Answer:
B
7 less than 3 times a number (X) is (3x-7), and then the sum of these two numbers means we have (3x-7)+X, and then we know this equals 109, leaving us with:
(3x-7)+x = 109
40 hours at 5.90 a hour so 40 hours he would make 236
Answer:
Step-by-step explanation:
1 tyres time to install is 56/4=14
which means it takes 14 minutes to install one tire.
so 12 tires would be 12 x 14 which is 168 minutes
A) 168 minutes
1 tire = 14 min
42 min/14 min=3
B) 3 tires
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.
so if x = -1, let's plug that in the second equation
-5(-1)+y = 5
5+y = 5
y = 0
