Example Question - given values
Here are examples of questions we've helped users solve.
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) \( 5x = \frac{10}{3} \).
Subtraction of Functions with Given Values
To solve for the value of h(-1) - g(-1), you'll first need to substitute x = -1 into both functions h(x) and g(x), and then perform the subtraction. h(x) = 2x^2 + x - 1 h(-1) = 2(-1)^2 + (-1) - 1 h(-1) = 2(1) - 1 - 1 h(-1) = 2 - 1 - 1 h(-1) = 0 g(x) = 4x - 5 g(-1) = 4(-1) - 5 g(-1) = -4 - 5 g(-1) = -9 Now calculate h(-1) - g(-1): h(-1) - g(-1) = 0 - (-9) h(-1) - g(-1) = 0 + 9 h(-1) - g(-1) = 9 Therefore, the value of h(-1) - g(-1) is 9, which corresponds to option (b).
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