Answer:
2
Step-by-step explanation:
let 'x' = number
x³ - x² = 2x
x³- x² - 2x = 0
x(x² - x - 2) = 0
x(x - 2)(x + 1) = 0
x = -1, 0, 2
the only positive solution is the number 2
Answer:
D. p + q = 7
Step-by-step explanation:
The slope of AB is ...
mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)
The slope of BC is ...
mBC = (q -1)/(9 -6) = (q -1)/3
We want the product of these slopes to be -1:
mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)
-(q-1)/(6 -p) = -1 . . . . cancel factors of 3
q -1 = 6 -p . . . . . multiply by -(6 -p)
q + p = 7 . . . . . matches choice D
Answer: 5 : 3
Step-by-step explanation:
The ratio of shirts to pants can be shown by putting the number if shirts and pants in the following manner:
Number of shirts : Number of pants
20 : 12
Then you have to take this to the lowest term. 4 is a factor of both numbers so when divided by 4 we get:
= 5 : 3
This is the ratio.
Two angles are said to be complementary, if the sum of the measures of the to angles is equal to 90 degrees.
Thus, given that HFG is complementary to ACB, them mHFG + mACB = 90 degrees.
From the figure, given that the line from point F meats line CE at point P, then HFG = CFP.
But mCFE = 90 degrees and mCFE = mCFP + mPFE
Also PFE = DFH
Thus, mCFE = mCFP + mPFE = mHFG + mDFH = 90 degrees
Recall that mHFG + mACB = 90 degrees
Thus, mHFG + mACB = mHFG + mDFH
Therefore, mACB = mDFH.
Total number of marbles in the bag =20
Number of blue marbles =4
Now we just want two blue marbles out of four.
Probability of taking out first marble which is blue =4/20
Now after we took out one blue marble , number of blue marbles left are 3.
Probability of taking out second marble which is blue =3/20
Total probability = 4/20 *3/20 = 12/400
So probability of taking out two blue marbles is 0.03 or 12/400.
