Answer:
The mathematical sciences are a group of areas of study that includes mathematics.
Step-by-step explanation:
9514 1404 393
Answer:
24
Step-by-step explanation:
Let d represent Donald's age now. Then Natali's age now is d+38. The age relationship 5 years ago was ...
(d+38) -5 = 3(d -5)
d +33 = 3d -15 . . . . . eliminate parentheses
48 = 2d . . . . . . . . . . . add 15-d
24 = d . . . . . . . . . . . . . divide by 2
Donald is 24 years old now.
_____
<em>Alternate solution</em>
You can also work this by considering that 5 years ago, Natalie's age was more than Donald's age by twice Donald's age then. Hence Donald was 38/2 = 19 at that time. Now, Donald is 19+5 = 24.
As the only prime factor of denominator is
2
, in fact there are three twos (
2
×
2
×
2
) we can can convert the fraction
7
8
by multiplying numerator and denominator by
5
×
5
×
5
.
Hence,
7
8
=
7
×
5
×
5
×
5
8
×
5
×
5
×
5
=
875
1000
=
0.875
(This is always possible if only prime factors of denominator are
2
's and
5
's - just multiply by as many
5
's and
2
's).
AX = B
1 -1 -1 x 0
0 -2 -1 y = -2
2 1 0 z -4
x
y = A^-1 B
z
x -1 1 1 0 6
y = 2 -2 -1 . 2 = -8
z -4 3 2 4 14
