Please help me answer the following questions. Thank you so much! In the system

Question

Please help me answer the following questions. Thank you so much! In the system of equations above, a and b are constants if the system has infinitely many solutions, what is the value of a + b? 10 41/4 45/4 18 In the figure above, an equilateral triangle and an isosceles triangle share a side. If b = a/2 - 12. what is the value of e ? the figure, the length of segment AB is 30. and the of sin A is 0.27. What is the value of cos B? Which of the following complex numbers is equivalent to 7 + 2i/2 - 3i ? (i = Squareroot-1) 7/2 - 2/3i 7/2 + 2/3i 8/13 - 25/13i 8/13 + 25/13i A television network fills breaks between television programs with short and long advertisements. Each long advertisement is 10 seconds longer than each short advertisement. If 7 short advertisements and 3 long advertisements were used to fill a break 3 minutes long, what is the length, in seconds, of each short advertisement? x - n/m = 1/8 In the equation above, m = 18 and n = 1/2 What is the value of x ?

Explanation / Answer

11) ( 7 + 2i ) / ( 2- 3i )

multiplying entire expression by conjugate of denominator

(7+2i) / ( 2- 3i)* (2+3i) / (2+3i)

( 14 + 25 i + 6i^2 ) / ( 4 - 9i^2 )

i^2 = -1

(25i + 8 ) / 13

= 25i / 13 + 8 / 13

(option D )

(x- n ) / m = 1/8

cross multiplying we get

8 ( x- n ) = m

8x - 8n = m

8x = m + 8n

x = ( m + 8n ) / 8

plugging the values of m and n

x = 18 + 8(1/2) / 8 = 22/8

x = 11/4

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