Answer:
20.
Given, complex number is 10+5i .
We need to find sum of the given complex number and its conjugate. The conjugate of 10+5i is 10-5i. Therefore, the sum will be 10+5i+10−5i=20.
Answer:number of cupcakes sold is 13
Number of cookies sold is 27
Step-by-step explanation:
Let x represent the number of cupcakes that Jane sold.
Let y represent the number of cookies that Jane sold.
Each cupcake sold for $2.25 and each cookie sold for $0.50. At the end of the day, Jean had sold $42.75 worth of cookies and cupcakes.
This means that
2.25x + 0.5y = 42.75 - - - - - - - - - -1
she sold 40 cupcakes and cookies combined, it means that
x + y = 40
Substituting x = 40 - y into equation 1, it becomes
2.25(40 - y) + 0.5y = 42.75
90 - 2.25y + 0.5y = 42.75
- 2.25y + 0.5y = 42.75 - 90
- 1.75y = - 47.25
y = - 47.35/-1.75
y = 27
x = 40 - y
x = 40-27 = 13
.
Take half of the coefficient of x (which is 2/5) and square it:
[ (1/2)(2/5) ]^2 = (1/5)^2 = 1/25, or 0.04
Thus, to rewrite x^2 + (2/5)x to include a perfect square trinomial,
x^2 + (2/5)x = x^2 + (2/5)x + (1/5)^2 - (1/5)^2, or
(x+1/5)^2 - (1/5)^2, or (x + 1/5)^2 - 1/25
