🧮 algebra

1. **State the problem:** We have two linear functions, Function A: $y=4x+3$ and Function B, which passes through points near $(-10,-10)$ and $(10,10)$, indicating it is the line $

1. The problem is to find the slope $m$ of the line passing through the points $(-7,7)$ and $(7,-7)$. 2. The formula for slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

1. **Problem:** Write an equation that represents the total cost $y$ for $x$ GB of data given a fixed fee of 10 plus 3 per GB. 2. **Formula:** The total cost $y$ can be expressed a

1. **State the problem:** Simplify the expression $$\left[\sqrt{s-1} + \ln \sqrt{s^{2} - 1^{2}}\right]^{-1}$$. 2. **Rewrite the expression inside the logarithm:** Note that $$1^{2}

1. Stating the problem: Solve the equation $\log_{2x}(4) = \log_x(2)$.\n\n2. Recall the change of base formula for logarithms: $\log_a b = \frac{\log b}{\log a}$. We will use natur

1. **State the problem:** Solve the quadratic equation $$10x^2 + x + 3 = 6$$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. **State the problem:** Solve the quadratic equation $$4q^2 + q + 1 = -3q$$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. **Постановка задачі:** Дано натуральне число $n > 1$. Потрібно знайти найменшу кількість натуральних чисел, факторіали яких у сумі дорівнюють $n! - 1$.

1. The problem is to understand the ratio $7 : 5 : 8$ and what it represents. 2. A ratio compares quantities to each other, showing their relative sizes.

1. **State the problem:** Solve the equation $$\sqrt{x} - 2 = \sqrt{x} 2x + 1$$. 2. **Rewrite the equation for clarity:** The equation is $$\sqrt{x} - 2 = 2x\sqrt{x} + 1$$.

1. **State the problem:** Simplify the expression $\frac{41}{49} \div \frac{1}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying

1. The problem is to analyze the system of linear equations from set 7: $$y = -\frac{1}{2}x - 2$$

1. The problem asks which logarithm property is demonstrated by the equation $5^{109-5-10939} = 1098$. 2. Let's clarify the properties of logarithms:

1. The problem asks which logarithm property is demonstrated by the equation $$109g8 + 1096 = 109g48$$. 2. First, let's rewrite the equation in a clearer form assuming the notation

1. **State the problem:** Prove by mathematical induction that for all positive integers $n$, $$1 + 4 + 4^2 + \cdots + 4^n = \frac{1}{3}(4^{n+1} - 1)$$

1. **Problem statement:** Given the sequence 5, 11, 17, 23, 29, find: (a) the expression for the nth term,

1. **State the problem:** Factor out the greatest common factor (GCF) from the expression $$18m^6 - 12m^2$$. 2. **Identify the GCF:**

1. **Solve the first system of inequalities:** Given:

1. **Stating the problem:** We have the charge formula for a repair:

1. **State the problem:** Solve the equation $19l - 57 = 19$ for $l$. 2. **Add 57 to both sides** to isolate the term with $l$:

1. The problem asks to find the value of $Q$, which represents the number of hours Khan worked overtime at double time. 2. To solve this, we need the formula relating total income,