🧮 algebra

1. **State the problem:** Calculate the total pay for 8 overtime hours at a rate of $13.50 per hour with time and a half. 2. **Formula:** Overtime pay rate = Regular pay rate \time

1. **State the problem:** Calculate the total pay for 35 regular hours at a rate of 8.81 per hour. 2. **Formula used:** Total pay = hourly rate \times number of hours

1. The problem asks to find the pay for a given condition, but the specific condition is not provided. 2. To solve pay-related problems, we typically use the formula: $$\text{Pay}

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} 5x - 2y + 3z = 6 \\ -4x + 6y - 7z = -3 \\ 3x + 2y - z = 6 \end{cases}$$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 4y + z = 9 \\ -x + 2y + 2z = 0 \\ 2x + 2y - z = 9 \end{cases}$$

1. **State the problem:** Daniel has two income options: hourly pay at 10 per hour and a salary of 110 per day. We need to write equations for each, graph the relations, and decide

1. The problem is to find the equation representing the table of values and verify if the given equations and graphs are correct. 2. The general form of a linear equation is $$y =

1. The problem is to solve a quadratic equation using the grade 10 quadratic formula. 2. The quadratic formula is given by $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ where $a$, $b$, and

1. **State the problem:** We have a rectangle with surface area 60 cm², length $x+9$, and width $x-8$. We need to find $x$ and the dimensions. 2. **Formula:** Area of rectangle = l

1. **Problem Statement:** We are asked to draw sets of counters representing given ratios and find how many different ways these can be done.

1. The problem is to find the value of $k$ for which the quadratic equation $$x^2 + (k+8)x + 9k = 0$$ has a real double root. 2. A quadratic equation $$ax^2 + bx + c = 0$$ has a re

1. **Problem statement:** Determine the condition on $k$ such that the quadratic equation $kx^2 + 3x + 6 = 0$ has two unique real roots. 2. **Formula used:** For a quadratic equati

1. **Énoncé du problème :** Soit la suite $(u_n)$ définie par $u_0=1$ et $u_{n+1} = \frac{5u_n + 3}{u_n + 3}$ pour tout $n \in \mathbb{N}$.

1. **State the problem:** Factor the expression $$18m - 27n$$. 2. **Identify the greatest common factor (GCF):** The coefficients are 18 and 27. The GCF of 18 and 27 is 9.

1. **State the problem:** Factor the expression $$54x + 15y - 9$$. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 54, 15, and 9. The GCF of 54, 15, and

1. **State the problem:** We need to find the cost of each item sold separately: small pizza ($x$), liter of soda ($y$), and salad ($z$). 2. **Write the system of equations from th

1. Énoncé du problème : Déterminer la nature de la fonction $f(x)=\frac{9x-10}{2x-3}$ et ses éléments caractéristiques. 2. Domaine de définition : La fonction est définie pour tous

1. **State the problem:** Solve the inequality $-2x - 76 > -66$. 2. **Isolate the variable term:** Add 76 to both sides to get rid of the constant on the left.

1. **State the problem:** Find the non-permissible values (values of $x$ that make the denominator zero) for the rational expression $$\frac{x^2 + 2}{x^2 - x - 6}$$ 2. **Formula an

1. The problem asks which inequality is true when $w = -2$. 2. We will substitute $w = -2$ into each inequality and check if the inequality holds.

1. Problema: Raskime begalinės nykstamosios geometrinės progresijos sumą, kai pirmasis narys $a_1=10$, o bendrasis vardiklis $r=\frac{1}{5}$.\n\n2. Formulė: Begalinės nykstamosios