Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i
======================================================
Work Shown:
[tex]\sqrt{24+10i} = a+bi\\\\\left(\sqrt{24+10i}\right)^2 = (a+bi)^2\\\\24+10i = a^2+2abi+b^2i^2\\\\24+10i = a^2+2abi+b^2(-1)\\\\24+10i = a^2+2abi-b^2\\\\24+10i = (a^2-b^2)+(2ab)i\\\\[/tex]
Equating terms, we have this system
[tex]\begin{cases}24 = a^2-b^2\ \text{.... real terms}\\10 = 2ab\ \text{.... imaginary terms}\end{cases}[/tex]
Solve the second equation for b to get b = 5/a
Plug that into the first equation to solve for 'a'
[tex]24 = a^2-b^2\\\\24 = a^2-\left(\frac{5}{a}\right)^2\\\\24 = a^2-\frac{25}{a^2}\\\\24a^2 = a^4-25\\\\0 = a^4-24a^2-25\\\\a^4-24a^2-25 = 0\\\\(a^2-25)(a^2+1) = 0\\\\(a-5)(a+5)(a^2+1) = 0\\\\[/tex]
Setting each factor equal to zero would lead to...
a-5 = 0 solves to a = 5a+5 = 0 solves to a = -5a^2+1 = 0 solves to a = i and a = -iWe're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5
If a = 5, then,
b = 5/a = 5/5 = 1
So
[tex]\sqrt{24+10i} = a+bi = 5+1i = 5+i[/tex]
or in short,
[tex]\sqrt{24+10i} = 5+i[/tex]
-----------------
If a = -5, then b = 5/a = 5/(-5) = -1
So it's very possible that we could also say
[tex]\sqrt{24+10i} = -5-i\\\\[/tex]
If you wanted to combine the two we would use the plus/minus notation like so
[tex]\sqrt{24+10i} = \pm(5+i)\\\\[/tex]
This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.
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Answer:
Your value of z is 71 degrees. The value of x is 11.
Step-by-step explanation:
You can determine the value of z by knowing that z and the 71 angle are vertical angles. Vertical angles are congruent to each other. We know that the x angle and the 71 angle are supplementary, or that they equal 180. So, set up the equations, and solve for x. :
[tex]180=71+(9x+10)\\180=81+9x\\99=9x\\x=11\\[/tex]
Answer correctly please !!!! Will mark Brianliest !!!!!!!!!!!!!
Answer:
19.3
Step-by-step explanation:
tan ? = opp./adj = 7/20
? = arctan 7/20 ≈ 19.3
Classify the triangle
There are 29 students in Mrs. Dixon's science class. On the last test, only 1 student earned the median score of 84.
How many students scored an 84 or lower?
A - 15
b - 14
C - 13
D - 12
Answer:
A
Step-by-step explanation:
Median can be described as the number that occurs at the middle of a set of observations.
for example, in the set of numbers, 1 2 3 4 5, the median is 3
median = (first number + last number) / 2
If there are 29 students,
median = (1 + 29) / 2 = 30/2 = 15
the 15th students scored 84
and students between 1 - 14 scored lower than 84
so, 15 students scored an 84 or lower
A sunflower grew 7 yards during the first week after it was planted. What is the height of the total sunflower in feet?
Answer:
21 feet
Step-by-step explanation:
Remember to get feet to yards, multiply the feet by 3 because there are 3 feet in one yard
in this case 7 × 3 = 21
And additionally to get yards to feet, divide by three because 1 yard = 3 feet
Mark as Brainliest
Based on the pattern in the picture, how many squares do you think will be used to create the 5th figure? make a table.
Answer:
I think it is 7 squares.
Step-by-step explanation:
As you can see they added 3 more squares to the first block which gave you 4. Then they added 5 squares to the second one. If you take the third block, you will count 7 squares on the outside of the third block.
ANSWER THIS PLEASE ILL GIVE THE BEST ANSWER BRAINLIST
Answer:
6
Step-by-step explanation:
Answer:
10 pieces with 8" left over
Step-by-step explanation:
[tex]8 \div \frac{3}{4} = 8 \times \frac{4}{3} = \frac{32}{3} = 10 \frac{2}{3} [/tex]
so there's 10 pieces and 2/3 of a leftover piece.
2/3 of a foot is
[tex] \frac{2}{3} (12) = 8[/tex]
so there are 8" left
Simplify by combining like terms: 3x + 2 + x + 7
A. 5x + 7
B. 3x + 9
C. 4x + 9
D. 6x + 7
i hate copy and pastes
Answer:
why they're so helpful
Step-by-step explanation:
Answer:
Me too it so much wooooorrrrkkk
Step-by-step explanation:
what is 15/3 equal to
Answer: 5
Step-by-step explanation:
Smh
stuck on this question, was due yesterday!!!!
Answer:
c
all the other numbers are too high
WHAT IS THE PROBABLITY OF GETTING FACE CARD?
Answer:
3/13?
Step-by-step explanation:
Kelly is making a rectangular garden that has a width of (2x + 3) and length of (2x - 4)
How much fertilizer would she need to lay down before she starts to
plant her flowers (area)?
The ages and grades of some of the 17 girls on a club soccer team are
shown in the table.
