Tonya's homework assignment has four problems a, b, c, d. Her teacher instructed her to simplify each expression and then find out its value. The value of a is 3/28, the value of b is 1/2, the value of c is 15/56 and the value of d is 1/15.
Each problem has two fractions. They are given below and should be simplified.
a) 2/7 × 3/8 = 1/7 × 3/4 = 3/28
b) 2/3 × 3/4 = 1/1 × 1/2 = 1/2
c) 3/7 × 5/8 = 15/56
d) 3/10 × 2/9 = 1/5 × 1/3 = 1/15
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Answer:
14 x 3 = 7 x <u>2</u> x 3 = 42
Step-by-step explanation:
14 x 3 = 42
so, 7 x 2 = 14
then, 14 x 3 = 42
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
Answer:
5 oil changes.
Step-by-step explanation:
60 = 12x + 15y
60 = 12x + 15(0)
60 = 12x + 0
60
---- = x
12
5 = x
