🧮 algebra

1. **Problem Statement:** An amount of 5000 is invested in three parts at 6%, 7%, and 8% per annum respectively. The total annual income is 358. The income from the first two inves

1. **State the problem:** We need to find two consecutive multiples of 9 whose product is 486. 2. **Define variables:** Let the first multiple be $9n$, where $n$ is an integer.

1. Simplify $\sqrt{72} + (\sqrt{3}\sqrt{6})$ and write in the form $a\sqrt{b}$ where $a,b$ are integers. - $\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}$

1. **Stating the problem:** We need to solve the equation or expression given by the user. Since the user did not specify a particular problem, let's consider a common algebra prob

1. **Problem a:** Simplify \(\left(\frac{6x^{3}}{7y^{3}}\right)\left(\frac{5x^{3}}{2y^{4}}\right)^{-1}\) and write as a fraction with no negative exponents. 2. Recall that \(\left(

1. **State the problem:** Simplify the expressions $$\sqrt[4]{25x^2}$$ and $$\sqrt[6]{81g^3}$$. 2. **Recall the formula:** The nth root of a product is the product of the nth roots

1. **Stating the problem:** A and B together can complete a work in 12 days.

1. **State the problem:** We are given two payment options for hockey players based on goals scored. We need to find missing values, calculate payments, draw graphs, and analyze th

1. **Problem Statement:** Identify the equation of a circle given its graph. 2. **Recall the standard form of a circle's equation:**

1. **State the problem:** Solve the equation $$\frac{5}{a - 4} + \frac{2}{a + 1} = \frac{-31}{a^2 - 3a - 4}$$ for $a$ and determine if the solutions are extraneous. 2. **Identify t

1. **State the problem:** Simplify the expression $$\frac{5x}{3x^2} - \frac{7}{6x}$$. 2. **Find a common denominator:** The denominators are $3x^2$ and $6x$. The least common denom

1. **State the problem:** We need to find the points where the rational function $$f(x) = \frac{x^2 + 6x}{x^2 + 4x - 12}$$ has discontinuities. 2. **Recall the rule for discontinui

1. **State the problem:** Expand and simplify the logarithm expression $$\log_2 \left( \frac{x^5}{8} \right)$$. 2. **Recall logarithm rules:**

1. **State the problem:** The water level of a lake decreases by 3% each week. The initial water level is 520 ft. We need to find the water level after 8 weeks. 2. **Formula used:*

1. The problem involves finding the value at the center of a triangle given the values at its three vertices. 2. The formula used here is the weighted average or centroid formula f

1. **State the problem:** The water level of a lake decreases by 3% each week. The initial highest water level is 520 ft. We need to find the water level after 8 weeks. 2. **Formul

1. **State the problem:** Simplify the expression $5\sqrt{96} - 7\sqrt{54}$ and identify which option matches the simplified result. 2. **Recall the rule:** To simplify expressions

1. **State the problem:** Simplify the expression $$\frac{x^{\frac{3}{4}} \cdot x^5}{x^{\frac{1}{4}}}$$ and identify which of the options A, B, C, or D matches the simplified form.

1. **State the problem:** Find the equation of the line passing through points $(-2,0)$ and $(0,4)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x

1. The problem is to solve the equation or expression you want to solve. Since you did not specify the exact problem, please provide the equation or expression you want solved. 2.

1. **State the problem:** We need to evaluate the expression $$x^3 + 3x^2y + y^3$$ given $$x=5$$ and $$y=-2$$. 2. **Recall the formula:** The expression resembles the expansion of