🧮 algebra

1. **State the problem:** We need to determine if each piecewise function $f(x)$, $h(x)$, and $g(x)$ has a range of $(-\infty,4)$. This means the output values of the function cove

1. **State the problem:** Determine if the range of each piecewise function $f(x)$ and $h(x)$ is $(-\infty, 4)$.\n\n2. **Recall:** The range of a function is the set of all possibl

1. **Nyatakan masalah:** Kita ingin menyederhanakan bentuk $$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}-\sqrt{5}}$$ dengan membuat penyebut menjadi rasional.

1. **Problem Statement:** We are given a graph of a linear function represented by a green ray starting at the point $(3, 5)$ with a closed dot and extending down to the right. 2.

1. **State the problem:** We are given a graph of a linear function represented by a line segment with open endpoints at approximately $(-4, -9)$ and $(1, -4)$. 2. **Identify the d

1. **State the problem:** We are given train times from Waterloo to Dartford for three different journeys. The total journey time from Waterloo to Dartford is always the same. We n

1. **State the problem:** Solve the inequality $$9 - 7x > 15$$ 2. **Isolate the variable term:** Subtract 9 from both sides:

1. Diberikan polinomial $$f(x) = x^4 - 2x^3 - 7x^2 - 5x - 6$$ dan diminta menentukan nilai polinomial tersebut untuk $$x = 3$$. 2. Substitusikan nilai $$x = 3$$ ke dalam polinomial

1. The problem is to simplify the expression $9x$. 2. This expression is already in its simplest form because it is a product of a constant and a variable.

1. The problem asks to express or understand the factor $10^{1e10000000}$. 2. The expression $10^{1e10000000}$ means $10$ raised to the power of $1 \times 10^{10000000}$.

1. **State the problem:** We need to find the time it takes for a printer to print a given number of photos, knowing that printing $6$ photos takes $2$ minutes. 2. **Identify the f

1. **State the problem:** Mil an's motorhome uses $3$ gallons of gas for every $21$ miles. We need to complete the table showing the number of gallons used and the distance travele

1. **State the problem:** Simplify or analyze the expression $$\frac{2x}{x^2 + 7x - 4}$$ where the numerator is $2x$ and the denominator is $x^2 + 7x - 4$. 2. **Factor the denomina

1. **State the problem:** Find the slope of the line passing through the points $(5, -1)$ and $(0, -7)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. **State the problem:** Find the slope of the line passing through the points $(-2, 5)$ and $(2, -5)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. **State the problem:** Determine if each given equation is linear. 2. **Recall the definition:** A linear equation in one variable $x$ has the form $y = mx + b$, where $m$ and $

1. We are asked to write each expression in radical form and simplify. 2. Recall the rule: $a^{m/n} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$.

1. Simplify $$\sqrt[4]{32z^{7}}$$ - Start by expressing 32 as a power of 2: $$32 = 2^{5}$$.

1. **Problem:** Simplify $$\sqrt[3]{3z^2}$$. **Step 1:** The cube root of a product is the product of the cube roots: $$\sqrt[3]{3z^2} = \sqrt[3]{3} \cdot \sqrt[3]{z^2}$$.

1. **State the problem:** We need to graph the linear equation $$3x + y = 9$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$:

1. **State the problem:** We need to graph the equation $$3x + y = 9$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$: