Evaluate (2 – 5i)(p + q)i when p = 2 and q = 5ia. 29i
b. 29i-20
c.-21i
d.29
Answers
Answer:
The value of the (2 – 5i)(p + q)i is 29i .
Option (a) is correct .
Step-by-step explanation:
As the expression given in the question.
= (2 - 5i) (p + q)i
Simplify the above
= (2 - 5i) (pi + qi)
= 2pi + 2qi - 5pi²- 5qi²
As i² = -1
Put in the above
= 2pi + 2qi + 5p +5q
= 2i × 2 + 2i × 5i + 5 × 2 + 5 × 5i
= 4i + 10i² + 10 + 25i
As i² = -1
= 4i - 10 + 10 + 25i
= 29i
Thus the value of the (2 – 5i)(p + q)i is 29i .
Option (a) is correct .
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Solve the equation 4n-7=-23
Answers
a. ∠QTS
b. ∠RTS
c. ∠PTN
d. ∠QT
2. ∠QTN and _____ are supplementary.
a. ∠QTS
b. ∠QTP
c. ∠RTS
d. ∠PTR
3. If ∠PTQ measures 29°, then PTN measures _____.
a. 51º
b. 45º
c. 61º
d. 71º
4. If ∠NTR measures 148°, then ∠RTS measures _____.
a. 12º
b. 32º
c. 22º
d. 42º
5. ∠PTN is adjacent to _____.
a. ∠QTR
b. ∠PTS
c. ∠RTS
d. ∠NTS
Answers
1. ∠QTR and RTS are complementary.
2. ∠QTN and QTS are supplementary.
3. If ∠PTQ measures 29°, then PTN measures 61.
4. If ∠NTR measures 148°, then ∠RTS measures 148.
5. ∠PTN is adjacent to PTS.
Answer: 4. Is actually 32 degrees. I believe the answer listed was a typo.
Answers
24 items - 11 items = 24 - 11 = 13 items are left
The correct result would be 13 items.
11 items are removed.
To find out how many items are left, we need to do subtraction.
24 - 11 = 13
13 items are left in the case.
Net
31 m
27 m
Calculate the size of the serving angle A.
Give your answer correct to the nearest degree.
C
The person serving stands at point A and tries to serve the ball somewhere between
point C and B on the edge of the opponent's side.
Do not include the degree symbol in your answer.
9 m
B
Answers
Answer:
To calculate the size of the serving angle A in the diagram of the volleyball court, you can use trigonometry.
You have the following information:
The distance from point A to point C is 9 meters.
The distance from point A to point B is 31 meters.
To find angle A, you can use the inverse tangent (arctan) function:
�
=
arctan
(
�
�
�
�
)
A=arctan(
AC
BC
)
Substitute the values:
�
=
arctan
(
31
9
)
A=arctan(
9
31
)
Now, calculate the angle:
�
≈
arctan
(
3.444
)
≈
73.4
8
∘
A≈arctan(3.444)≈73.48
∘
Rounded to the nearest degree, the size of the serving angle A is approximately 73 degrees.
Step-by-step explanation:
Sure, I'll explain it in a simpler way:
Imagine you're standing at point A on the volleyball court, and you want to serve the ball towards point C or point B. Point C is 9 meters away, and point B is 31 meters away from you.
To find out how wide the angle is between where you stand (point A) and where you want to serve the ball (between points C and B), we can use a special math trick. It's like saying, "How much do I need to aim to the left or right?"
We use something called "arctan" to figure it out. When we do the math, we find that the angle A is about 73 degrees. So, you need to aim your serve at about a 73-degree angle to get the ball between points C and B on the other side of the court.
Answers
Answer:
$1,200
Step-by-step explanation:
Let x be the amount of money deposited in the mutual fund. The interest earned by that investment can be determined as the amount deposited times the interest rate:
The value the second deposited can be determined as x+$2,400 and its interest earned is defined in the same manner as the first deposit's:
The total interest on both investment equals the sum of both interests:
$1,200 were invested in the mutual fund.
B.(x + 22)2 – 121
C.(x + 7)2 – 47
D.(x – 15)2 + 94