🧮 algebra

1. **State the problem:** We are given two numbers, say $x$ and $y$, with two conditions: - Their sum is less than 2.

1. Let's start with the first problem: \(y = 5^x\). 2. This is an exponential function where the base is 5 and the exponent is \(x\).

1. **State the problem:** Simplify the expression $$\frac{\sqrt{10(\sqrt{2} + \sqrt{10})} + \sqrt{3}(5\sqrt{12} + \sqrt{15})}{(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2})}$$ and expr

1. **State the problem:** Simplify the expression $14 \times 3\sqrt{5} \times \sqrt{15}$. 2. **Recall the rules:** The product of square roots can be combined as $\sqrt{a} \times \

1. The problem provides two sets of coordinate pairs (x, y) and asks to analyze them. 2. We will focus on the first table only, as per instructions to solve the first problem compl

1. The problem provides two tables of values with variables $x$ and $y$ and asks to analyze or find a relationship between $x$ and $y$ for each table. 2. To find the relationship,

1. The problem is to convert the fraction $\frac{41}{50}$ into a decimal. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $$\text{D

1. **State the problem:** We are given the quadratic function $g(t) = -16t^2 + 30t$ which models height in feet as a function of time $t$ in seconds. 2. **Identify the coefficients

1. **State the problem:** We need to find the equation of the line graphed, which passes through points approximately $(-3, -2)$ and $(3, 4)$ and intersects the y-axis near $-2$. 2

1. **State the problem:** Determine which of the given functions represents a nonlinear function of $x$. 2. **Recall the definition:** A function is linear if it can be written in

1. Problem: Evaluate the expression $y^2 + 3y - 4$ when $y = 9$. 2. Formula and rules: To evaluate a polynomial at a given value, substitute the value for $y$ and follow the order

1. The problem asks to fill in the box for each expression, which typically means to find the missing value or simplify the expression. 2. Since no specific expressions are given,

1. The problem is to find the values of A, B, and C for the number 11. 2. Usually, A, B, and C represent digits or coefficients in an equation or expression. Since the problem is n

1. The problem is to explain the function notation $f$. 2. In mathematics, $f$ usually denotes a function, which is a rule that assigns each input exactly one output.

1. **State the problem:** Convert the scientific notation $1.2 \times 10^2$ into a standard number. 2. **Recall the rule for scientific notation:** $a \times 10^n$ means move the d

1. **State the problem:** We are given the function $f(x) = -\frac{1}{5}x$ and asked to graph it, then reflect the graph across the y-axis and write the function $g(x)$ describing

1. The problem asks for the speed of an earthworm that wriggles 27 inches in 9 minutes. 2. Speed is calculated using the formula:

1. **State the problem:** Simplify and solve the equation $12s - 4s + 2 = 10$ for $s$. 2. **Combine like terms:** The terms $12s$ and $-4s$ are like terms because they both contain

1. **State the problem:** Solve the equation $4 + 3(p - 13) = 7$ for $p$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses:

1. The problem is to analyze the function $\rho(x) = e^{-x}$.\n\n2. This is an exponential decay function where the base of the exponent is $e$, the natural exponential constant ap

1. Let's clarify the problem: You want to know where unknown variables typically appear in mathematical expressions or equations. 2. Unknown variables are usually represented by le