🧮 algebra

1. **State the problem:** A gopher runs from the southeast corner of a rectangular yard to the opposite corner by running the width and then the length, each 6.1 meters, and then r

1. The problem asks for the expression representing the perimeter of a rectangle with width $(10f + 8)$ cm and length $(5f - 3)$ cm. 2. Recall the formula for the perimeter $P$ of

1. **State the problem:** Solve the equation $$\frac{2x+4}{x} + \frac{x+2}{x-2} = \frac{3x}{x-2}$$ for $x$. 2. **Identify the domain restrictions:** The denominators cannot be zero

1. **State the problem:** Simplify the expression $$\frac{3}{x-3} - \frac{5}{x+2}$$. 2. **Find a common denominator:** The denominators are $x-3$ and $x+2$. The common denominator

1. **State the problem:** We are given the function $$h(x) = (-x + 2)^2$$ and the parent function $$f(x) = x^2$$. We need to identify the transformations applied to $$f(x)$$ to get

1. **State the problem:** We are given the function $h(x) = (x - 4)^2$ and the parent function $f(x) = x^2$. We need to identify the transformations applied to $f(x)$ to get $h(x)$

1. The problem asks to identify which quadratic functions have specific domain and range properties based on their graphs. 2. Recall that the domain of a function is the set of all

1. **State the problem:** We need to find the range of each quadratic function given either by formula or table of values. 2. **Recall the general form and range of a quadratic fun

1. **Stating the problem:** Calculate the total pay for an employee who works 35 regular hours and 5 overtime hours, given the regular hourly rate and overtime multiplier. 2. **Giv

1. **Problem Statement:** Calculate the gross pay for a sales job with a base salary and commission. 2. **Given:** Base salary = 350 per week, Commission rate = 8% = 0.08, Sales =

1. **State the problem:** We need to find the positive solution to the quadratic equation $$7x^2 - 20x - 32 = 0.$$\n\n2. **Recall the quadratic formula:** For an equation $$ax^2 +

1. The problem is to find one solution to the equation $$3x(x - 4)(x + 5) = 0$$. 2. The zero product property states that if a product of factors equals zero, then at least one of

1. **State the problem:** We are given two functions: the original cubic function $f(x) = x^3$ and a transformed function $h(x) = -(x + 2)^3 - 4$. We want to understand the transfo

1. The problem asks to describe the transformation from the function $f(x) = x^3$ to $g(x) = (x + 4)^3$. 2. Recall that for a function $f(x)$, the transformation $f(x + h)$ shifts

1. **State the problem:** Solve the compound inequality $x \leq -2$ OR $x > 3$ and express the solution in interval notation. 2. **Understand the inequality:** The solution include

1. **State the problem:** Simplify the expression $$\frac{(-3mn)^2 \cdot 64(m^2 n)^3}{16m^2 n^4 (mn^2)^3} \times \frac{24(m^2 n^2)^4}{3(m^2 n^3)^2}$$ 2. **Recall exponent rules:**

1. **State the problem:** Factor the quadratic expression $$4x^2 + 4x - 15$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that m

1. **Problem:** Factor the quadratic expression $3x^2 - 11x - 4$. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multiply to $a \times c$ an

1. The problem is to analyze and graph the function $y=\left(\frac{1}{10}\right)^x$. 2. The formula for exponential functions is $y=a^x$ where $a>0$ and $a\neq1$.

1. **State the problem:** Solve the inequality $$3(3x - 4) \leq 24$$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** We need to graph the function $y=\left(\frac{1}{3}\right)^x$, find its y-intercept, domain, and range.