🧮 algebra

1. Let's first restate the problem or the context of the steps so far to ensure clarity. 2. Step 4 usually involves applying a key formula or simplifying an expression further.

1. **State the problem:** Multiply the expression $4 \times 10^8 \times 2 \times 10^9$ and simplify it. 2. **Rewrite the expression grouping coefficients and powers of 10:**

1. **State the problem:** Calculate $ (3.9 \times 10^2) \times 10^7 $ and express the answer in standard form. 2. **Recall the rule for multiplying powers of 10:** When multiplying

1. The problem asks to calculate $3 \times (2 \times 10^3)$ and express the answer in standard form. 2. Recall that standard form (scientific notation) is written as $a \times 10^n

1. The problem asks us to find the value of $a$ in the equation $$10^6 \times 10^3 = 10^a$$. 2. We use the rule of exponents that states when multiplying powers with the same base,

1. **State the problem:** We are given the quadratic expression $x^2 + 7x + 10$ and need to:

1. **State the problem:** We need to find the value of $a$ such that the coefficient of $x^3$ in the expansion of $(2 + ax)^4$ is $-64$. 2. **Recall the binomial expansion formula:

1. The problem is to solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. The formula to solve quadratic equations is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

1. **State the problem:** We need to find the value of the constant $a$ given that the coefficient of $x^3$ in the expansion of $(1 + a x)^9$ is 5376. 2. **Recall the binomial expa

1. **State the problem:** Solve the simultaneous equations: $$4x - 2y = -13$$

1. **State the problem:** Solve the equation $$0 = 1300x + 800000$$ for $x$. 2. **Formula and rules:** To solve a linear equation of the form $$ax + b = 0$$, isolate $x$ by subtrac

1. **State the problem:** Simplify the expression for $y$ given by $y = 2500x - 800000 - 1200x$. 2. **Identify like terms:** The terms $2500x$ and $-1200x$ are like terms because b

1. **Stating the problem:** We are given a pattern with inputs and outputs: 123=12

1. **Problem:** Sketch the graph of $f(x) = -x(x - 8)(x - 1)$. - The function is a cubic polynomial with roots at $x=0$, $x=8$, and $x=1$.

1. **Problem statement:** Tyler thinks of a number $x$. We need to write expressions for the following situations: 2. **Part a:** Doubles the number and subtracts 3.

1. **State the problem:** Solve the equation $$\frac{y-6}{-3} = \frac{-3}{-3}$$ for $y$. 2. **Simplify the right side:** Since $$\frac{-3}{-3} = 1$$, the equation becomes $$\frac{y

1. The problem is to simplify the expression $$\frac{y-6}{-3}$$. 2. The formula used here is the division of a binomial by a constant, which can be rewritten as $$\frac{a-b}{c} = \

1. **State the problem:** Simplify the expression $$-\frac{4}{3} - \frac{1}{4}$$. 2. **Formula and rules:** To subtract fractions, find a common denominator. The common denominator

1. **State the problem:** Calculate the product of $-3$ and $\frac{4}{9}$. 2. **Formula used:** When multiplying a whole number by a fraction, multiply the whole number by the nume

1. **State the problem:** Find the product of the mixed numbers $3 \frac{4}{9}$ and $4 \frac{1}{3}$ and write the answer as a mixed number in simplest form. 2. **Convert mixed numb

1. The problem is to solve the equation or expression labeled as #1 in the table (please provide the specific problem for exact solution). 2. Since the exact problem is not given,