If ΔONP is dilated from point N by a scale factor of segment NL over segment NP, which additional transformation could determine
2 answers:
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Answer: The correct number of balls is (b) 4.
Step-by-step explanation: Given that a single winner is to be chosen in a random draw designed for 210 participants. Also, there is an equal probability of winning for each participant.
We are using 10 balls, numbered through 0 to 9. We are to find the number of balls which needs to be picked up, regardless of order, so that each of the 210 participants can be assigned a unique set of numbers.
Let 'r' represents the number of balls to be picked up.
Since we are choosing from 10 balls, so we must have
The value of 'r' can be any one of 0, 1, 2, . . , 10.
Now,
if r = 1, then
If r = 2, then
If r = 3, then
If r = 4, then
Therefore, we need to pick 4 balls so that each participant can be assigned a unique set of numbers.
Thus, (b) is the correct option.
Okay so you need to use the Pythagorean theorem which is a^2 + b^2 = c^2
13^2 + b^2 = 47
169 + b^2 = 2,209
Move constant to the right
b^2 = 2,209 - 169
Subtract the numbers
b^2 = 2,040
Take the root of both sides
The final steps an answers are above on the image;)
13^2 + b^2 = 47
169 + b^2 = 2,209
Move constant to the right
b^2 = 2,209 - 169
Subtract the numbers
b^2 = 2,040
Take the root of both sides
The final steps an answers are above on the image;)
Given that:
Parent equation :
Transformed function :
Solution:
Let Parent equation be . Then,
...(1)
The translation is defined as
.... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
, So graph of parent function compressed vertically by factor
.
, so the graph of parent function shifts 32 units right.
, so there is no vertical shift.
Therefore, the graph of parent function compressed vertically by factor and shifts 32 units right to get the graph of c(x).