🧮 algebra

1. The problem is to calculate $16$ divided by $-2$, and then divide the result by $2$. 2. First, divide $16$ by $-2$:

1. The problem is to divide 0.8 by -2. 2. Write the expression as a fraction: $$\frac{0.8}{-2}$$.

1. Stating the problem: Calculate the value of $\frac{-1000}{-10}$.\n\n2. Simplify the division: Dividing a negative number by another negative number results in a positive number.

1. **State the problem:** Write each expression as a single power of 4. 2. **Recall:**

1. **State the problem:** We need to find the smallest value of the expression $$n + \frac{100}{n}$$ where $n$ is a positive real number. 2. **Rewrite the expression:** The functio

1. The problem is to find the smallest value (minimum) of the quadratic expression $$n^2 - 5n + 1$$. 2. A quadratic expression in the form $$an^2 + bn + c$$ with $$a > 0$$ opens up

1. Stating the problem: Simplify the expression $a^{\log_a b}$.\n\n2. Recall the logarithm power rule: For any positive $a \neq 1$ and positive $b$, $a^{\log_a b} = b$. This is bec

1. **Problem 1:** Given $x = \sqrt{7} - \sqrt{5}$, express $\frac{1}{x}$ in the form $\sqrt{a} + \sqrt{b}$. Step 1: Start with $\frac{1}{x} = \frac{1}{\sqrt{7} - \sqrt{5}}$.

1. Stating the problem: We want to find the greatest limit of the function $$f(n) = \frac{\sqrt{n}}{9 + n}$$ as $$n$$ approaches infinity or other relevant points. 2. Consider the

1. State the problem: Solve the quadratic equation $$3x^2 + 10x - 8 = 0$$. 2. Calculate the discriminant: $$\Delta = b^2 - 4ac = 10^2 - 4 \times 3 \times (-8) = 100 + 96 = 196$$.

1. Stating the problem: Solve the quadratic equation $x^2 - 4 = 0$. 2. Add 4 to both sides to isolate the square term:

1. The problem is to find the missing number represented by "?" in the sequence: 8 15 6, 4 7 6, 2 5 9, 15 ? 4. 2. Let's examine each group of three numbers to identify a pattern.

1. Stating the problem: Solve the quadratic equation $$x^2 + 2x + 1 = 0$$. 2. Recognize that this is a quadratic equation in standard form $$ax^2 + bx + c = 0$$ where $$a=1$$, $$b=

1. State the problem: Solve the quadratic equation $2x^2+4x=0$. 2. Factor the equation: Factor out the greatest common factor $2x$:

1. The problem is to solve the quadratic equation $x^2 + 3x = 0$. 2. To solve this, start by factoring the expression on the left side.

1. The problem is to expand and simplify the expression $ (a + 2)(a^2 - 2a + 4) $. 2. Use the distributive property (FOIL or expansion) to multiply each term in the first parenthes

1. Stating the problems: a. Evaluate 7 \(\frac{3}{5}\) - 8 \(\frac{2}{7}\)

1. The problem is to solve the equation $$|x+4| = 0$$. 2. Recall that the absolute value of a number is zero only when the number itself is zero.

1. The problem is to determine the condition under which the equation $|x| = a$ has two solutions. 2. Recall that the absolute value function $|x|$ outputs the distance of $x$ from

1. The statement says "2 2/3 is an improper fraction." Let's first understand what an improper fraction is. 2. An improper fraction is a fraction where the numerator (top number) i

1. The problem asks whether $\frac{2}{3}$ is the reciprocal of $-\frac{2}{3}$. 2. Recall that the reciprocal of a number $x$ is defined as $\frac{1}{x}$.