Answer:
Of the statements given, the one that is not always true about a parallelogram is that A. The diagonals are congruent.
Numbers 41,378 or words forty one thousand three hundred seventy eight
Answer:
Answer:
The cross product is 47 i - 61 j + 17 k.
Step-by-step explanation:
Given that-
a = < -1, -3, -8 > , b = < 7, 4, -5 >
The cross product is
a × b =\begin{gathered}\left[\begin{array}{ccc}i&j&k\\-1&-3&-8\\7&4&-5\end{array}\right]\end{gathered}⎣⎢⎡i−17j−34k−8−5⎦⎥⎤
= i ( - 3 × -5 - 4 × -8 ) - j ( -1 × -5 - (-8) × 7 ) + k ( -1 × 4 - 7 × -3 )
= i ( 15 + 32 ) -j ×( 5 + 56 ) + k ( -4 + 21 )
= i ( 47) - j (61 ) + k (17)
= 47 i -61 j + 17 k
As we know that if two vectors A & B are perpendicular then
A . B = 0
So here only the given vector b = < 7,4, -5> is perpendicular to the resulting vector .
Step-by-step explanation:
47, -61, 71>; yes
Answer:
40 bottles of juice
60 bottles of water
Step-by-step explanation:
let w represent water, let j represent juice. set up a system of equations:
w+2j=140
w+j=100
isolate the w by itself on the bottom equation:
w=100-j
solve the top equation by substitution, substituting 100-j for w:
w+2j=140
100-j+2j=140
100+j=140
j=40
this means that they bought 40 bottles of juice.
to find the amount of bottles of water the bought, substitute 40 for j in either of the equations (i did it in the bottom one, because it's easier):
w=100-j
w=100-40
w=60
so, they bought 60 bottles of water.
Answer:
-2/3
Step-by-step explanation:
We are trying to find the slope given two points
m = ( y2-y1)/(x2-x1)
= ( -1-3)/( 2- -4)
= ( -1-3)/( 2+4)
-4/6
-2/3
