Answer:
<h2>x = 9/17</h2>
Step-by-step explanation:
3(7x-1)=4x+6 distribute
21x - 3 = 4x + 6 combine similar terms
21x - 4x = 6 + 3 simplify
17x = 9
x = 9/17
The mean is calculated by adding up all of the given numbers and dividing by the number of numbers.
Lets, for ease of understanding, say that the first three number were 64...
Mean=(64+64+64)/3=192/3=64
Now, lets solve for the mean where 'x' is the unknown fourth number and 128 is the mean. (since, the answer said that when the fourth number was added the mean, 64, was doubled '64*2=128')
128=(64+64+64+x)/4
128=(192+x)/4
Multiply both sides by 4
512=192+x
subtract 192 from both sides
320=x
The missing number is 320..
Now lets double check our work.
Mean=(64+64+64+320)/4=512/4=128
Answer=320
Answer:216 is your answer
Step-by-step explanation:
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
The answer is b. Ordered pairs
