi's bank balance in September varies according to an absolute value function. He started with 1600, had 100 on the 9th day, and the lowest balance was

1. **State the problem:** Kofi's bank balance in September varies according to an absolute value function. He started with 1600, had 100 on the 9th, and the lowest balance was -900

1. **State the problem:** Harley has 6 pints of lemonade.

1. প্রথম সমস্যাটি হলো: যদি $x + \frac{1}{3x} = 4$ হয়, তাহলে $9x^2 + \frac{1}{x^2}$ এর মান কত? 2. আমরা জানি,

1. **State the problem:** We need to find four consecutive even integers whose sum is -364. We want to find the least (smallest) of these integers. 2. **Define variables:** Let the

1. **State the problem:** We need to find three consecutive integers whose sum is 147. We want to find the least of these integers. 2. **Define variables:** Let the least integer b

1. **State the problem:** We need to find three consecutive odd integers whose sum is 57. 2. **Define variables:** Let the first odd integer be $x$. Since the integers are consecut

1. **State the problem:** We need to find the greatest integer among 4 consecutive odd integers whose sum is 256. 2. **Define variables:** Let the smallest odd integer be $x$. Then

1. **State the problem:** We need to find three consecutive even integers whose sum is 24. 2. **Define variables:** Let the first even integer be $x$. Then the next two consecutive

1. The problem is to find how to set two equations equal to each other. 2. Suppose we have two equations: $y = f(x)$ and $y = g(x)$.

1. **State the problem:** We are given two sets of points in the plane: $$A = \{(x,y) : y = \frac{1}{x}, x \neq 0, x \in \mathbb{R}\}$$

1. **State the problem:** Solve for $x$ in the equation $$(2^{x+1})^x \cdot 2^{1-2x} = 1728.$$\n\n2. **Simplify the expression:** Use the power of a power rule $$(a^m)^n = a^{mn}$$

1. State the problem: Solve the equation $2^{4x} = 16^{2x}$ for $x$. 2. Express 16 as a power of 2: Since $16 = 2^4$, rewrite the right side as $16^{2x} = (2^4)^{2x}$.

1. **State the problem:** We need to solve the simultaneous linear equations using the graph method: $$3x + y = 2$$

1. Calculate $-45 + 55 - (-8)^2$. First, compute $(-8)^2 = 64$.

1. Énoncé du problème : Trouver tous les antécédents de 0 par la fonction $f$ définie par $f(x) = (-4x)(-3x - 6)$. 2. Exprimer $f(x)$ :