🧮 algebra

1. The problem asks to translate the graph of a parabola 3 units to the left using a table of points. 2. The original parabola has vertex at approximately $(3, -4)$ and x-intercept

1. **Stating the problem:** We want to find two different combinations of transformations that change the function $f(x) = 5x + 3$ into $g(x) = 15x - 12$. 2. **Understanding transf

1. The problem asks to identify the parent cubic function and describe the transformation represented by the given function. 2. The parent cubic function is generally given by $$f(

1. The problem is to simplify the expression $\frac{1}{7} \div 2$.\n\n2. The formula for division of fractions is: $\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}$.\n\n3. Appl

1. **State the problem:** Simplify the expression $1 \div \frac{7}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reci

1. **State the problem:** We are given that \(\frac{1}{3}\) of a shape is shaded, and we need to calculate \(\frac{1}{3} \div 2\). 2. **Recall the division rule for fractions:** Di

1. **State the problem:** We need to find the sum of the fractions $\frac{1}{7} + \frac{1}{5} + \frac{1}{2}$ and express the result in its simplest form. 2. **Formula and rules:**

1. The problem is to calculate the division of two fractions: $\frac{5}{14} \div \frac{15}{7}$.\n\n2. The formula for dividing fractions is to multiply the first fraction by the re

1. **State the problem:** We need to multiply the fractions $\frac{6}{13}$, $\frac{9}{77}$, and $\frac{11}{2}$ and simplify the result to its lowest terms. 2. **Write the multiplic

1. **State the problem:** We need to find the value of the question mark (?) in the equation $$? \div \frac{3}{5} = 8$$

1. **State the problem:** We need to find the difference between the fractions $\frac{7}{11}$ and $\frac{7}{15}$ and express the answer in simplest form. 2. **Formula and rules:**

1. The problem asks to find the sum of the integers from 1 to 10. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n=10$.

1. **State the problem:** We need to order the given expressions from least to greatest. 2. **Evaluate each expression:**

1. **State the problem:** Solve the system of equations: $$9^x (27)^y = 1$$

1. **State the problem:** Simplify the expression $$\frac{x+8}{x^2+9x+20} + \frac{x+5}{x^2+7x+12}$$ ignoring restrictions on the variable. 2. **Factor the denominators:**

1. Masalah: Cari nilai $x$ dalam persamaan linear $3x + 5 = 20$.\n\n2. Formula yang digunakan: Untuk menyelesaikan persamaan linear, kita perlu mengasingkan $x$ di satu sisi persam

1. The problem involves understanding logarithmic relationships and solving for variables given certain logarithmic values. 2. We use the logarithm properties and linear equations.

1. **State the problem:** We are given the polynomial function $$f(x) = 2x^3 + x^2 - 18x - 9$$ and need to determine which of the statements A, B, C, or D is true. 2. **Recall the

1. **State the problem:** We need to determine which binomial among $x-6$, $x+2$, $x+4$, and $x-7$ is NOT a factor of the polynomial $$x^3 - 11x^2 + 16x + 84.$$\n\n2. **Recall the

1. **State the problem:** We are given that $x - 1$ is a factor of the polynomial $x^3 - kx + 2x$ and need to find the value of $k$. 2. **Recall the Factor Theorem:** If $x - a$ is

1. **State the problem:** Solve the equation $$11b - 17 = -3b + 39$$. 2. **Write down the formula and rules:** To solve for $b$, we need to isolate $b$ on one side of the equation