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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

During a 5-second time interval, the average acceleration a, in meters per second squared, of an object with an initial velocity of 12 meters per second is defined by the equation $a equals, the fraction with numerator v subscript f, end subscript, minus 12, and denominator 5$ , where v_f is the final velocity of the object in meters per second. If the equation is rewritten in the form v_f = xa + y, where x and y are constants, what is the value of x ?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

The correct answer is 5. The given equation can be rewritten in the form $v subscript f equals, x a, plus y$ , like so:

$a, equals, the fraction with numerator v subscript f, end subscript, minus 12, and denominator 5$

$v subscript f, end subscript, minus 12, equals 5 a$

$v subscript f equals, 5 a, plus 12$

It follows that the value of x is 5 and the value of y is 12.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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