🧮 algebra

1. **State the problem:** Solve the equation $$0 = (x - 1)(x - 3)$$ for $x$. 2. **Recall the zero product property:** If a product of two factors equals zero, then at least one of

1. **State the problem:** Calculate the value of the expression $$D = 2.75 \times \log 7.7 - \left(\frac{1}{7.7}\right)^{0.5}$$ where \(\log\) denotes the logarithm base 10.

1. **State the problem:** Calculate the value of $$D$$ given the formula $$D = 2.75 \times \log A - \sqrt{\frac{1}{A}}$$ where $$A = 7.7$$ million. 2. **Write the formula and expla

1. **State the problem:** We are given a linear relationship between the total cost $y$ and the number of months $x$ for operating a café. The cost function is $y = 20000 + 6000x$.

1. **State the problem:** We are given data points for $x$ and $y$ and asked to draw the graph of $y$ against $x$ for $0 \leq x \leq 15$ (part c), and to find a possible value of $

1. **State the problem:** Solve for $M$ in the equation $$-\frac{5}{6} + M = \frac{4}{3}.$$\n\n2. **Isolate $M$:** Add $\frac{5}{6}$ to both sides to get $$M = \frac{4}{3} + \frac{

1. **State the problem:** There are 35 kids in a class with boys to girls ratio of 3:4. We need to find how many boys and girls are there. 2. **Use the ratio formula:** If the rati

1. The problem is to find the ratio of 35 to the ratio 3:4. 2. A ratio compares two quantities. The ratio 3:4 means for every 3 parts of one quantity, there are 4 parts of another.

1. **State the problem:** Solve the polynomial equation $$6x^2 - 6 = 0$$. 2. **Write the formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we is

1. **State the problem:** Simplify the expression $$\frac{20x^2 + 8x}{5x + 2}$$. 2. **Identify the formula and rules:** We want to simplify a rational expression by factoring the n

1. **State the problem:** Solve the equation $$e^{x^2} = e^{7x} \cdot \frac{1}{e^{12}}$$ for $x$. 2. **Rewrite the right side:** Using the property of exponents $$\frac{1}{e^{12}}

1. **State the problem:** Find the domain and range of the function $$f(x) = \frac{7x}{9x - 1}$$. 2. **Find the domain:** The domain consists of all real numbers $x$ for which the

1. The problem asks for multiplication sums where a whole number multiplied by a fraction equals a given fraction. We need to find pairs of whole numbers and fractions that satisfy

1. The problem involves comparing two ratios: $4:30$ and $5:14$ minutes. 2. To compare ratios, convert each ratio to a fraction and simplify if possible.

1. **State the problem:** Find the domain of the rational function $$F(x) = \frac{7x(x - 3)}{5x^2 - 21x - 54}$$. 2. **Recall the domain rule for rational functions:** The domain in

1. **State the problem:** Simplify the expression $$\frac{3a + 2}{2a^2 + 11a + 5} - \frac{a - 2}{6a^2 - 7a - 5} \div \frac{2a}{3a^2 - 5a}$$. 2. **Factor all quadratic expressions:*

1. **State the problem:** Solve the quadratic equation $2a^2 = 6 + 8a$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero

1. **State the problem:** Find the complex zeros of the polynomial function $$f(x) = x^3 - 12x^2 + 49x - 58$$ and write $$f(x)$$ in factored form. 2. **Use the Rational Root Theore

1. The problem is to create a math question for practice. 2. Let's consider a simple algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$.

1. **State the problem:** Solve the quadratic equation $8x^2 + 16x = 42$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side to set the equation to ze

1. **Stating the problem:** We will learn how to add, subtract, multiply, and divide fractions, which are common operations in grade 7 math. 2. **Important rules and formulas:**