Select all the correct expressions in the table which expressions are equivalent to the given complex number 45+2i

The expressions are given below:

Complex numbers are numbers that consist of two parts — a real number and an imaginary number.

Given:

45+ 2i

9+4 i + 2( 4 + 7i)(1- 2i)

= 9 +4i + 2( 4 - 8i + 7i +14)

=9 + 4i + 36 - 2i

= 45 - 2i

and,

(9 + 4i )+ (36 - 2i)

=45 + 2i

Hence, learn more about complex number here:

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(02.07)A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.

A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.

Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p

In which step did the student first make a mistake and how can it be corrected?

Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

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Becky bought 8 oatmeal cookies for $6.00.

Part A
Which graph represents the situation?
A graph showing cost in dollars on the y axis and number of cookies on the x axis. A line begins at the origin and passes through the points 1 point 5 comma 1 point 7 5, 5 comma 6, and 6 comma 7 point 5 0.
A graph showing cost in dollars on the y axis and number of cookies on the x axis. A line begins at the origin and passes through the points 1 comma 1 point 6, 3 comma 5 point 2 5, and 4 comma 7 point 5 0.
A graph showing cost in dollars on the y axis and number of cookies on the x axis. A line begins at the origin and passes through the points 2 comma 1 point 5, 6 comma 4 point 5, and 8 comma 6.
A graph showing cost in dollars on the y axis and number of cookies on the x axis. A line begins at the origin and passes through the points 2 comma 0 point 7 5, 6 comma 2 point 2 5, and 8 comma 3.
Part B
Look at the graph you chose in Part A. Do the number of cookies and the cost have a proportional relationship?
Use the drop-down menus to show and explain your answer.



Choose...
; the graph
Choose...
a straight line through the
Choose...
.

Part C
What does the point (1, 0.75) represent in this situation? What does the point (0, 0) represent?



1 cookie costs $0.75; no cookies cost $0



1 cookie costs $7.50; no cookies cost $0



0.75 dozen cookies cost $1; 0 dozen cookies cost $0



1 dozen cookies cost $0.75; 0 dozen cookies cost $0

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O B. Debit Purchases, $7,500, credit Accounts Payable, $7,500
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O D. Debit Inventory, $7,500, credit Cash, $7,500

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