🧮 algebra

1. **State the problem:** Calculate the shop owner's profit on 8 spark plugs. 2. **Given data:**

1. **State the problem:** We need to find the labor cost per hour if the job takes 1.7 hours and the labor flat rate is 80.00. 2. **Identify the formula:** Labor cost per hour = \f

1. **State the problem:** Calculate the sales tax to the nearest cent for the parts only, given a 5% sales tax rate. 2. **Identify the parts and their costs:**

1. **State the problem:** Find the value of $$\left((\log_2 16)^2\right)^{\frac{1}{\log_2(\log_2 16)}} \times \left(\sqrt{5}\right)^{\frac{1}{\log_5 5}}$$. 2. **Recall important ru

1. **State the problem:** Find the value of $$\left((\log_2 16)^2\right)^{\log_2(\log_2 16)} \times \left(\sqrt{5}\right)^{\frac{1}{\log_5 5}}$$. 2. **Recall important formulas and

1. **State the problem:** Find the value of $$\frac{(\log_2 16)^2}{\log_2(\log_2 16)} \times \frac{\sqrt{5}}{\log_5 5}$$. 2. **Recall important formulas and rules:**

1. **State the problem:** Solve the inequality $$\frac{(2-x)^3 (x-21)^6}{(2x-3)^2} \ge 0.$$\n\n2. **Identify critical points:** The numerator is zero at $x=2$ and $x=21$. The denom

1. **State the problem:** Simplify the expression $$\frac{n!}{(n-4)!}$$ assuming $n$ is an integer and $n \geq 4$. 2. **Recall the factorial definition:** For any integer $k \geq 0

1. **State the problem:** Evaluate the expression $$\frac{17!}{3!(17-3)!}$$ and determine if the result is an integer or not. 2. **Recall the formula:** This expression matches the

1. **State the problem:** Evaluate the expression $ (4 + 3)! $ and determine if the result is an integer or not. 2. **Recall the factorial definition:** For any positive integer $n

1. **State the problem:** Simplify the expression $$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$$ without using a calculator. 2. **Formula and rules

1. Simplify $\frac{10^{15}}{10^3}$ using the rule $\frac{a^m}{a^n} = a^{m-n}$. $$\frac{10^{15}}{10^3} = 10^{15-3} = 10^{12}$$

1. Simplify $\frac{10^{15}}{10^3}$ using the quotient rule for exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ $$\frac{10^{15}}{10^3} = 10^{15-3} = 10^{12}$$

1. The problem asks for the three inequalities that define the unshaded triangular region bounded by three lines. 2. The first boundary is a solid decreasing line through points (0

1. **Problem statement:** Find the equation of the line passing through points $A(5,-2)$ and $B(7,3)$. 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,

1. The problem asks: Why 54? We interpret this as understanding the number 54 in a mathematical context. 2. Let's explore the properties of 54.

1. **Stel het probleem vast:** We hebben een totaal van 52 kaarten, maar er zijn er een aantal verloren gegaan. We noemen het aantal overgebleven kaarten $x$.

1. **Énoncé du problème :** Exercice 4 : On considère la suite arithmétique $(u_n)$ de premier terme $u_0=3$ et de raison $2$.

1. **Problem statement:** In a park, circular flower beds with diameter $d = 4.90$ m are created.

1. The problem asks to complete a chart analyzing characteristics of three exponential functions: $y=(2.5)^x$, $y=4(2)^x$, and $y=3\left(\frac{1}{2}\right)^x$. 2. The general form

1. **State the problem:** Solve the inequality $$\frac{x^2 - 2x - 8}{x^3 + x} \geq 0$$. 2. **Factor numerator and denominator:**