Multiply both numerator and denominator of 
by the complex conjugate of the denominator, -2+9i.
Multiplication can be transformed into difference of squares using the rule: 
.
By definition, i² is -1. Calculate the denominator.
Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.
Do the multiplications in 
.
Combine the real and imaginary parts in -10+45i+6i+27.
Do the additions in 
.
Divide 17+51i by 85 to get 
.
The real part of 
is 
.
Answer:
The measure of angle ABT is 28°
Step-by-step explanation:
* Lets revise the bisector of a angle
- If a ray bisects and angle that mean the ray divide the angle into
two equal parts in measure
- Ex: if the ray BD bisects angle ABC, then the measure of angle ABD is
equal to the measure of angle CBD
* Lets solve the problem
∵ BT bisects ∠ABC
∴ m∠ABT = m∠CBT
∵ m∠ABT = 4x - 16
∵ m∠CBT = 2x + 6
- Equate the two values
∴ 4x - 16 = 2x + 6
- Lets solve the equation by subtracting 2x from both sides and
adding 16 to both sides
∴ 4x - 2x = 6 + 16
∴ 2x = 22 ⇒ divide both sides by 2
∴ x = 11
- Lets find the measure of angle ABT
∵ m∠ABT = 4x - 16
- Substitute x by 11
∴ m∠ABT = 4(11) - 16 = 44 - 16 = 28°
* The measure of angle ABT is 28°
9514 1404 393
Answer:
False
Step-by-step explanation:
The given formula is the "explicit" formula for the sequence.
The recursive formula would be ...
a[1] = 160
a[n] = 1/2·a[n-1] . . . . each term expressed in as a function of previous terms
The given statement is false.
There are many ways to solve simultaneous linear equations. One of my favorite for finding integer solutions is graphing. The attached graph shows the solution to be ...
... (x, y) = (4, 7)
_____
You can also use Cramer's Rule, or the Vedic math variation of it, which tells you the solution to
is given by
Here, that means
... x = (9·67-5·75)/(9·8-5·3) = 228/57 = 4
... y = (75·8-67·3)/57 = 399/57 = 7
_____
A (graphing) calculator greatly facilitates either of these approaches.
