If #p# = ap3+ bp - 1 where a and b are constants, and #-5# = 3, what is the value of #5#?
5
0
-2
-3
-5
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Manhattan PS- symbolism should be easy but I'm very confused
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scottchapman
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FOLLOW THE DIRECTIONS.scottchapman wrote:If #p# = ap³ + bp - 1, where a and b are constants, and #-5# = 3, what is the value of #5#?
5
0
-2
-3
-5
#p# = ap³ + bp - 1
implies
#-5# = a(-5)³ + b(-5) - 1 = -125a - 5b - 1.
Since #-5# = 3, we get:
-125a - 5b - 1 = 3.
-125a - 5b = 4
125a + 5b = -4.
#p# = ap³ + bp - 1
implies
#5# = a(5)³ + b(5) - 1 = 125a + 5b - 1.
Since 125a + 5b = -4, 125a + 5b - 1 = -4-1 = -5.
The correct answer is E.
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In general, these symbol problems give you a definition first, then specific numbers.
For instance, suppose I said that
x$y = 3x + 2y
That means that for ANY values of x and y, the $ sign tells us to triple x, double y, then add these together. For instance
10$9 = 3*10 + 2*9
since in this case x = 10 (it's the number on the left) and y = 9 (it's the number on the right).
Your problem works the same way.
#p# = ap³ + bp - 1 says take p, then plug it into the equation on the right. We have p = -5, so
#-5# = a*(-5)³ + b*(-5) - 1
We're ALSO told that #-5# = 3. Since #-5# = 3 and = a*(-5)³ + b*(-5) - 1, we can set these equal, giving
3 = a*(-5)³ + b*(-5) - 1
or
4 = -125a -5b
(The color-coding will make sense in a sec.)
We're asked for the value of #5#, or 125a + 5b - 1.
We know that 125a + 5b - 1 = -(-125a - 5b) - 1 = -4 -1 = -5, so we're set!
For instance, suppose I said that
x$y = 3x + 2y
That means that for ANY values of x and y, the $ sign tells us to triple x, double y, then add these together. For instance
10$9 = 3*10 + 2*9
since in this case x = 10 (it's the number on the left) and y = 9 (it's the number on the right).
Your problem works the same way.
#p# = ap³ + bp - 1 says take p, then plug it into the equation on the right. We have p = -5, so
#-5# = a*(-5)³ + b*(-5) - 1
We're ALSO told that #-5# = 3. Since #-5# = 3 and = a*(-5)³ + b*(-5) - 1, we can set these equal, giving
3 = a*(-5)³ + b*(-5) - 1
or
4 = -125a -5b
(The color-coding will make sense in a sec.)
We're asked for the value of #5#, or 125a + 5b - 1.
We know that 125a + 5b - 1 = -(-125a - 5b) - 1 = -4 -1 = -5, so we're set!
