🧮 algebra

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.

1. **State the problem:** We need to find an equation for the total amount of money $y$ the teacher spends on pencils as a function of the number of students $x$.

1. **State the problem:** We want to understand what $8^{1/2}$ means using the properties of integer exponents and define it consistently. 2. **Use the power of a power rule:** The

1. **State the problem:** We need to find the discount percentage when the original price is $7 and the sale price is $3.57. 2. **Formula for discount percentage:**

1. **State the problem:** We need to find the sales tax percentage when a $5 item costs $5.20 after tax. 2. **Formula:** The total price after tax is given by $$\text{Total Price}

1. **State the problem:** Simplify the expression $2\sqrt{45} + 2\sqrt{90} + 3\sqrt{45}$. 2. **Recall the rule:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and simplify square

1. **State the problem:** Simplify the expression $$\sqrt{500} + \sqrt{20} + 11\sqrt{5}$$. 2. **Recall the rule:** The square root of a product can be written as the product of squ

1. The problem is to solve the equation $20 = 8$ for $x$. However, this equation as stated is not valid since $20$ does not equal $8$. It seems you want to solve one of the listed

1. **State the problem:** Solve the system of linear equations: $$14p + 4s = 128$$

1. **State the problem:** We are given the system of linear equations:

1. **State the problem:** We are given the sum of the first $n$ terms of a sequence as $$S_n = n(n+1)(n+2)$$ and need to find the 10th term, $a_{10}$. 2. **Recall the formula for t

1. **State the problem:** Graph the quadratic function $y = 6x^2 + 5x - 4$ and find the x-intercepts, y-intercept, axis of symmetry, and vertex. 2. **Formula and rules:**

1. **State the problem:** We are given the height function of an object in terms of time $t$: $$h = -16t^2 + 60t + 3$$ and we want to understand its behavior. 2. **Identify the typ