🧮 algebra

1. The problem states that the function $s$ is in the form $$y = ax^2 + c$$ where $a < 0$ and $c > 0$. 2. Important rules for quadratic functions in this form:

1. **State the problem:** Simplify the expression $2(m + 3)(m + 5) + 4(2m + 3)$. 2. **Use the distributive property:** Expand each product.

1. **State the problem:** Simplify the expression $5(x^0 y)$. 2. **Recall the rule:** Any nonzero number or variable raised to the zero power equals 1, i.e., $x^0 = 1$.

1. The problem asks to describe the transformation from the graph of $g(x) = x^2$ to $h(x) = -\left(\frac{x}{2}\right)^2$. 2. The original graph $g(x) = x^2$ is a parabola opening

1. Problema: Factorizar la expresión $a(x+1) + b(x+1)$. 2. Fórmula: Para factorizar expresiones con un factor común, usamos $A\cdot C + B\cdot C = (A+B)\cdot C$.

1. **State the problem:** Solve the system of equations using elimination: $$-7x + 10y = 6$$

1. **State the problem:** Solve the system of equations using elimination: $$-9x - 4y = -4$$

1. El problema parece ser evaluar o simplificar expresiones con potencias y números dados. 2. Para el primer ejercicio: "9 8 7 6 4 5^1" interpretamos que se quiere evaluar $5^1$ y

1. **Problem statement:** Given the function $f(x) = \frac{\ln(2x - 3)}{3x + 4}$, find its domain, zeros, sign, parity, symmetry, asymptotes, extrema, inflection points, and sketch

1. **State the problem:** Simplify the expression $$\frac{2^3 \times 2^2}{3^4}$$. 2. **Recall the laws of exponents:** When multiplying powers with the same base, add the exponents

1. **State the problem:** Simplify the expression $$(y - 3)(y - 1) - (y + 2)(y - 6)$$. 2. **Use the distributive property (FOIL) to expand each product:**

1. The problem asks to find the unit rate (rate per one unit on the horizontal axis) for each graph. 2. The unit rate formula is $$\text{unit rate} = \frac{\text{change in vertical

1. The problem asks: "It takes Jacob 24 minutes to eat a bucket of ice cream, and Alisha 36 minutes to eat the same amount. If they have 5 buckets to share, how long will it take t

1. **State the problem:** Calculate the area of a square given length $= \frac{x-1}{x+1}$ and width $= \frac{2x}{15}$. 2. **Recall the formula for the area of a square:**

1. **State the problem:** We have an original total cost estimate of 240000 for constructing a house.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x = 2 \\ x + 3y = 6 \\ 4x - 5y = 7 \end{cases}$$

1. The problem is to identify the graph of the equation $$y=\sqrt[3]{x}+2$$. 2. The cube root function $$y=\sqrt[3]{x}$$ is an odd function with a characteristic S-shaped curve pas

1. The problem is to identify the graph of the equation $$y - 3 = \sqrt{x - 2}$$. 2. This equation can be rewritten as $$y = 3 + \sqrt{x - 2}$$.

1. **State the problem:** Identify the equation of the graph described. 2. **Analyze the given options:**

1. The problem is to identify the equation of the graph given three options: $$y + 1 = \sqrt[3]{x}$$

1. The problem is to identify the graph of the function $$f(x) = \sqrt{x - 4} + 3$$. 2. The general form of a square root function is $$f(x) = \sqrt{x - h} + k$$, where $(h, k)$ is