🧮 algebra

1. The problem asks to express each expression in terms of $y=3^x$ and simplify. 2. Recall the properties of exponents:

1. **State the problem:** Solve for $x$ in the equation $\frac{2x - 3y}{4} = w.$ 2. **Isolate the term with $x$:** Multiply both sides by 4 to eliminate the denominator:

1. **State the problem:** Solve for $x$ in the equation $$\frac{3x + 4y}{5} = z.$$ 2. **Isolate the term with $x$:** Multiply both sides by 5 to eliminate the denominator:

1. For each relation, determine the domain, range, and whether it is a function. **a)** Relation: $\{(-3,0), (-1,1), (0,1), (4,5), (0,6)\}$

1. **Problem Statement:** Determine which of the following statements are true for the functions $f : \mathbb{R} \to \mathbb{R}$ and $g : \mathbb{R} \to [0, \infty)$ defined by $f(

1. **Determine domain, range, and function status for each relation:** **a)** Relation: $\{(-3,0), (-1,1), (0,1), (4,5), (0,6)\}$

1. **Problem 17:** The area of the rectangle exceeds the area of the square by 2 cm². Find $x$. 2. **Step 1: Define the areas.**

1. **State the problem:** Solve for $x$ in the equation $X = 2^x$ when $X = 2^x$ and $X=2^x$ is given as $2^x = 2^x$. 2. **Rewrite the problem:** The problem is to find $x$ such th

1. Problem 14: A contractor has 560 workers to complete a stadium part in 9 months but now must finish in 5 months. Find extra workers needed. 2. Use the work formula: Work = Numbe

1. **Problem Statement:** Convert the repeating decimal $0.\overline{236}$ into a fraction. 2. **Define the repeating decimal as a variable:** Let $x = 0.236236236\cdots$

1. **State the problem:** Solve the equation $$x^4 - 10x^2 + 9 = 0$$ for $x$. 2. **Use substitution:** Let $y = x^2$. Then the equation becomes $$y^2 - 10y + 9 = 0$$.

1. The problem is to solve the equation or system given by "solve all". Since no specific equation or system is provided, I will assume the user wants a general explanation on how

1. **Find the L.C.M of 10, 15, and 25.** The Least Common Multiple (L.C.M) of numbers is the smallest number that is a multiple of all the given numbers.

1. **State the problem:** Given points $(-4,16)$, $(4,16)$, $(-5,25)$, and $(5,25)$, find the function that fits these points. 2. **Analyze the points:** Notice the points are symm

1. The problem is to find the relation or equation that connects given variables or quantities. 2. To find a relation, first identify the variables involved and what is known about

1. **Problem (a): Solve** $$\frac{4}{x - 1} = \frac{x}{2x^2 + 3x - 5}$$ 2. **Step 1: Factor the denominator on the right side**

1. The problem asks: If A can finish work in $n$ days, what part of work does A finish in 1 day? The formula for work done per day is $\frac{1}{n}$.

1. **State the problem:** Calculate the value of the expression $$10 \times 50 + 242 \times 214 + \frac{215}{2358} + \frac{214}{e^5} + 34$$. 2. **Recall the order of operations:**

1. **Problem statement:** Given the functions $f(x) = 2x + 3$ and $g(x) = x^2$, calculate: (i) $f(f(x))$

1. **State the problem:** Find the value(s) of $x$ that satisfy the equation $$\frac{x(x - 3)}{(x + 1)^2} = \frac{3}{5}$$

1. **State the problem:** Calculate the sum $$\sum_{r=4}^{n-1} (6r^5 + 2^r + 7)$$ for a general upper limit $n-1$. 2. **Break down the sum:** The sum can be separated into three su