🧮 algebra

1. **State the problem:** Multiply the fractions $\frac{2}{3}$ and $\frac{7}{9}$. 2. **Formula for multiplying fractions:** To multiply two fractions, multiply the numerators toget

1. **State the problem:** Multiply the fractions $\frac{4}{7}$ and $\frac{8}{9}$. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators toget

1. **State the problem:** Solve the linear equation $$4x + 10 = -26$$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Su

1. **State the problem:** Solve the equation $$27 = x^3$$ for real number $$x$$. 2. **Formula and rules:** To solve for $$x$$ when given $$x^3 = a$$, use the cube root formula:

1. **State the problem:** Calculate the product of $3.2 \times 10^5$ and $2 \times 10^9$ and write the answer in scientific notation. 2. **Recall the rule for multiplying numbers i

1. **State the problem:** We are given the linear function $y = -10x + 2$ and need to fill in the table for the values of $x = -1, 0, 1, 5$. 2. **Formula:** The function is $y = -1

1. **State the problem:** Evaluate the expression $10^{-5}$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** Simplify the expression $\sqrt{3} \cdot \sqrt{2}$. 2. **Recall the property of square roots:** The product of square roots can be combined as $\sqrt{a} \c

1. **State the problem:** Find the slope and y-intercept of the line given by the equation $$y = 4x - 1$$. 2. **Recall the slope-intercept form:** The equation of a line in slope-i

1. **Stating the problem:** We have a function $f: \mathbb{R} \to \mathbb{Z}$ defined by $f(x) = \lfloor 2x - 1 \rfloor$, where $\lfloor \cdot \rfloor$ denotes the floor function (

1. **State the problem:** Calculate the sum of $1.13 \times 10^{6}$ and $6.8 \times 10^{3}$ and write the answer in scientific notation. 2. **Recall the rule:** To add numbers in s

1. **State the problem:** Calculate $$(4.15 \times 10^{-3}) - (3.64 \times 10^{-3})$$ and write the answer in scientific notation. 2. **Recall the rule:** When subtracting numbers

1. **State the problem:** Simplify the expression $$(3.4a - 1.7b) + (2.5a - 3.9b)$$. 2. **Use the distributive property and combine like terms:**

1. **State the problem:** Solve the inequality $$\frac{3}{x} - 5 < 16$$ for $$x$$. 2. **Add 5 to both sides:**

1. **Solve the equation** $y - 12x + 3 = \frac{4}{7}$ for $y$. Start by isolating $y$ on one side:

1. **State the problem:** Solve the equation $$\sqrt{2x - 1} + \sqrt{x - 1} = 5$$ and verify the solutions. 2. **Rewrite the equation:** Let $$a = \sqrt{2x - 1}$$ and $$b = \sqrt{x

1. The problem asks for the domain and range of the function $$f(x) = \sqrt{x + 7} - 2$$. 2. The domain of a square root function $$\sqrt{g(x)}$$ requires the expression inside the

1. The problem asks to identify the graph that shows the inverse of the function $f(x)$, which is an increasing S-shaped curve passing through the origin. 2. The inverse function $

1. **State the problem:** Solve the quadratic equation $$-2x^2 + 6x + 7 = 0$$ using the quadratic formula without simplifying the fraction. 2. **Recall the quadratic formula:** For

1. **Stating the problem:** Reduce the expression $$(3a+b)\cdot(2a-4b)-5a^2$$.

1. The problem is to divide the fraction $\frac{9}{1}$ by the fraction $\frac{7}{6}$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times