1) m-13=7
2)m-13=7
m-13+13=7+13
m=20
so he had $20 he spent $13 so $7 was left!
BRAINLIEST???
Answer: $1980
Step-by-step explanation:
First, let’s find out her monthly sales by adding up the 4 weekly sales.
2400+ 3200 + 5200 + 1200 = 12000
Next, find the amount of commission on 12000
4%/100=0.04
12000*0.04=480
Next add her commission to her monthly wage of 1500
1500+480=1980
Answer:
120 grams
if they are all the same size
Answer:
Solution : 6 + 6i
Step-by-step explanation:
![-3\left[\cos \left(\frac{-\pi }{4})\right+i\sin \left(\frac{-\pi }{4}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi }{2}\right)\right]](https://tex.z-dn.net/?f=-3%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%29%5Cright%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%5Cright%29%5Cright%5D%5Ccdot%20%5C%3A2%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B2%7D%5Cright%29%5Cright%5D)
This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )
( Multiply both expressions )
![-6\sqrt{2}\left[\cos \left(\frac{-\pi }{4}+\frac{-\pi \:\:\:}{2}\right)+i\sin \left(\frac{-\pi \:}{4}+\frac{-\pi \:\:}{2}\right)\right]](https://tex.z-dn.net/?f=-6%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%2B%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%7D%7B4%7D%2B%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%5Cright%5D)
( Simplify
for both
and
)
= 
( Substitute )

Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )
sin(π / 4) = √2 / 2 = cos(π / 4)
( Substitute )
=
= 
=
= 
=
- Therefore our solution is option a.
Step-by-step explanation:
For problem 1,
Let the required number be x,
2 x/4 = 11/4
or, (8+x)/4 = 11/4
or, 8+x = 44/4
or, 8+x = 11
or, x = 11-8
so, x = 3
For problem 2,
Let the required number be y,
y/10 = 4/5
or, 5y = 40
or, y = 40/5
so, y = 8