18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.
<u>Step-by-step explanation:</u>
Let x = kg of 15% copper alloy
Let y = kg of 60% copper alloy
Since we need to create 90 kg of alloy we know:
x + y = 90
51% of 90 kg = 45.9 kg of copper
So we're interested in creating 45.9 kg of copper
We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:
0.15x + 0.60y = 45.9
but
x + y = 90
x= 90 - y
substituting that value in for x
0.15(90 - y) + 0.60y = 45.9
13.5 - 0.15y + 0.60y = 45.9
0.45y = 32.4
y = 72
Substituting this y value to solve for x gives:
x + y = 90
x= 90-72
x=18
Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
Answer:
x = ± 2i
Step-by-step explanation:
note that
= i
x² = - 12 ( take square root of both sides )
x = ±
= ±
= ± 2i
Answer:
12
Step-by-step explanation:
The given geometric series is

We want to determine the first term of this geometric series.
Recall that the explicit formula is

To find the first term, we put n=1 to get:

This gives us:


Therefore the first term is 12
Answer:
151°
Step-by-step explanation:
Supplementary angles equal 180°, so all you have to do here is subtract 29 from 180 to get 151° as the supplement.
we know that
if JKLM is a rectangle
then
diagonals
MK=JL
so
MK=2*MN------> MK=2*25 ft------> MK=50 ft
JL=MK----> JL=50 ft
therefore
the answer is
JL is 50 ft