The two labeled angles are alternate interior angles, and as such, they are the same.
From this result you can build the equation
and solve it for x: subtract 13x from both sides to get
and add 2 to both sides to get
Check: if we plug the value we found we have
So the angles are actually the same, as requested.
Answer:
Step-by-step explanation:
Neither are a function because they do not pass the vertical line test.
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.
Divide the time he traveled by the distance to find how fast he travels 1 mile, then multiply that by 5 miles:
12 minutes / 2 miles = 6 minutes per mile.
6 minutes per mile x 5 miles = 30 total minutes.
10.2
and
5.6
and
7.9
Hope this helped :)
