🧮 algebra

1. **State the problem:** We have data points showing the relationship between years of experience ($x$) and amount charged per hour ($y$). We want to find the line of best fit and

1. **State the problem:** Solve the equation $$3(x + 5) = 33$$ for $$x$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. **Stating the problems:** We have three algebraic expressions/equations to solve or simplify:

1. **State the problem:** Solve the equation $$3(3v - 8) = 21$$ for the variable $v$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** We have a scatter plot showing the relationship between time spent watching TV (x) and time spent doing homework (y). We want to find the line of best fit

1. **State the problem:** Solve the equation $$2(2u + 7) = 42$$ for the variable $u$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses:

1. The problem asks to find 70% of 62. 2. To find a percentage of a number, use the formula:

1. The problem asks to find 30% of 38. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. **State the problem:** Find 20% of 54 without using a calculator. 2. **Formula:** To find a percentage of a number, use the formula:

1. Given ratios $\frac{a}{b} = 13$ and $\frac{b}{c} = 17$, find $a+b+c$ where $a,b,c \in \mathbb{N}$. Step 1: Express $a$ and $b$ in terms of $c$:

1. **Problem:** Given $a,b,c \in \mathbb{N}$ with the system: $$\begin{cases} a \cdot b = 13 \\ b \cdot c = 17 \end{cases}$$

1. **State the problem:** Solve the equation $$0 = (3x - 4)^2 - 7(3x - 4) + 10$$ for $x$. 2. **Use substitution:** Let $$y = 3x - 4$$ to simplify the equation to $$0 = y^2 - 7y + 1

1. **State the problem:** Solve the quadratic equation $$(3x - 4)^2 - 7(3x - 4) + 10 = 0.$$\n\n2. **Use substitution:** Let $y = 3x - 4$. The equation becomes $$y^2 - 7y + 10 = 0.$

1. **State the problem:** Devi spent fractions of her money on lunch and a book, then used the remainder to buy a poster costing 60 more than the book. We need to find the initial

1. **Тодорхойлолт:** $x^2 + (k+2)x + 25 = 0$ тэгшитгэлийн нэг шийдтэй байх нөхцөл юу вэ? 2. **Формул:** Квадрат тэгшитгэлийн дискриминант $D = b^2 - 4ac$

1. **Problème 9a**: Trouver la mesure manquante du côté d'un carré dont le périmètre est donné par $$P = 32x^2 + 20x - 16$$ mètres. 2. La formule du périmètre d'un carré est $$P =

1. **Problem Statement:** You need to find four types of lines (positive slope, negative slope, zero slope, undefined slope) from photos, identify two points on each, calculate the

1. **State the problem:** We need to simplify and understand the expression $$\frac{1}{x \cdot (40^4 + x^2 \cdot 2) \cdot (40^1 + x^2)}$$. 2. **Rewrite the expression:** The expres

1. Stating the problem: We need to simplify and understand the expression $$\frac{1}{x \cdot (4 + x^2)^{41} \cdot (1 + x^2)}$$. 2. The expression involves powers and products in th

1. **State the problem:** We want to find the partial fraction expansion of the function $$\frac{1}{x(40^4 + x^2)^2(1 + x^2)}.$$\n\n2. **Rewrite the function:** The denominator is

1. **State the problem:** Solve the equation $|y| + 11 = 16$ for $y$. 2. **Recall the definition and properties of absolute value:** The absolute value $|y|$ represents the distanc