🧮 algebra

1. **State the problem:** We need to find the width of a box when the length is 30 inches, given the length to width ratio is 6:1. 2. **Formula and explanation:** The ratio means \

1. **State the problem:** Factor the polynomial $$x^4 + x^3 + x^2 + x$$. 2. **Identify common factors:** Notice that each term contains at least one factor of $$x$$.

1. The first set is \{(1,2), (3,4), (5,6), (7,8), (9,10)\}. Each input (first element) is unique and maps to a unique output (second element). This means no two different inputs sh

1. The first sequence is 2, 2.5, 3, 3.5, 4, 4.5. 2. To identify the type, check the difference between consecutive terms:

1. The problem is to analyze the linear equation $16x - 10y = 20$. 2. First, we can rewrite the equation in slope-intercept form $y = mx + b$ to understand its graph.

1. The problem is to graph the linear equation $9x + 12y = -36$. 2. To graph this equation, we first find the intercepts.

1. The problem involves two linear equations: \(y = x - 5\) and \(9x + 12y = -36\).\n\n2. First, let's analyze the equation \(y = x - 5\). This is in slope-intercept form \(y = mx

1. **Identify the type of relation given the set of points**: $\{(1,1), (2,2), (3,3), (-1,4), (5,5)\}$. - A function assigns exactly one output for each input.

1. **State the problem:** Solve the linear equation $$10x + 4y = 0$$ for $y$ in terms of $x$. 2. **Isolate $y$:** To express $y$ in terms of $x$, subtract $10x$ from both sides:

1. **State the problem:** We are given the linear equation $x - y = -3$ and need to understand its graph and intercepts. 2. **Rewrite the equation in slope-intercept form:** Solve

1. The problem is to simplify and understand the function $y = \sqrt{x^2 - 4x + 4}$.\n\n2. First, recognize that the expression inside the square root is a quadratic trinomial. We

1. The problem asks to sketch the graph of the equation $$y = 3 - \sqrt{x + 1}$$ by transforming the graph of $$y = \sqrt{x}$$. 2. Start with the base graph $$y = \sqrt{x}$$, which

1. Factorizar el trinomio $x^2 + 7x + 12$. Buscamos dos números que multiplicados den 12 y sumados den 7: 3 y 4.

1. Solve the inequality $3x^2 + 5x - 2 \geq 0$. First, find the roots of the quadratic equation $3x^2 + 5x - 2 = 0$ using the quadratic formula:

1. **State the problem:** We need to find the value of $T$ that satisfies the equation $$\frac{T \times T \times T}{T + T + T} = 6.$$ 2. **Rewrite the equation:** The numerator is

1. **State the problem:** We need to find the value(s) of $x$ such that $$3^x = x^9.$$ 2. **Analyze the equation:** The equation equates an exponential function $3^x$ with a polyno

1. **State the problem:** We need to find a quadratic function modeling an archway with maximum height 4 m and maximum width 4 m, then check if an object 3 m wide and 1.6 m tall fi

1. **Nyatakan masalah:** Kita ingin menentukan jumlah minimum bus dan minibus yang disewa untuk mengangkut minimal 600 siswa dengan biaya sewa maksimal 44000000. 2. **Definisikan v

1. Masalah ini berkaitan dengan menentukan banyaknya pasangan (x, y) yang memenuhi kendala dalam pembuatan roti manis rasa cokelat (x) dan rasa keju (y). 2. Dari deskripsi grafik,

1. **Elevar potencias y simplificar:** - $(2x^3 y)^2 = 2^2 (x^3)^2 y^2 = 4x^6 y^2$

1. The problem asks if $3^{\frac{1}{x}}$ is the same as $3^{-x}$.\n\n2. Let's analyze the expressions: $3^{\frac{1}{x}}$ means 3 raised to the power of the reciprocal of $x$.\n\n3.