Since the 3 of them are like terms, we have to ADD all 3 of them.
4x+2x+7x= 13x
The legs are 5 inches long.
Use the Pythagorean theorem:
The length of the hypotenuse of the triangle is approximately 7 inches long.
Answer:Test one is 84% correct
Test two has a total of 20 questions
Test three he has 28 answers right
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.
Answer:
C.
Step-by-step explanation:
The minus sign (of the multiplier -1/3) changes the direction of z by 180°. The magnitude of the multiplier 1/3 reduces the magnitude of the product to 1/3 that of z. The graph that has these characteristics is graph C.
