Example Question - evaluate expression
Here are examples of questions we've helped users solve.
Factorial Expression Evaluation
The image shows a mathematical problem that asks to evaluate the expression: \[ \frac{7!}{8!} \] Here "!" represents the factorial operation, which means the product of all positive integers up to that number. For example, \(7!\) is \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\). Now let's evaluate the expression by writing out the factorials: \[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] Substituting these into the original equation: \[ \frac{7!}{8!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \] In this fraction, every term in \(7!\) cancels out with its corresponding term in \(8!\), except for the 8 in the denominator: \[ \frac{7!}{8!} = \frac{1}{8} \] So the evaluated expression is \(\frac{1}{8}\).
Solving an Expression for a Given Value
To solve the expression given in the image for x = -1, we will plug in x = -1 and simplify: Expression: 8(x+1)^2 - 2(x^2 + 6x) Plugging in x = -1 gives: 8(-1 + 1)^2 - 2((-1)^2 + 6(-1)) = 8(0)^2 - 2(1 - 6) = 0 - 2(-5) = 0 + 10 = 10 Therefore, the correct answer is not listed among the choices provided in the image. If this is a question from a test, there might be an error in the question or the answer choices.
Solving for Expression with Given Values
To solve the question, we need to find which expression equals \( \frac{10}{3} \) when \( x = \frac{2}{3} \). Let's start by evaluating each expression with \( x = \frac{2}{3} \): A) \( 4x - 2 \) \[ 4\left(\frac{2}{3}\right) - 2 = \frac{8}{3} - 2 = \frac{8}{3} - \frac{6}{3} = \frac{2}{3} \] B) \( 2 - 8x \) \[ 2 - 8\left(\frac{2}{3}\right) = 2 - \frac{16}{3} = \frac{6}{3} - \frac{16}{3} = -\frac{10}{3} \] C) \( 8x - 6 \) \[ 8\left(\frac{2}{3}\right) - 6 = \frac{16}{3} - 6 = \frac{16}{3} - \frac{18}{3} = -\frac{2}{3} \] D) \( 5x \) \[ 5\left(\frac{2}{3}\right) = \frac{10}{3} \] Option D, \( 5x \), gives us the correct value of \( \frac{10}{3} \) when \( x = \frac{2}{3} \). Therefore, the correct answer is D) \( 5x = \frac{10}{3} \).
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