2 - 3i is just another of writing (2, -3) in the cartesian plane, the 2-3i however is using the "imaginary axis" for the imaginary plane, is all however the imaginary axis is simply the equivalent of the y-axis. Likewise 9+21i is just (9,21), so let's just use the distance formula.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{21})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-2]^2+[21-(-3)]^2}\implies d=\sqrt{(9-2)^2+(21+3)^2} \\\\\\ d=\sqrt{7^2+24^2}\implies d=\sqrt{49+576}\implies d=\sqrt{625}\implies d=25](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B-3%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B9%7D~%2C~%5Cstackrel%7By_2%7D%7B21%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%3D%5Csqrt%7B%5B9-2%5D%5E2%2B%5B21-%28-3%29%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%289-2%29%5E2%2B%2821%2B3%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%3D%5Csqrt%7B7%5E2%2B24%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B49%2B576%7D%5Cimplies%20d%3D%5Csqrt%7B625%7D%5Cimplies%20d%3D25)
<span>y-intercept when x = 0
so if x = 0, y = -3
answer
</span><span>y-intercept (0, -3)</span>
Answer:
Option D. y = 5x + 1
Step-by-step explanation:
From the question given above, the following data were:
Input (x) >>>>>> Output (y)
0 >>>>>>>>>>>> 1
1 >>>>>>>>>>>> 6
2 >>>>>>>>>>>> 11
3 >>>>>>>>>>>> 16
4 >>>>>>>>>>>> 21
To know the the correct answer to the question, we shall apply the equation given in each option to see which will satisfy the table. This can be obtained as follow:
For Option a
y = 3x + 3
x = 0
y = 3(0) + 3
y = 0 + 3
y = 0
y = 3x + 3
x = 1
y = 3(1) + 3
y = 3 + 3
y = 6
For Option b
y = 5x – 4
x = 0
y = 5(0) – 4
y = 0 – 4
y = – 4
y = 5x – 4
x = 1
y = 5(1) – 4
y = 5 – 4
y = 1
For Option c
y = 10x – 9
x = 0
y = 10(0) – 9
y = 0 – 9
y = – 9
y = 10x – 9
x = 1
y = 10(1) – 9
y = 10 – 9
y = 1
For Option d
y = 5x + 1
x = 0
y = 5(0) + 1
y = 0 + 1
y = 1
y = 5x + 1
x = 1
y = 5(1) + 1
y = 5 + 1
y = 6
From the illustrations made above, only option d satisfy the table. Thus, option d gives the correct answer to the question.
Answer:
5 cm
7cm
Step-by-step explanation:
The absolute value of a number can never be negative. That's because it represents the distance of a number from zero on a number line. The number

is

digits to the left of zero on a number line. So, the absolute value of

would be

.
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish