Hi there!
Since the triangle is equilateral, all of its sides are congruent. This means that to solve, we can set the two given equations equal to each other.
2(x - 8) = 1/2x + 8
2x - 16 = 1/2x + 8
1.5x - 16 = 8
1.5x = 24
x = 16
Now that we know what x is, we can plug that in for x in the equation for ZY.
2(16 - 8) = ZY
ZY = 2(8)
ZY = 16 units
And here is the work to show that XZ is also 16.
1/2(16) + 8 = XZ
XZ = 8 + 8
XZ = 16
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Step-by-step explanation:
Point A = (-1, -3).
Midway of AB = (-3, 2).
Let Point B = (x, y).
Then (-1, -3) - (-3, 2) = (-3, 2) - (x, y).
=> (2, -5) = (-3-x, 2-y).
We have -3 - x = 2 and 2 - y = -5.
So x = -5 and y = 7.
Hence, point B = (-5, 7).
Answer:
C x = 4096
Step-by-step explanation:
log8 x = 4
Raise each side to the base of 8
8^ log 8 (x) = 8^4
x = 8^4
x = 4096
Simple interest means the interest at the end of each year will always be 8% of 2000 (assuming he doesnt pay some of it off), and will not be compounded with the existing interest.
To get a percentage, multiply by the percentage/100, in this case i.e. multiply by 0.08.
2000*0.08 = $160.
Therefore he has $160 of interest each year to pay.
Now we just need to work out how many lots of 160 go into 640, i.e. divide through.
640/160 = 4 - therefore he has had the loan for 4 years.
