🧮 algebra

1. **Problem:** Determine the speeds of accessing files in the Finance bucket folders by year and by month after 4 days. 2. **Given functions:**

1. Let's first clarify what the number 5 represents in the given context. 2. If 5 is part of an equation or expression, please provide the full problem for precise assistance.

1. The problem states we need to find the cost of fencing a garden with given dimensions and a cost per meter. 2. First, identify the perimeter of the garden. The garden dimensions

1. The problem is to understand and express the cube of the variable $g$, which is written as $g^3$. 2. Cubing a number or variable means multiplying it by itself three times: $$g^

1. **State the problem:** We are given the function $$g(x) = 1 + x^2$$ and need to analyze its properties. 2. **Identify the type of function:** This is a quadratic function, where

1. The expression provided is $((x^2 - y^2) + 1 (x y^2))$. Let's clarify and rewrite it for proper interpretation: $$x^2 - y^2 + xy^2$$ 2. We can analyze the function $f(x,y) = x^2

1. **State the problem:** We have two investments that pay out every 4 years and every 6 years respectively. We want to find out after how many years both investments will pay out

1. **State the problem:** Simplify the expression $$(2y - 11)(y^2 - 3y + 2).$$ 2. **Apply distributive property (FOIL):** Multiply each term in the first polynomial by each term in

1. The problem is to simplify the expression consisting of two fractions: $\frac{a^3}{1}$ and $\frac{a^3}{4}$.\n\n2. Write the expression clearly: $$\left[ \frac{a^3}{1}, \frac{a^3

1. **State the problem:** There were some children at a party. Each child took a gift for each of their friends, and altogether there were 81 gifts. We need to find out how many ch

1. **State the problem:** Simplify the expression $$(a^{7})^{4} (a^{5})^{1}$$ and identify the simplest form. 2. Use the power of a power rule: $$(a^{m})^{n} = a^{m \cdot n}$$.

1. State the problem: We need to simplify the expression $$(5r + 7)(5r - 7)$$. 2. Recognize the form: This is a product of two binomials in the form $(a + b)(a - b)$, which is a di

1. Stated problem: Multiply the binomials $ (4n + 3)(n + 9) $. 2. Use the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second

1. **Stating the problem:** Simplify and solve the equation $$31 \times 7(t^2 + 5t - 9) + t = t(7t - 2) + 13$$ for $t$. 2. **Expand the left side:**

1. Problem a: Simplify $a^{3/2} \cdot a^{4/3}$. Use the exponent multiplication rule $a^m \cdot a^n = a^{m+n}$:

1. **State the problem:** Simplify the algebraic expression $$2ab(7a^4b^2 + a^5b - 2a)$$. 2. **Distribute** $2ab$ to each term inside the parentheses:

1. **State the problem:** Solve the system of equations \(8 = 2^{x+y}\) and \(1 = 3^{x-y}\) simultaneously. 2. **Rewrite the equations using properties of exponents:**

1. **State the problem:** We want to solve the system of equations simultaneously: $$8 = 2(x+y)$$

1. **Find the domain and range of the function** $h(x) = \sqrt{x^2 - 4}$. Step 1: The expression under the square root, called the radicand, must be non-negative for $h(x)$ to be r

1. The problem is to determine the value or nature of "H", which is not clearly specified. 2. Since no further context or equation involving "H" is given, it is impossible to proce

1. The domain of a function is the set of all possible input values (usually $x$ values) for which the function is defined. 2. To determine the domain, identify values of $x$ that