🧮 algebra

1. **State the problem:** Find the equation of the line with slope $\frac{1}{3}$ and y-intercept 5. 2. **Recall the slope-intercept form:** The equation of a line is given by $$y =

1. Problem Q11: If 5 workers can complete a task in 4 days, how many days will it take 10 workers, assuming the same efficiency? 2. Formula: The work done is constant, so $\text{Wo

1. **State the problem:** Simplify the expression $21x + 14$. 2. **Identify the common factor:** Both terms $21x$ and $14$ have a common factor of $7$.

1. Problem Q9: Write the ratio of repeat customers to new customers. Given: Total customers = 200, Repeat customers = 80

1. **State the problem:** Factor the cubic polynomial expression $$24x - 2x^2 - 2x^3$$ completely. 2. **Write the polynomial:** $$24x - 2x^2 - 2x^3$$

1. **State the problem:** Factor the cubic polynomial $$x^3 - 15x^2 + 50x$$ completely. 2. **Identify common factors:** Notice that each term contains an $$x$$, so factor $$x$$ out

1. **State the problem:** Simplify the expression $$(2a^2b)^3 (4b^5)^2$$. 2. **Recall the exponent rules:**

1. **Problem Q6:** Write the ratio of full-time staff to part-time staff in simplest form. Given: Full-time staff = 12, Part-time staff = 18.

1. **Problem Q9:** Out of 200 customers, 80 are repeat customers and the rest are new customers. Write the ratio of repeat customers to new customers. 2. **Step 1:** Calculate the

1. **State the problem:** Solve the system of equations: $$x - y = 2$$

1. **State the problem:** We need to find the average number of visits per day given that a company website receives 2,400 visits in 8 days. 2. **Formula used:** The average (mean)

1. **State the problem:** We have a population model given by the formula $$P = 71.2e^{0.0329t}$$ where $t=1$ corresponds to the year 1971. We want to find the year when the popula

1. **State the problem:** We need to solve the equation or expression provided by the user. Since no specific problem was given, let's consider a general example: Solve for $x$ in

1. **State the problem:** Rewrite the radical expressions with positive exponents. 2. **Recall the rule:** A radical expression like $\sqrt[n]{x}$ can be written as $x^{\frac{1}{n}

1. The problem is to simplify the expression $$-14f^{\frac{1}{3}} b^5 \div \left(5 p^{\frac{1}{3}} y h\right)$$. 2. We start by writing the division as a fraction:

1. **State the problem:** Simplify the expression $2 - -2$. 2. **Understand the operation:** The expression contains a subtraction followed by a negative sign. Subtracting a negati

1. **State the problem:** A company produces 480 units in 8 hours. We need to find the production rate per hour. 2. **Formula:** Production rate per hour = \frac{\text{Total units

1. **State the problem:** We need to find the two possible values of $r$ that satisfy the equation $$\frac{216}{r^2} + 19 = 25.$$\n\n2. **Isolate the fraction:** Subtract 19 from b

1. The problem is to simplify an expression with a negative exponent. 2. Recall the rule for negative exponents: $$a^{-n} = \frac{1}{a^n}$$ where $a \neq 0$ and $n$ is a positive i

1. Solve the equation $8t = 56$. 2. To solve for $t$, divide both sides by 8:

1. The problem is to evaluate the expression $$(-8)^{\frac{2}{3}}$$. 2. Recall the rule for rational exponents: $$a^{\frac{m}{n}} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$$ whe