🧮 algebra

1. **State the problem:** Josie wants to make lemonade servings using the recipe amounts: syrup 3/4 oz, lemon juice 2 1/4 oz, and water 5 oz per serving. She has 20 oz syrup, 33 oz

1. **State the problem:** We need to analyze and understand the function $f(x) = \sqrt{x} - 3$. 2. **Recall the domain of the square root function:** The expression inside the squa

1. **State the problem:** We have a building with 26 apartments of sizes 90, 120, 140, and 150 m². The number of 120 m² apartments is $x$, and the number of 90 m² apartments is unk

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. **Problem 7:** Find the slope-intercept form of the line graphed on the coordinate plane. 2. **Step 1: Identify two points on the line.**

1. **Problem:** Factorize the expression $9x^2 + 8x - 1$. 2. **Formula and rules:** To factorize a quadratic expression $ax^2 + bx + c$, we look for two numbers that multiply to $a

1. The problem is to simplify the expression $2 \times 7 + 3x + 15$. 2. Use the order of operations: multiplication before addition.

1. **Problem Statement:** Given graphs of parabolas, write expressions for the parabolas that match the graphs where pairs of parabolas are identical.

1. **State the problem:** Find the equation of the straight line passing through points (-5, 0) and (0, 5) in the form $y = mx + c$. 2. **Formula used:** The equation of a line is

1. **Stating the problem:** We are given a line passing through points $(-2,0)$ and $(0,4)$. We need to find:

1. The problem is to solve the equation for $x$: $$3x + 5 = 20$$ 2. The formula used here is to isolate $x$ by performing inverse operations. We want to get $x$ alone on one side o

1. Задатак: Израчунати вредности тригонометријских функција углова $\alpha$ и $\beta$ ако је $c=10$ cm и $b=6$ cm. 2. Формула: Користимо Питагорину теорему и дефиниције тригонометр

1. **State the problem:** Find the number $x$ such that when added to $1\frac{1}{3}$, the result is 2. 2. **Write the equation:**

1. **State the problem:** Find the equation of the line passing through the points (-6,6), (-1,1), (2,-2), and (6,-6). 2. **Formula used:** The equation of a line in slope-intercep

1. **State the problem:** Expand and fully simplify the expression $$(2x - 1)(x - 5)(x + 6)$$. 2. **Formula and rules:** To expand the product of multiple binomials, first multiply

1. **Problem 8a:** Complete the table for the function $$3x + 4y = 36$$. Given values:

1. **State the problem:** We have two simultaneous equations: (1) $x - 4y = 12$

1. The problem is to find the two solutions to the equation $$(5x - 1)(x - 2) = 0$$. 2. According to the zero product property, if the product of two factors is zero, then at least

1. **State the problem:** Find the two solutions to the equation $$(3x - 1)(x - 5) = 0$$. 2. **Formula and rule:** The zero product property states that if a product of two factors

1. **Planteamiento del problema:** Resolver el sistema de ecuaciones por el método de sustitución: $$\begin{cases} 4x = 5 - 5y \\ 9x + 8y = 13 \end{cases}$$

1. **Planteamiento del problema:** Dividir el polinomio $x^{2} - 4x - 15 + 18$ entre el binomio $x - 6$. 2. **Simplificación inicial:** Primero simplificamos el polinomio en el num