Answer:
2√37
Step-by-step explanation:
Given some complex number z, |z| is what's called <em>magnitude </em>of a complex number -- its distance from 0. Unlike the more straightforward process of finding the absolute value of a real number (a number on the number line) complex numbers are <em>two-dimensional</em>, and so to talk about their magnitude, we need to bring in the Pythagorean theorem.
The real and imaginary part of the complex number 12 - 2i represent the point (12, -2) on the complex plane. Drawing lines perpendicular to the real and imaginary axes and joining them with a line from the origin to the point gives us a right triangle with legs 12 and 2. Using the Pythagorean theorem, the hypotenuse, |12 - 2i|, must be equal to
. We can pull a 4 out of the 148 to give us
![\sqrt{4\cdot37}=\sqrt{4}\sqrt{37}=2\sqrt{37}](https://tex.z-dn.net/?f=%5Csqrt%7B4%5Ccdot37%7D%3D%5Csqrt%7B4%7D%5Csqrt%7B37%7D%3D2%5Csqrt%7B37%7D)
Slope = (-14-1)/(7-1) = -15/6
y = mx + c
y = -15/6 x + c
at (1,1)
1 =-15/6(1) + c
c = 1 + 15/6 = 21/6
y = -15/6 x + 21/6 or
6y = -15x + 21
Answer:
6. 8
7. 10
8. 29
Step-by-step explanation:
6. 3+5
7. 5+5
8. 24+5
Answer:
![\bold{a = \dfrac{24}{7}}](https://tex.z-dn.net/?f=%5Cbold%7Ba%20%3D%20%5Cdfrac%7B24%7D%7B7%7D%7D)
Step-by-step explanation:
Kindly refer to the attached for the values labelled to the line XZ.
The point Y is in between XZ.
It can be clearly observed that XZ is made up of sum of two lines XY and YZ.
So, we can write:
XZ = XY + YZ ....... (1)
We are given the values of line segments:
XY = 4a
YZ = 9a and
XZ = 6a+24
To find: Value of variable 'a'.
Solution:
Putting all the values in equation (1):
![6a+24 = 4a + 9a\\\Rightarrow 6a+24=13a\\\Rightarrow 7a=24\\\Rightarrow \bold{a = \dfrac{24}{7}}](https://tex.z-dn.net/?f=6a%2B24%20%3D%204a%20%2B%209a%5C%5C%5CRightarrow%206a%2B24%3D13a%5C%5C%5CRightarrow%207a%3D24%5C%5C%5CRightarrow%20%5Cbold%7Ba%20%3D%20%5Cdfrac%7B24%7D%7B7%7D%7D)
So, value of variable is
![\bold{a = \dfrac{24}{7}}](https://tex.z-dn.net/?f=%5Cbold%7Ba%20%3D%20%5Cdfrac%7B24%7D%7B7%7D%7D)
Answer:
The answers A, B, and C all work for this problem. The answer D is the only one that does not.
Step-by-step explanation:
When looking at two parenthesis being multiplied together and being equal to 0, we know that at least one of the parenthesis must be equal to 0 for it to be true. In A and C, the first parenthesis will be equal to 0 due to a = -6.
(a + 6)
(-6 + 6)
(0)
And in B, we can see that the second parenthesis would be equal to 0 due to b = 1
(b - 1)
(1 - 1)
(0)
Now we can try the D options, but will note that they do not work for either parenthesis.
(a + 6)(b - 1)
(0 + 6)(0 - 1)
(6)(-1)