Answer:
<h3>
y = 20</h3><h3 />
Step-by-step explanation:
line RPN = 180 = 4y - 10 + 90 + y
180 - 90 + 10= 5y
100 = 5y
y = 100/5
y = 20
Answer:
2x³ + 11x² + 8x - 16
Step-by-step explanation:
Multiply:
(x + 4) (2x² +3x - 4)
2x³ + 3x² - 4x + 8x² + 12x - 16
Combine like terms:
2x³ + 11x² + 8x - 16
We are asked to simplify the expression
![\frac{-7x}{5y} \cdot \frac{5x}{-7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-7x%7D%7B5y%7D%20%5Ccdot%20%20%5Cfrac%7B5x%7D%7B-7%7D%20%20)
,
what we do is, we form a single fraction where the numerator is the product of the numerators, and the denominator is the product of the denominators, that is:
![\frac{-7x}{5y} \cdot \frac{5x}{-7}= \frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-7x%7D%7B5y%7D%20%5Ccdot%20%5Cfrac%7B5x%7D%7B-7%7D%3D%20%5Cfrac%7B-7%5Ccdot5%20%5Ccdot%20x%20%5Ccdot%20x%7D%7B5%20%5Ccdot%28-7%29%20%5Ccdot%20y%7D%20)
simplify the common numbers and terms in the numerator and denominator:
![\frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y}=\frac{5 \cdot x \cdot x}{5 \cdot y}=\frac{x \cdot x}{y}= \frac{ x^{2} }{y}](https://tex.z-dn.net/?f=%5Cfrac%7B-7%5Ccdot5%20%5Ccdot%20x%20%5Ccdot%20x%7D%7B5%20%5Ccdot%28-7%29%20%5Ccdot%20y%7D%3D%5Cfrac%7B5%20%5Ccdot%20x%20%5Ccdot%20x%7D%7B5%20%20%5Ccdot%20y%7D%3D%5Cfrac%7Bx%20%5Ccdot%20x%7D%7By%7D%3D%20%5Cfrac%7B%20x%5E%7B2%7D%20%7D%7By%7D%20)
Answer:
Answer:
(a) ![w=2+5i-6=-4+5i](https://tex.z-dn.net/?f=w%3D2%2B5i-6%3D-4%2B5i)
Multiplicative inverse of w will be ![\frac{1}{-4+5i}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B-4%2B5i%7D)
(B) As w is same as the product of ![z_1\ and\ z_2](https://tex.z-dn.net/?f=z_1%5C%20and%5C%20z_2)
So there multiplicative inverse will also be same
Step-by-step explanation:
We have given two complex numbers
and ![z_2=3+2i](https://tex.z-dn.net/?f=z_2%3D3%2B2i)
(a) First we have to find ![w=z_1z_2](https://tex.z-dn.net/?f=w%3Dz_1z_2)
So ![w=(1+i)(2+3i)=2+3i+2i+6i^2=2+5i+6i^2](https://tex.z-dn.net/?f=w%3D%281%2Bi%29%282%2B3i%29%3D2%2B3i%2B2i%2B6i%5E2%3D2%2B5i%2B6i%5E2)
As we know that ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
So ![w=2+5i-6=-4+5i](https://tex.z-dn.net/?f=w%3D2%2B5i-6%3D-4%2B5i)
Multiplicative inverse :
It is that number when multiply with the number which we have have to find the multiplicative inverse gives result as 1
So multiplicative inverse of w will be ![\frac{1}{-4+5i}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B-4%2B5i%7D)
Because when we multiply
with
it gives result as 1
(b) As w is same as the product of ![z_1\ and\ z_2](https://tex.z-dn.net/?f=z_1%5C%20and%5C%20z_2)
So there multiplicative inverse will also be same
Answer:
(-4, 2), (-1, -3), (2,0), (4,3).