The expression which is equivalent to √(-9) is 3i.
<h3>What is Complex number?</h3>
A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
Here, given expression;
y = √(-9)
y = √9 X √(-1)
y = 3√(-1)
y = 3i
Thus, the expression which is equivalent to √(-9) is 3i.
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X= number of dimes
x+6= number of quarters
5(x+6)= number of nickels
$5.40= 540 cents
Add the number of each coin and set it equal to the total in cents.
x + (x + 6) + 5(x + 6)= $5.40
multiply 5 by parentheses; change dollar total to cents
x + (x + 6) + (5 * x) + (5 * 6)= 540
x + (x + 6) + 5x + 30= 540
combine like terms
7x + 36= 540
subtract 36 from both sides
7x= 504
divide both sides by 7
x= 72 dimes
x + 6= 78 quarters
5(x + 6)= 390 nickels
CHECK
72 + 78 + 390= 540
540= 540
ANSWER: There are 72 dimes, 78 quarters and 390 nickels.
Hope this helps! :)
Answer: 15 grams
If he had 100 grams of candy bar, then 30% of that is 30 grams (since 30/100 = 30%). Cut this in half and we end up with 30/2 = 15.
Another way to find the answer is to multiply 50 and 0.30 which is the decimal form of 30%. So we have 50*0.30 = 15 which is the same answer.
This problem can be solved by the chicken rabbits method or you can just do simple algebra.
I.) Chicken and rabbits method
First assume all 110 coins are dimes and none are quarters.
We will have a total value of 11 dollars
Now for each dime we switch out for a quarter, we adds 15 cents to the total value.
18.50-11=7.50 dollars
There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.
This also meant that we need to switch out 50 dimes for 50 quarters.
So we have 50 quarters.
That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.
Let's say there are x dimes and y quarters.
Set up equation
x+y=110
10x+25y=1850
Now solve multiply first equation by 10
10x+10y=1100
subtract
15y=750
y=50
Now we set the numbers of quarters to y so the answer is 50 quarters.
I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.
Step-by-step explanation:
Use the identity
on the left side.
![\dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Ccos%20%5B2%28%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20%5Calpha%29%5D%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
Now use the identity
on the left side.
