🧮 algebra

1. **State the problem:** We need to divide $4.05 \times 10^{-1}$ by $1.5 \times 10^{-1}$. 2. **Write the division as a fraction:**

1. **State the problem:** Calculate the square of the number $1.5 \times 10^{-2}$. 2. **Formula used:** To square a number in scientific notation, use $\left(a \times 10^{b}\right)

1. **State the problem:** Solve the equation $4^{3x} = 8x - 3$ for $x$. 2. **Analyze the equation:** The left side is an exponential function $4^{3x}$ and the right side is a linea

1. **State the problem:** Find 15% of 20. 2. **Formula:** To find a percentage of a number, use the formula:

1. The problem asks to find 50% of 70. 2. To find a percentage of a number, use the formula:

1. **Problem statement:** We need to describe the transformations applied to the graph of $y=f(x)$ to obtain the graphs of the given functions. 2. **Recall transformation rules:**

1. We are asked to graph each quadratic equation and label the vertex and axis of symmetry. 2. The vertex form of a quadratic is $y = a(x-h)^2 + k$, where $(h,k)$ is the vertex and

1. **State the problem:** Solve the equation $-2(3x + 5) + x - 5 = -45$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses.

1. The problem asks to describe the transformations applied to the graph of $y=f(x)$ to obtain each new function. 2. Recall the general transformation rules:

1. **State the problem:** Solve for $x$ in the equation $$-4x + 2(x + 4) = -7x - (x + 1)$$. 2. **Apply the distributive property:** Multiply through the parentheses:

1. **State the problem:** Solve for $x$ in the equation $$3x - 2(8x + 8) = -(7x - 10) - 2x.$$\n\n2. **Apply the distributive property:** Multiply $-2$ by each term inside the paren

1. **State the problem:** Solve the equation $$-2(x + 2) - x - 3 = 8$$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses.

1. **State the problem:** Solve the linear equation $$2(-4x + 2) - 3x - 3 = 8$$ for $x$. 2. **Apply the distributive property:** Multiply 2 by each term inside the parentheses:

1. The problem is to simplify an expression, but since no specific expression was given, let's consider a general approach to simplification. 2. Simplification involves reducing an

1. **State the problem:** Solve the linear equation $$-10x + 3(3x + 4) + 1 = -3(7x + 3)$$ for $x$. 2. **Apply the distributive property:** Multiply inside the parentheses.

1. **State the problem:** Solve the linear equation $$2x = -1 + 8(2x + 1)$$ for $x$. 2. **Apply the distributive property:** Multiply $8$ by each term inside the parentheses:

1. **State the problem:** Solve the equation $$-5 = 3x - 14$$ for $$x$$. 2. **Add 14 to both sides** to isolate the term with $$x$$:

1. **State the problem:** Solve the equation $$-6x - 7 = 17$$ for $x$. 2. **Add 7 to both sides** to isolate the term with $x$:

1. Planteamos el problema: calcular el producto de los polinomios $B(x)$ y $C(x)$. 2. Los polinomios dados son:

1. **Problem:** Simplify the polynomial $(x + 2)(x + 7)$. 2. **Formula:** Use the distributive property (FOIL method) for binomials: $$(a + b)(c + d) = ac + ad + bc + bd$$

1. The problem is to find the fraction that completes the equation $$4 \frac{1}{6} = 4 \frac{\Box}{\Box}$$. 2. We start by understanding that $$4 \frac{1}{6}$$ is a mixed number, w