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.
There are a total of 76 teachers and students watching a school play. There are 4 teachers and 40 girls.
Write the ratio of boys to girls in lowest terms.
Given that : There are a total of 76 teachers and students watching a school play. There are 4 teachers and 40 girls.
Need to find : the ratio of boys to girls in lowest terms.
Firstly we need to find out the number of boys . For that subtract the number of teachers and girls from total number of teachers and students. That will be ,
[tex]\implies \sf n( boys) = 76 - 4 - 40 =\red{ 32 }[/tex]
Therefore our required ratio will be:-
[tex]\implies \sf 32 : 40 = \boxed{\sf 4:5 }[/tex]
Hence the required answer is 4:5 .
the ratio of colored papers to white papers is 3/8 if there are 48 white papers, how many coloured papers are there
The number of coloured papers as per the given problem is 18.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
Given that,
The ratio of coloured papers to white papers is 3/8.
And, the number of white papers is 48.
Suppose, the number of coloured papers be x.
Then, as per the question the following equation can be obtained,
3/8 = x/48
=> x = 3/8 × 48
=> x = 18
Hence, the number of coloured papers is 18.
To know more about ratio and proportion click on,
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all of the following are equivalent except...
A. 8x + 3x
B. (8+3)x
C. 11x
D. 11x^2
Answer:
d) [tex]11x^2[/tex] because that would be the same as [tex]11x * 11x[/tex]
If the probability that a student in school wears contacts is 0.38 and the probability that a student in the same school has a car is 0.42, what is the probability that a student wears contacts and has a car?
Answer:
Probability [Student wears contacts and has a car] = 0.1596
Step-by-step explanation:
Given:
Probability [Student in school wears contacts] = 0.38
Probability [Student in the same school has a car] = 0.42
Find:
Probability [Student wears contacts and has a car]
Computation:
P[A and B] = P(A) × P(B)
So,
Probability [Student wears contacts and has a car] = Probability [Student in school wears contacts] x Probability [Student in the same school has a car]
Probability [Student wears contacts and has a car] = 0.38 x 0.42
Probability [Student wears contacts and has a car] = 0.1596
What is the height h of the flagpole in meters?
A. 10m
B. 12m
C. 18m
D. 20m
I REALLY NEED HELP PLS HELP ME ON THIS MATH
Answer:
Ok, we can define a function as a relation that maps elements from a set (the domain) into elements from another set (the range), such that each element in the domain can be mapped into only one element of the range.
2) Here you choose the autographed poster, and we know that each one of these costs $10.
So, if the artist sold x posters, then he/she would earn x times $10:
earnings = $10*x
So we can create a function:
f(x)
such that f(x) represents the total earnings of the artist for selling x posters.
And we already know the equation for the earnings, so the function will be:
f(x) = $10*x
3) Now, it asks us if the values:
-2, -1, 0, and 1
be appropiate for the domain of the function.
Remember that x represents the number of posters that the artist sold.
Then, if we take x = -2 or x = -1 (like the first two given values) this would mean that the artist sold a negative number of posters, which has no real sense in the situation given. So we can conclude that these values should not be in the domain of the function.
For the other two cases, 0 and 1, these two can be in the domain, because these represent the case where the artist sold only one poster and the case where the artist did not sell any poster (that are two possible cases)
A recipe for lemonade requires 10 parts of water to every 6 parts of lemon juice. How many cups of water should be added to 30 cups of lemon juice to make the lemonade? I dont understand how many "parts" of water = 1 cup
Answer:
50 cups
Step-by-step explanation:
ratio of water to juice = 10 : 6 = 5 : 3
amount of cup = (5 x 30) / 3 = 50
A) 350 – 180 B) 468 – 257 C) 2,456 – 2,388 D) 986 – 799 E) 687 – 623A) 350 – 180 B) 468 – 257 C) 2,456 – 2,388 D) 986 – 799 E) 687 – 623v
Answer:
Whats ur quetsion?
Create a step function for the following graph, be sure to watch holes in the graph. NEED HELP ASAP!
Answer:
See below
Step-by-step explanation:
This is a piece-wise function.
4, -4≤ x ≤ -2
f(x) = 2, -2 ≤ x < 2
-3, 2 ≤ x ≤ 4
Can someone please help me with number 4 ASAP please and ty!
Answer:
Option DStep-by-step explanation:
Here,
3x - 5
There is 3 as coefficient of x and -5 constant.
Hence,
Option D is correct
Which of the following is not a step in the process of multiplying rational expressions?
O Factor the numerator & denominator
o Write the answer as one fraction
O Cancel out like factors in the numerator and denominator
O Combine like terms
Answer:
combine like terms
Step-by-step explanation:
Pretty sure it's the correct answer.
Select all the expressions that have a value of 22 - 33 +29.
