Answer:
vertically opposite angles
Answer:
Trace a line between the intersection of the two circles.
Step-by-step explanation:
This is a very important technique, the next thing you do is trace a line in between the intersection of the circles and that would intercept your circle. I will show you in a drawing.
there are 12 inches in 1 foot, so 6 inches is really just half a foot, thus 3'6" is really just 3.5' or 3½ feet.
now, let's convert those mixed fractions to improper fractions and then subtract, bearing in mind our LCD will be 8.
![\bf \stackrel{mixed}{4\frac{5}{8}}\implies \cfrac{4\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{45}{8}-\cfrac{7}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)45~~-~~(4)7}{8}}\implies \cfrac{45-28}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B5%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%208%2B5%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B45%7D%7B8%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B45%7D%7B8%7D-%5Ccfrac%7B7%7D%7B2%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%208%7D%7D%7B%5Ccfrac%7B%281%2945~~-~~%284%297%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B45-28%7D%7B8%7D%5Cimplies%20%5Ccfrac%7B17%7D%7B8%7D%5Cimplies%202%5Cfrac%7B1%7D%7B8%7D)
The answer that you should get is D
Answer:
6 < x < 30
Step-by-step explanation:
By the Hinge Theorem, we know that
Angle BAC > Angle DAC
The two triangles that make the diamond have two equal sides. The third side of the upper triangle is longer than the third side if the lower triangle. To fit in the longer side, line AB had to be pushed outwards, forming a larger angle.
When we compare the two angles 48 and (2x-12), we now know that 48 is larger.
48 > 2x-12
48+12 > 2x
60 > 2x
60/2 > x
x < 30
Furthermore, angle DAC can't be negative or zero
2x - 12 > 0
2x > 12
x > 6