🧮 algebra

1. The problem is to identify Tom's first mistake in finding the inverse of the function $f(x) = 4x - 2$ and how to correct it. 2. Tom's steps are:

1. The problem is to find the inverse of the function $$f(x) = \frac{1}{2}x + 7$$. 2. To find the inverse function, we start by replacing $$f(x)$$ with $$y$$:

1. **State the problem:** Keith is finding the inverse of the function $f(x) = 7x + 5$ and suspects an error in his steps. 2. **Recall the formula and rules for finding inverses:**

1. **State the problem:** Find the inverse function of \( f(x) = \frac{3 - x}{7} \). 2. **Recall the formula for inverse functions:** To find the inverse, swap \( x \) and \( y \)

1. The problem is to convert the fraction $\frac{1}{4}$ into a decimal number. 2. To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom n

1. Simplify (a) $\log_a b^m$ and (b) $\log_a b^n$. Using the logarithm power rule: $\log_a b^m = m \log_a b$ and $\log_a b^n = n \log_a b$.

1. **State the problem:** Find the value of $x$ such that $$\sqrt[3]{4^{2x}} + \frac{1}{2} = \frac{1}{32}.$$ 2. **Rewrite the cube root:** Recall that the cube root of a number is

1. Le problème consiste à évaluer l'expression $g^{-1}(9)$, c'est-à-dire trouver l'antécédent de 9 par la fonction $g$. 2. Pour cela, il faut connaître la fonction $g$ et sa foncti

1. **State the problem:** We need to compare the decimals 2.36, 2.403, 2.6, and 2.402 to the decimal shown in the diagram, which is approximately 2.40. 2. **Understand the diagram

1. The problem is to determine which of the given inequality sentences are true. 2. Recall the meaning of inequality symbols:

1. The problem asks us to determine which of the given inequalities or equalities are true. 2. Let's analyze each statement one by one:

1. The problem is to determine which of the given comparison sentences are true. 2. We will evaluate each comparison:

1. The problem asks us to determine which of the given inequalities are true. 2. Let's analyze each inequality one by one:

1. The problem is to simplify the expression \( \sqrt{x}625 \).\n2. First, clarify the expression: it likely means \( \sqrt{x} \times 625 \) or \( 625 \sqrt{x} \).\n3. The square r

1. The problem is to solve the equations shown in the images. Since no images are provided, please upload the images or type the equations you want solved. 2. Generally, to solve a

1. The problem is to solve an equation or expression by substituting numbers and simplifying step-by-step. 2. First, identify the equation or expression to solve. For example, if t

1. **State the problem:** We need to find the Average Tax Rate (ATR) for Alice, Ben, and Carrie given a tax rule: for each dollar earned above 500000, the worker pays 50% tax on th

1. The problem is to find the value of $a$ in the expression or equation given (though the exact equation is not specified). 2. To solve for $a$, we need the equation or expression

1. Planteamos el problema: Dados los vectores $a = (3, 5, 0)$ y $b = \left(-\frac{1}{4}, 0, \frac{5}{3}\right)$, hallar el vector $x$ tal que $$6b + 5x = a.$$\n\n2. Usamos la propi

1. The problem is to solve a quadratic equation given values for $a$, $b$, and $c$ in the standard form $$ax^2 + bx + c = 0$$. 2. The formula to find the roots of the quadratic equ

1. **Problem statement:** We have a traffic network with 4 nodes (A, B, C, D) and 5 flow variables $x_1, x_2, x_3, x_4, x_5$ representing vehicle flow rates on roads. We need to se