if a polynomial a2+ x+b passing through the point 3,0and 5,0 find a and b
Answers
Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.
Dividing both sides of 5x = 4 by 5 yields x =
_4
5
. Te value of x can now be
substituted into the expression 10x + 3, giving 10 ( _4
5 ) + 3 = 11.
Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and
10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.
Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,
contradicting the given equation, 5x + 6 = 10. For example, choice A is
incorrect because if the value of 10x + 3 were 4, then it would follow that
x = 0.1, and the value of 5x + 6 would be 6.5, not 10.
Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.
Ten, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives
5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting
2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Terefore, the solution to the
given system of equations is (2, −2).
Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substi-
tuting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. Te value of y can then
be found in the same way as before.
Choices A, C, and D are incorrect because when the given values of x and
y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the
equations are not true. Tese answers may result from sign errors or other
computational errors.
Choice A is correct. Te price of the job, in dollars, is calculated using
the expression 60 + 12nh, where 60 is a fxed price and 12nh depends on the
number of landscapers, n, working the job and the number of hours, h, the job
takes those n landscapers. Since nh is the total number of hours of work done
when n landscapers work h hours, the cost of the job increases by $12 for each
hour a landscaper works. Terefore, of the choices given, the best interpretation
of the number 12 is that the company charges $12 per hour for each landscaper.
Choice B is incorrect because the number of landscapers that will work each
job is represented by n in the equation, not by the number 12. Choice C is
incorrect because the price of the job increases by 12n dollars each hour,
which will not be equal to 12 dollars unless n = 1. Choice D is incorrect
because the total number of hours each landscaper works is equal to h. Te
number of hours each landscaper works in a day is not provided.