Answer:
B. and E.
Step-by-step explanation:
2^(2)-3^(3)+29 = 6
The number of employees in each industry in Seattle was recorded and rounded to the nearest
10 thousand. The results are displayed in the dot plot above. According to the dot plot, what is
the median number of employees, in thousands?
Answer:
20
Step-by-step explanation:
In the question, "35 is what percent of 40?" what is the 35?
Answer:
35 is the 'is' and 40 is the 'of'
Step-by-step explanation:
is/of = %/100
35/40 = x/100
cross-multiply to get:
40x = 3500
x = 3500/40
x = 87.5
I WILL GIVE BRAINLIEST!!!!!
Find an equation for the line below.
Answer:
y = 2/3x + 2.5
Step-by-step explanation:
What is the volume of the rectangular prism?
177*((177+(9-4+7)) +90/8=
Answer:
33464.25
Step-by-step explanation:
Using BODMAS : brackets, division, multiplication, addition
[tex]177\times ((177+(9-4+7)) +\frac{90}{8}\\\\177\times (177+12) +\frac{90}{8}\\\\177\times 189 +\frac{90}{8}\\\\\\177 \times 189 + 11.25\\\\33453 + 11.25\\\\33464.25[/tex]
Answer:
35444.25
Step-by-step explanation:
OFC by computing them
match the equation below
which does not describe the equation
[tex] \sqrt{x = - 2} [/tex]
Answer:
which of what ?
and the equation is not right. I don't know what you mean.
do you mean x = sqrt(-2) ?
all I can tell you just based on that assumption is that you can transform that into
[tex]x = \sqrt{2} \times i[/tex]
you know,
[tex]i = \sqrt{ - 1} [/tex]
but what else you might need is completely unclear.
The expression 6k is an algebraic expression where 6 is the number of dollars Andrew earns per hour doing odd jobs and k is the number of hours he works. What expression describes the number of hours Andrew worked if he earned $30.00?
Answer: 30 = 6(5) thirty equals six times five.
Step-by-step explanation: Divide the total money earned by the pay Andrew gets for every hour to find how many hours Andrew worked to get that amount of money.
$30.00 = 6k
Have a nice day.
A survey of 125 freshmen business students at a local university produced the results listed below. How many students took history and math, but not music? 30 took history; 32 took math; 33 took music; 14 took history but not math; 9 took math and music; 13 took history and music; 2 took all three
Answer:
Total Number of students taking Math and History and not music are 68.
Number of students who took both math and history at the same time is 6.
Step-by-step explanation:
History = 30
Math = 32
Music= 33
Math and Music= 9
History and Music= 13
History and Music and Math = 2
History but not math = 14
We have to find students taking history and math but not music.
Total number of students = 125
From the figure number of students taking Math and History and not music are
=30+6+32= 68
Number of students who took both math and history at the same time is 6.
A sphere has a radius of 3 centimeters.what is the volume of the sphere
Answer:
Step-by-step explanation:
WENEGADE WAIDER
[tex]36\pi cm {3}[/tex]
This prism has a right triangle for a base. What is the volume of the prism?
length = 6 x 1/3 = 2 inches
width = 4 x 1/3 = 4/3 inches
height = 8 x 1/3 = 8/3 inches
volume = lwh = 2 x 4/3 x 8/3 = 64/9 cubic inches
Another approach is the following:
There are 6 x 4 x 8 = 192 cubes inside the prism,.
Each cube has a volume of 1/27 cubic inches.
Therefore total volume = 192 x 1/27 = 192/27 = 64/9
An angle whose measure is 92° is in standard position. In which quadrant does the terminal side of the angle fall?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer:D:quadrant IV
Step-by-step explanation:
You welcome
Answer:
B. quad 2
Step-by-step explanation:
Other person is wrong, its b edge 2021
question in picture,
find all angles that satisfy the equation below.
What is the domain of f?
PLZZZZ HELP!!!
First to answer will get brainly!!!PLZZZZZZ
Answer:
-7
Step-by-step explanation:
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixons shadow is 18 feet long and Ariadne’s shadow is 15 feet long. If Dixon is 6 feet tall how tall is Ariadne?
Answer:
Step-by-step explanation:
It would be 3ft.
Answer:
5 ft
Step-by-step explanation:
HELP ASAP
Solve for x.
x = [?]
X - 6
8x + 24
Answer:
x=18
Step-by-step explanation:
Both angles are supplementary angles and form 180
Set your formula up as following
(x-6) + (8x+24) = 180
x+8x-6+24=180
9x=180+6-24
9x=162
x=162/9
x=18
Now substitute 18 for x to get your angles and check your work .
In the triangle below, DF = x + 4 and AC = 4x – 6. Solve for x. Type your numerical
answer.
Answer:
x= 7
Step-by-step explanation:
Midsegment theorem!
x+4 = 1/2 (4x-6)