Answer
Find out the value of g(3) by using the function g(x) = x² + 2 given in the question .
To proof
The function given in the question is
g(x) = x² + 2
Take x = 3
put x = 3 in the g(x) = x² + 2
than it becomes
g(3) = 3² + 2
solving the above
we get
g(3) = 9 + 2
g(3) = 11
Thus g(3) = 11 and option (c) is correct .
Hence proved
Well, i would use the distance formula to find the distance between the two points. Only issue- you do not have the other point, so lets find it!
We have the point 4,6. 4 is the x, and 6 is the y.
Lets start with 4 since the x works with the left and right aspect of the location. It says M has been translated 8 units to the left, meaning we go back 8. So if we are at 4, and we go back (A.K.A. Subtract) 8, we will be at -4.
Now lets move onto the y, which works with the up and down aspect of the location. It says M has been translated 9 unites down, meaning the point will be heading down and getting smaller. So if we are at 6, and we go down (A.K.A. subtract) 9, then we will be at -3.
So now we have the coordinates of point M (4,6) and point M' (-4,-3) so we can now complete the distance formula!
The distance formula helps determine the distance between two points. It looks like this: D = √(x₂-x₁)²+(y₂-y₁)²
Though it does not matter which order you use the coordinates in, i am choosing to use M and then M'.
So, starting with the X, X₂ will be -4 and X₁ will be 4.
Again, starting with the Y, Y₂ will be -3 and Y₁ will be 6.
So, the formula plugged in will look like this: d = √(-4 - 4)² + (-3 - 6)²
Solving it out, we first need to work within the parenthesis. Can you solve it?
Our outcome will be this: -8² + -9². But, since we are squaring (And a negative times a negative equals a positive) you can just write 8² + 9²
8²= 64
9²= 81
64+81 = 145.
So, the distance between point M and point M' would be 145 units
Hope this helps!
If it does not, please let me know so i can try to help!
Answer:
The formula for calculate the distance (d) between two points is: Given the points (9,-12) and (6,3), you can identify: Substitute these coordinates into the formula to find the equation that correctly shows how to determine the distance between the given points (9,-12) and (6,3)
Step-by-step explanation:
Complete Questions:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers.
a. 40
b. 48
c. 56
d. 64
Answer:
a. 0.35
b. 0.43
c. 0.49
d. 0.54
Step-by-step explanation:
(a)
The objective is to find the probability of selecting none of the correct six integers from the positive integers not exceeding 40.
Let s be the sample space of all integer not exceeding 40.
The total number of ways to select 6 numbers from 40 is 
.
Let E be the event of selecting none of the correct six integers.
The total number of ways to select the 6 incorrect numbers from 34 numbers is:
Thus, the probability of selecting none of the correct six integers, when the order in which they are selected does rot matter is
Therefore, the probability is 0.35
Check the attached files for additionals
I'm not sure but I think it's 40 water stations...