15 years old
16 years old
0
2
9th grade
10th grade
10
Which two-way frequency table correctly shows the marginal frequencies?
A. 9th grade, 15 years old: 2. 16 years old: 0. total: 2. 10th grade, 15 years old: 15. 16 years old: 10. total: 25. total, 15 years old: 17. 16 years old: 10. total: 27.
Answer:
Table DStep-by-step explanation:
Looking at the tables, we observe that:
A. Total number is 27, but should be 17 ⇒ incorrectB. First column total is wrong; 2 + 5 = 10 ⇒ incorrectC. Total is 19, but should be 17 ⇒ incorrectD. All look correctAnswer:
The answer is D.
Step-by-step explanation:
what is the answer on this question
Your Answer..
V=10in³
Hope This Helps You
A comic costs $3 and a mystery series costs $5 each.If Ken spend all his money on the comics, he has $6 left. If he wants to buy the mystery series, he needs another $8. How many comics or mystery books is Ken buying? How much money does he have?
Whoever posts this on jiskha gets 50 points
Answer:
7 books
$27
Step-by-step explanation:
3x + 6= 5x - 8
3x - 5x = -14
-2x= -14
x= 7 books
he has (3×7)+6= $27
Let comics be c and mystery be m
Cost be y
c=m
The equations are
y=3m+6y=5m-8Solve for m
3m+6=5m-82m=18m=7booksHe has
7(3)+621+6$27Ani was told to write the number four and eight hundredths. She wrote 4.8. Was Ani correct or incorrect
Y
х
B В
The transformation below is applied
to AXYZ
(XY) → (0.5x, 0.5y)
What are the coordinates of point X"?
0 62.0.5)
(0.5,-2)
(2.0.5)
0 1.2, 0.5)
Answer:
(-2, 0.5) first
Step-by-step explanation:
X (-4, 1) → X' (-4*0.5, 1*0.5)
X'(-2, .5)
Find the measure of the arc.
A
146°
E
ĀC = [ ? ]
Answer:
90°
Step-by-step explanation:
m arc AC = 90°
_____________
The measure of the arc length AC is 90 degrees.
What is an arc length of a circle?The arc length of a circle is the distance between two points on the curve of the circle.
We have,
The arc length and the angles with the center on a circle are equal.
So,
Arc length AC makes a 90-degree angle with the center of the circle.
Now,
Arc AC = 90 degrees.
Thus,
The measure of the arc length AC is 90 degrees.
Learn more about arc lengths here:
https://brainly.com/question/16403495
#SPJ7
Find the area of the figure F2 cm
2 cm
5 cm
5 cm
Answer:
the answer would be 20cm^2 i took a quiz.
Step-by-step explanation:
4•(-6) • (-2) =
plz help
Answer:
should be 48
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
Apply rule- a * (-b) = -a * b
4 * (-6)
= -24(-2)
= 48
Hope this helps:)
Calculate the volume of the composite solid.
Answer:
about 33.52 in^3
Step-by-step explanation:
Volume of composite figure = volume of cone + volume of hemisphere
Volume of a cone = 1/3(nr^2h)
n = 3.14
r = radius
h = height
1/3 x 3.14 x 2^2 x 4 = 16.74 inches^3
volume of a hemisphere = (2/3) x (n) x (r^3)
n = 3.14
r = radius
2/3 x 3.14 x 2^3 = 16.74 inches^3
16.74 inches^3 + 16.74 inches^3 = 33.49
what do u add to 5 5/8 to make 9 ?
Answer:
5+5=9and mark me as brainlestttt
Answer:
27/8
Step-by-step explanation:
9 - 5 5/8 = 27/8
Thomas bought shoes for $45.50. The tax rate on the shoes was 8%. What is the total amount that Thomas paid for his shoe purchase?
Answer:
$49.14 is the total amount
$3.64 is the sales tax
Step-by-step explanation:
45.5 x 0.08 = 3.64
45.5 + 3.64 = 49.14
A triangle PQR is right angled at R, with PQ=80cm and R=60cm. find QR?
Step by step PLS PYTHAGORUS THEOREM
Answer:
Solution given:
A triangle PQR is right angled at R, with hypotenuse{h}PQ=80cm
and
base[b]PR=60cm.
perpendicular [P]= QR
by using Pythagoras law
h²=p²+b²
80²=QR²+60²
QR²=80²-60²
QR=[tex]\sqrt{2800}[/tex]
QR=20[tex]\sqrt{7}[/tex]=52.9=53cm
QR=53cm.
which expression represents the area of this shape
Answer:
which shape pls
Step-by-step explanation:
A car wash detailed 288 cars in 8 hours. At what rate did the car wash detail cars in cars per hour?
A.
34 cars per hour
B.
37 cars per hour
C.
36 cars per hour
D.
35 cars per hour
Answer:
a
Step-by-step explanation:
Figure J is the result of a transformation on figure I. Which transformation would accomplish this?
Answer:
A rotation 180 clockwise about the origin
Step-by-step explanation:
if you want me to explain, I can in the comments
Which of the following angles in standard position has a measure between 90° and
180°?
the diameter of a circle is 24 meters what is the circumference
Answer:
The circumfrence is 75.36
Step-by-step explanation:
I hope this helps