🧮 algebra

1. **State the problem:** A company wants to reduce its number of stores by 40% over two years. 2. After the first year, the company has already reduced the stores by 20%. We need

1. The problem is to understand or verify the expression $6 + 8\sqrt{2}$. 2. This expression is a sum of a rational number 6 and an irrational number $8\sqrt{2}$.

1. The problem is to understand what it means when the denominator of a fraction is 1. 2. A fraction is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominat

1. **State the problem:** We want to show that $\frac{4 + \sqrt{8}}{\sqrt{2} - 1}$ can be written in the form $a + b\sqrt{2}$ where $a$ and $b$ are integers. 2. **Rationalize the d

1. **State the problem:** Expand and simplify the expression $$(4x^2 - y^2)^2$$ as a polynomial in standard form. 2. **Recall the formula:** The square of a binomial difference is

1. The problem is to expand and simplify the expression $$(5x^4 + y^2)^2$$ into a polynomial in standard form. 2. Use the formula for the square of a binomial: $$(a + b)^2 = a^2 +

1. The problem asks us to expand and simplify the expression $$\left( 2x^5 - y^2 \right)^2$$ as a polynomial in standard form. 2. Recall the formula for the square of a binomial: $

1. The problem is to expand the expression $$(2x^5 - y^2)^2$$. 2. Use the formula for the square of a binomial: $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.

1. **Problem:** Find the square root of the discriminant of the quadratic equation $$2x^2 + 3x - 5 = 0$$. 2. The discriminant $$\Delta$$ of a quadratic equation $$ax^2 + bx + c = 0

1. The problem asks for the sum of the roots of the quadratic equation $$3x^2 - 5x + 2 = 0$$. 2. Recall that for a quadratic equation $$ax^2 + bx + c = 0$$, the sum of the roots is

1. **State the problem:** We have populations of four countries: England, Wales, Scotland, and Northern Ireland, given in scientific notation and ordinary numbers. We want to under

1. **State the problem:** Mrs. Allen made a deposit of $150 and 11 monthly payments of $118 each to buy a refrigerator. 2. **Calculate the total amount of the monthly payments:**

1. Stating the problem: Simplify the expressions \(\frac{2a - 1}{5a} - \frac{4b - 3}{10b}\) and \(\frac{2x + 1}{x} + \frac{3y - 2}{y} - 5\). 2. Simplify the first expression:

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square, which can be written as $x \times x$.

1. **State the problem:** We have a car with a sale price of 15200.

1. We are given the expression $\sqrt[3]{\frac{81}{3}}$ and need to write it in the form $3^k$ and find $k$. 2. Simplify the fraction inside the cube root:

1. **Simplify** $\frac{5y^4}{y^{-2}}$. Step 1: Recall the rule for dividing powers with the same base: $\frac{a^m}{a^n} = a^{m-n}$.

1. **State the problem:** We are given the ratio of analysts to field agents as 3:5 and the total number of agents as 40. We need to find the number of analysts. 2. **Understand th

1. The problem asks for the domain of the function defined by the absolute value expression $|x^3 - 7|$. 2. The domain of a function is the set of all input values $x$ for which th

1. **State the problem:** We are given a stove with a cash price of 1500.