🧮 algebra

1. The problem is to solve the equation $$(x + 9)^2 - (x + 8)^2 = (2x + 11)^2.$$\n\n2. Use the formula for the square of a binomial: $$(a \pm b)^2 = a^2 \pm 2ab + b^2.$$\n\n3. Expa

1. **State the problem:** Patrick read $w$ pages. Belvedere read 2.25 times as many pages as Patrick, so Belvedere read $2.25w$ pages.

1. **State the problem:** We are given a linear model for the number of hot coffees sold, $y = -0.7x + 80$, where $x$ is the temperature in degrees Fahrenheit. We want to find the

1. **Stating the problem:** We want to evaluate the sum $$2 + r + 2 + q + 2 + \cdots + \sqrt{2} = 2 \cos \frac{\pi}{2(n+1)}$$.

1. Problema: Raskite funkcijos f(x) = \sqrt{4x^2 - 12x + 9} apibrėžimo sritį. 2. Formulė ir taisyklės: Kadangi funkcija apibrėžta su kvadratinės šaknies ženklu, po šaknimi esanti i

1. The problem is to solve the quadratic equation $x^2 - 3x - 10 = 0$. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$.

1. **State the problem:** Evaluate the expression $$\sqrt{9^3 - 3^4} \times 2 + \frac{64}{2^3} - 5$$. 2. **Recall the order of operations:** Parentheses, exponents, multiplication

1. The problem asks to analyze three graphs and determine if each represents a function, and to find their domain and range. 2. For graph 4:

1. Problem: Wyznacz równanie symetralnej odcinka AB, gdzie A ma współrzędne (2,1), a B ma współrzędne (6,3). 2. Symetralna odcinka to prosta prostopadła do odcinka AB i przechodząc

1. **State the problem:** Solve the simultaneous equations: $$y = -x + 2$$

1. The problem asks to write down the two inequalities describing the unshaded region on the graph. 2. The first line is solid with equation $y = 2x + 1$. Since the shaded region i

1. **State the problem:** We need to find the three inequalities that define the unshaded region on the graph.

1. **Problem:** Liu deposited 3500 into a savings account 2 years ago with a simple interest rate of 4%. We need to find how much interest Liu earned. 2. **Formula for simple inter

1. **State the problem:** Solve the equation $$19^{4 - 2x} - 8 = 38$$ and round the solution to the nearest ten-thousand. 2. **Isolate the exponential term:** Add 8 to both sides t

1. Planteamos el sistema de ecuaciones a resolver por el método de reducción: $$\begin{cases} 3X + 4Y = -6 \\ 2X + 3Y = 13 \end{cases}$$

1. The problem is to express a given improper fraction as a mixed number in simplest form. 2. The formula to convert an improper fraction $\frac{a}{b}$ to a mixed number is:

1. The problem is to divide the fractions $\frac{4}{7}$ by $\frac{1}{3}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}

1. Planteamos el sistema de ecuaciones a resolver por el método de reducción: $$\begin{cases} 3X + 4Y = -6 \\ 2X + 3Y = 13 \end{cases}$$

1. El problema es factorizar el denominador de la función \(G(s) = \frac{1}{(s+2)(s^2 + 10s + 7)}\). 2. El denominador ya está parcialmente factorizado como \((s+2)(s^2 + 10s + 7)\

1. The problem asks for the cube of 5. 2. The cube of a number $n$ is calculated using the formula:

1. **State the problem:** A band has 24 male members. There are $x$ more male members than female members. We need to write an expression for the total number of members in the ban