Answer:
In both cases, we have similar figures.
This means that the shape of the figures is the same, but the size is different:
PQST is similar to STNR and to NRPQ
VUYZ is similar to YZWX and to VUWX
this means that, for example, in problem 18, the ratio between ST and NR must be the same as the ratio between PQ and ST. This happens because the measure increases by the same scale factor.
With this in mind, we can solve the problem:
18)
ST = 7.5
NR = 5.5
Then the quotient ST/NR is:
ST/NR = 7.5/5.5
And, as we said above:
PQ/ST = ST/NR
PQ/7.5 = 7.5/5.5
PQ = (7.5/5.5)*7.5 = 10.23
19) Here we should have:
YZ/VU = WX/YZ
Then:
22.9/35 = WX/22.9
(22.9/35)*22.9 = WX = 14.98
Step-by-step explanation:
calculate the area of the shape(s) on the inside and then the area of the sphape on the outside, then subtract the inside's area from the outside shape. im still working on this one, check back in a bit.
Answer:
This number line show the inequality x > 2
Answer:
Option (3)
Step-by-step explanation:
w = ![\frac{\sqrt{2}}{2}[\text{cos}(225) + i\text{sin}(225)]](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5B%5Ctext%7Bcos%7D%28225%29%20%2B%20i%5Ctext%7Bsin%7D%28225%29%5D)
Since, cos(225) = cos(180 + 45)
= -cos(45) [Since, cos(180 + θ) = -cosθ]
= -![\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
sin(225) = sin(180 + 45)
= -sin(45)
= -![\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
Therefore, w = ![\frac{\sqrt{2}}{2}[-\frac{\sqrt{2}}{2}+i(-\frac{\sqrt{2}}{2})]](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5B-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2Bi%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%5D)
= ![-\frac{2}{4}(1+i)](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B4%7D%281%2Bi%29)
= ![-\frac{1}{2}(1+i)](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D%281%2Bi%29)
z = 1[cos(60) + i(sin(60)]
= ![[\frac{1}{2}+i(\frac{\sqrt{3}}{2})](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B2%7D%2Bi%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29)
= ![\frac{1}{2}(1+i\sqrt{3})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%281%2Bi%5Csqrt%7B3%7D%29)
Now (w + z) = ![-\frac{1}{2}(1+i)+\frac{1}{2}(1+i\sqrt{3})](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D%281%2Bi%29%2B%5Cfrac%7B1%7D%7B2%7D%281%2Bi%5Csqrt%7B3%7D%29)
= ![-\frac{1}{2}-\frac{i}{2}+\frac{1}{2}+i\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7Bi%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%2Bi%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
= ![\frac{(i\sqrt{3}-i)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28i%5Csqrt%7B3%7D-i%29%7D%7B2%7D)
= ![\frac{(\sqrt{3}-1)i}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Csqrt%7B3%7D-1%29i%7D%7B2%7D)
Therefore, Option (3) will be the correct option.