🧮 algebra

1. **State the problem:** We are given two functions $S(s) = s^2 + s + 1$ and $T(s) = s - 5$. We need to find the sum $S(s) + T(s)$. 2. **Formula used:** To add two functions, we a

1. The problem asks to find the composition of functions $(fg)(x)$ where $f(x) = 1 - x^2$ and $g(x) = 1 - x$. 2. The composition $(fg)(x)$ means $f(g(x))$, which is the function $f

1. **Problem:** Given $f(x) = 2x^2 + 1$, find $g(x)$ where $g(x) = 2[f(x)]^2 - 1$. 2. **Formula:** To find $g(x)$, substitute $f(x)$ into the expression for $g(x)$:

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$\begin{cases} 2x + y = 8 \\ 2x - y = 12 \end{cases}$$

1. The problem asks to find which matrices among A, B, C, and D are equivalent. 2. Two matrices are equivalent if they have the same dimensions and the same corresponding elements.

1. The problem is to combine the terms $-288x$ and $-288x$. 2. When combining like terms, you add or subtract their coefficients while keeping the variable part the same.

1. **State the problem:** Simplify the expression $4x \times -72$. 2. **Formula and rules:** Multiplying a variable term by a constant involves multiplying the constants and keepin

1. **State the problem:** We are given expressions for the sides of a quadrilateral and need to find the values of $a$ and $b$. 2. **Analyze the quadrilateral:** The quadrilateral

1. **State the problem:** Max wants to find out how many bottles of soda he must sell so that his total sales equal his total expenses. 2. **Define variables and costs:** Let $x$ b

1. **State the problem:** Two dogs start running toward a ball from different distances and speeds. We want to find the time when both dogs are the same distance from the ball.

1. **Problem Statement:** Consider the function $$f(x) = \frac{1}{x^2 + x - 6}$$.

1. **State the problem:** Find a polynomial function in factored form with zeros 2 (of multiplicity 2) and 3, passing through the point (1, 6). 2. **Write the general form:** Since

1. The problem is to simplify or analyze the expression $\frac{3\ln x + 7}{\sin^2 x}$. 2. The expression is a fraction where the numerator is $3\ln x + 7$ and the denominator is $\

1. **State the problem:** We have two sets of scores X and Y: | X | Y |

1. **State the problem:** Factor the quadratic expression $8x^2 - 2x - 10$ by extracting the greatest common factor (GCF). 2. **Identify the GCF:** The GCF of the coefficients 8, -

1. The problem is to solve the equation given by the user, but since no specific equation was provided, let's consider a general approach to solving algebraic equations. 2. The gen

1. **State the problem:** We need to match each quadratic function to its corresponding graph. 2. **Recall the general form of a quadratic function:** $$f(x) = ax^2 + bx + c$$ wher

1. The problem asks to solve an equation graphically, but no specific equation is provided. 2. To solve an equation graphically, you plot the functions on a coordinate plane and fi

1. Vamos resolver o sistema 3.1 pelo método gráfico. O sistema é:

1. **Write a rule for the line that contains the points (0, \frac{3}{4}) and (2 \frac{1}{2}, 3 \frac{1}{4})** Step 1: Identify the points as \( (0, \frac{3}{4}) \) and \( (2.5, 3.2

1. **Write a rule for the line that contains the points (0, \frac{3}{4}) and (2 \frac{1}{2}, 3 \frac{1}{4})**. Step 1: State the problem.