🧮 algebra

1. **State the problem:** We are asked to analyze the function $x^2$. 2. **Formula and rules:** The function is $y = x^2$, which is a quadratic function. Quadratic functions have t

1. **State the problem:** Solve the quadratic equation $5x^2 - 35x = 0$. 2. **Formula and rules:** To solve quadratic equations, we can factorize or use the quadratic formula. Here

1. **State the problem:** Add the mixed fractions $3 \frac{4}{9}$ and $2 \frac{2}{4}$.\n\n2. **Convert mixed fractions to improper fractions:**\n- $3 \frac{4}{9} = \frac{3 \times 9

1. The problem asks to find $fog(-1)$ given that $g(3) = 9$ and that $f$ and $g$ are functions involved in a composition. 2. Function composition $fog(x)$ means $f(g(x))$, so we fi

1. **State the problem:** Solve the quadratic equation $7x^2 - 28 = 0$ for $x$. 2. **Formula and rules:** To solve quadratic equations of the form $ax^2 + bx + c = 0$, we can isola

1. **State the problem:** Solve the quadratic equation $$3x^2 + 3x - 60 = 0$$. 2. **Formula and rules:** The general quadratic equation is $$ax^2 + bx + c = 0$$. The solutions can

1. **State the problem:** Solve the quadratic equation $$3x^2 + x - 60 = 0$$. 2. **Formula used:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, use the quadrati

1. The problem is to calculate $\frac{3}{4} + \frac{2}{5}$ and express the answer as a mixed number. 2. To add fractions, we need a common denominator. The denominators are 4 and 5

1. The problem is to evaluate the expression $32^{\frac{1}{2}}$. 2. Recall that raising a number to the power of $\frac{1}{2}$ is equivalent to taking the square root of that numbe

1. The problem is to simplify the fraction $\frac{168}{14}$. 2. To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

1. **State the problem:** Calculate the sum of one seventh and two fifths, i.e., $\frac{1}{7} + \frac{2}{5}$.\n\n2. **Formula and rules:** To add fractions, they must have a common

1. **Problem Statement:** (a) Find the Highest Common Factor (HCF) of 54 and 90.

1. **State the problem:** Solve the quadratic equation $$3x^2 + x - 20 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equ

1. **Stating the problem:** We have 10 triangles, each with three numbers at the vertices and one number inside a circle at the center. We need to analyze the relationship between

1. The problem is to find the value of 200 multiplied by 3/4 percent. 2. Recall that percent means per hundred, so 3/4% is equal to $\frac{3}{4} \times \frac{1}{100} = \frac{3}{400

1. **Problem Statement:** Find the equation of the line passing through the points (-5, -5), (-2, -2), (3, 3), and (7, 7). 2. **Formula Used:** The equation of a line in slope-inte

1. The problem is to determine which value or expression should be placed in the blank space. 2. To solve this, we need more context or the equation where the blank appears.

1. **State the problem:** We are given a vertical line passing through points (7, 5) and (7, -4).

1. **State the problem:** We are given a polynomial $$p(x) = 2x^3 + ax^2 - 24x + b$$ with two conditions: - $$x + 3$$ is a factor of $$p(x)$$.

1. **State the problem:** We need to find how many socks weigh the same as one oven mitt. 2. **Given information:** The balance scale shows one oven mitt on the left side and five

1. **State the problem:** Solve for $x$ and $y$ in the equation $$\frac{x \cdot \sqrt{y}}{2} = \sqrt{\frac{3}{2}} \cdot \sqrt{\frac{9}{2}}$$ without using a calculator.