Answer:
Option A
Step-by-step explanation:
Since X,Y and Z are on the same line, The gradient is the same so far as the point chosen are on the same line.
Step-by-step explanation:
y = x² − 14x + 24
To convert to vertex form, complete the square. Take half of the second coefficient, square it, then add the result to both sides.
(-14/2)² = 49
y + 49 = x² − 14x + 49 + 24
y + 49 = (x − 7)² + 24
y = (x − 7)² − 25
The vertex is (7, -25).
If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)
and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-
O = (0,0) , A = (1, 1), B = (sqrt2+ 1 , 1) , C = (sqrt2, 0)
Slope of the diagonal OB = 1 / (sqrt2 + 1)
Slope of the other diagonal AC = - 1 / (sqrt2 - 1)
Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1
This proves that the diagonals are perpendicular.
The probability of obtaining two blue marbles without replacement is equal to 0.15.
We are given that:
The number of yellow marbles = 3
Number of red marbles = 9
Number of Blue marbles = 8
Total marbles = 3 + 9 + 8
Total marbles = 20
Now, we have to calculate the probability of obtaining two blue marbles without replacement.
The probability will be:
P( obtaining two blue marbles without replacement ) = 8 / 20 × 7 / 19
P( obtaining two blue marbles without replacement ) = 56 / 380
P( obtaining two blue marbles without replacement ) = 0.15
Therefore, the probability of obtaining two blue marbles without replacement is equal to 0.15.
Learn more about probability here:
brainly.com/question/24756209
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