🧮 algebra

1. The problem is to simplify and factor the quadratic expression given: $2x^2-24x+72$. 2. First, note the expression is a quadratic trinomial.

1. **State the problem:** Find the equivalent expression with rational exponents for $\left(\sqrt{2xy}\right)^3$. 2. **Rewrite the square root as a rational exponent:** The square

1. We are given the expression $3x^2 - 4x + 1$. 2. To analyze or simplify this quadratic expression, we can factor it if possible.

1. Stated problem: Simplify the quadratic expression $2x^2 + 15x + 28$. 2. Factor the quadratic expression by finding two numbers that multiply to $2 \times 28 = 56$ and add to $15

1. The problem demonstrates how a function maps elements from a domain to a range. 2. From Figure 1.2, the function $f$ takes an input $x$ from the domain and produces an output $f

1. Problem: Given $a = b + c$ with $b = 7.13$ (correct to 2 decimal places) and $c = 8900$ (correct to 2 significant figures), find the upper bound of $a$. 2. Find upper bounds:

1. Problem: An object thrown vertically upward has height given by $$h = -16t^2 + 96t$$. Find when the height is 144 feet.

1. The problem is to understand the expression $x = 10t + 4f$. 2. Here, $x$ is expressed in terms of two variables, $t$ and $f$, where the coefficient of $t$ is 10 and the coeffici

1. Stating the problem: Solve for the variables in the equation $$2x(5t+2f)=10$$. 2. Expand the left-hand side: Multiply 2x with each term inside the parentheses.

1. The interval notation provided is $[-3, \infty)$. 2. This means all numbers starting from $-3$ including $-3$ itself, and extending to positive infinity.

1. Solve the equation $$\frac{1}{x} = \frac{2}{3x - 1}$$ First, cross multiply to get rid of the fractions:

1. Problem: Given $f(x) = 2 - x$ and $g(x) = -2x + 3$, find:\ a. $f + 2g$ and evaluate $(f + 2g)(2)$\

1. **State the problem:** Find the domain of the function $$f(x) = \ln(x^2 - 12x)$$. 2. **Recall the domain condition for natural logarithm:** For $$f(x) = \ln(u)$$, the argument $

1. Stating the problem: Solve the equation $$(2x - 5)^2 = -9$$. 2. Analyze the equation: The left side is a square of a real expression, which is always non-negative. The right sid

1. Solve the equation $0 \cdot 6 - 5 \cdot 4 = 3 \cdot 2 - x - x$. Simplify both sides:

1. The problem is to simplify the expression $5x + 5$. 2. Identify the common factor in both terms. Here, the number 5 is common in $5x$ and $5$.

1. We are given the inequality involving a function $f(x)$: $$\sqrt{x} + 7 \leq f(x) \leq \frac{x - 1}{2}.$$\n\n2. This inequality states that the value of the function $f(x)$ is b

1. Let's state the problem: Simplify the expression $5x + 5$. 2. Look at the terms: Both terms contain a factor of 5.

1. **Stating the problem:** You have two given equations involving fractions and triangular operations represented by downward (▼) and upward (▲) triangles:

1. Mari kita mulai dengan menyatakan masalahnya: Temukan jumlah semua faktor prima dari bilangan $27000001$. 2. Untuk menemukan faktor prima, pertama kita harus melakukan faktorisa

1. **Stating the problem:** We need to construct and interpret a table of values for two linear relations and graph the relations.