Question

which of the following expressions represents nine decreased by half of x?
\\(\boldsymbol{\frac{1}{2}x - 9}\\)
\\(\boldsymbol{9 - \frac{1}{2}x}\\)
\\(\boldsymbol{\frac{x - 9}{2}}\\)
\\(\boldsymbol{\frac{9 - x}{2}}\\)
question 10
evaluate \\(3x^2 - 2xy + 4y^2\\) for \\(x = -3\\) and \\(y = 2\\).
\\(\boldsymbol{1}\\)
\\(\boldsymbol{10}\\)
\\(\boldsymbol{31}\\)
\\(\boldsymbol{55}\\)

Explanation:

First Question:

Step1: Parse the phrase

"Nine decreased by half of x" means start with 9, subtract half of x. Half of x is $\frac{1}{2}x$.

Step2: Form the expression

The operation is $9 - \frac{1}{2}x$.

Step1: Substitute $x=-3, y=2$

Substitute values into $3x^2 - 2xy + 4y^2$:
$3(-3)^2 - 2(-3)(2) + 4(2)^2$

Step2: Calculate each term

$3(9) - 2(-6) + 4(4) = 27 + 12 + 16$

Step3: Sum the terms

$27 + 12 + 16 = 55$

Answer:

$\boldsymbol{9 - \frac{1}{2}x}$

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Second Question: