Hello,
[tex]Let's\ say \\\\z=\sqrt{3+4*i} =a+b*i\\\\z^2=3+4*i=(a+b*i)^2=a^2-b^2+2i*a*b\\\\\\if \ a\neq 0\\\left\{\begin{array}{ccc}a^2+b^2&=&3\\2ab=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b=\dfrac{2}{a}\\a^2-(\dfrac{2}{a})^2=2\\\end{array}\right.\\\\\\a^4-4=3*a^2\\a^4-3a^2-4=0\\\\\Delta=(-3)^2-4*1*(-4)=25=5^2\\\\a^2=4\ or \ a^2=-1 (impossible)\\\\So:\\(a=2\ and\ b=1)\ or\ (a=-2\ and\ b=-1)\\[/tex]
Roots are thus 2+i and -2-i
There is an other using a geometrical formula (formule de Moivre)
The polynomial 3x2 – 10x + 8 has a factor of 3x – 4. What is the other factor of 3x2 – 10x + 8?
x – 2
x – 4
x – 6
x – 8
Answer:
x-2
Step-by-step explanation:
Dividing 3x2 – 10x + 8 by 3x-4 we get x-2.
Someone help me please !!!!!
Answer:
a=15 and x=7
Step-by-step explanation:
first we need to plug in the number to the variable than we try to get a and x by themselves.
If < W and < Y are supplementary, and < W = 121 °, then what would < Y measure?
Select one:
a. 121 °
b. 69 °
c. 59 °
d. 13 °
Answer:
Option c. 59°
Step-by-step explanation:
<W+<Y=180
121+<Y=180
<Y=180-121
<Y=59
Answered by GAUTHMATH
I need help bad? What’s the answer
Answer:
76°,60°
Step-by-step explanation:
sum of angles of a triangle=180
x+64+x+80+44=180
2x+188=180
2x=180-188=-8
x=-8/2=-4
so angles are -4+60=60°
and -4+80=76°
true or false
is this a function 0 goes to 0 4 goes to 1 8 goes to 2 and 12 goe to 3
Answer:
Step-by-step explanation:
True. The function appears to be f(x) = x/4.
For f (x) - 4x +1 and g(x) = ? -5, find (fºg)(4).
[tex](f\circ g)(x)=f(g(x))=4(x^2-5)+1=4x^2-19[/tex]
[tex](f\circ g)(4)=4\cdot4^2-19=64-19=\boxed{45}[/tex]
Hope this helps.
somone needs to have a guide ready for homework.
Answer:
wait what???
Step-by-step explanation: Is that even a question?
what is office personnel?
Answer:
Office personnel refers to the office chief, sectional chiefs and assistants that carry out all the administrative as well as clerical functions jointly to archive the objectives of an organization.
Is -3y = 5x + 4 perpendicular
Answer:
no it is not perpedicular
Step-by-step explanation:
I plugged the equation into a graphing calculator and the line does not appear to be perpendicular
Answer:
3y = 5x+4
3y=9x
yx=9/3
yx=3
x + y = 3, 4y = -4x - 4
System of Equations
Answer:
no solutions
Step-by-step explanation:
Hi there!
We're given this system of equations:
x+y=3
4y=-4x-4
and we need to solve it (find the point where the lines intersect, as these are linear equations)
let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable
we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4
y=-x-1
now we have y set as an expression containing x
substitute -x-1 as y in x+y=3 to solve for x
x+-x-1=3
combine like terms
-1=3
This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.
Therefore the answer is no solutions
Hope this helps! :)
The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution
What is the first step when applying properties of operations to divide 73.85 by 4.1?
Multiply the divisor and dividend by 10.
O Multiply the divisor and dividend by 100.
• Divide the divisor and dividend by 10.
• Divide the divisor and dividend by 100.
Step-by-step explanation:
divide the divisor and dividend by 10
Find the value of y.
A.74 B.20 C.66 D.62
Answer:
It's letter D.
Step-by-step explanation:
3.14÷60×50= 2.61 but you have to opposite remember if the number is a little number you have to opposite and that is the answer 6.2 but do not joy like this . so the real answer is 62
Write the following expression in exponential form:
16x16x16x1.6
0416
0164
16x4
O 16+ 4
Answer:
16x16x16x1.6
Step-by-step explanation:
here's your answer hope it helps you
7x-49=y
Solve for x?
The solution for x is x = (y + 49)/7.
Given that an equation 7x - 49 = y, we need to determine the equation in for of x,
To solve for x in the equation 7x - 49 = y, we'll isolate x on one side of the equation.
Here's the step-by-step process:
Start with the given equation: 7x - 49 = y.
Add 49 to both sides of the equation to isolate the term with x:
7x = y + 49.
Divide both sides of the equation by 7 to solve for x:
(7x)/7 = (y + 49)/7.
Simplify:
x = (y + 49)/7.
Therefore, the solution for x is x = (y + 49)/7.
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A student drops their notes and their papers scatter. The fact that the papers scatter and do not remain neatly stacked is an illustration of :
Answer:
-- increase in entropy
-- second law of thermodynamics
Step-by-step explanation:
The 1st law of thermodynamic states that there is conservation of energy, i.e. we cannot create energy and we cannot destroy energy also in an isolated system.
The given example is not a representative of the 1st law.
The [tex]\text{2nd law of thermodynamics}[/tex] states that there is a natural tendency of an isolated system to [tex]\text{degenerate}[/tex] into a more [tex]\text{disordered state.}[/tex] Before dropping the notes and papers were in an isolated ordered system.
After dropping the papers scattered and did not remain in a stack position. It moves into a more disordered state.
Begore dropping down the notes and papers, they were in a stable position, i.e. no kinetic energy is there. No randomness when the notes and the papers were dropped. There is an increase in kinetic energy. There is randomness among the molecules by bombardment. So there is an increase in entropy.
Thus, above illustrations represents :
an increase in entropythe second law of thermodynamicsGiven that g(x)=x2, find each of the following.
a) g(3)
b) g(-1)
c) g( - x)
d) g(2y)
e) g(1 + h)
a) g(3) = (Simplify your answer.)
Step-by-step explanation:
a)
g(3) = 9
b)
g(-1) = 1
c)
g(-x) = x²
d)
g(2y) = 4y²
e)
g(1 + h) = 1 + h² + 2h
using the identity (a +b)² = a² + b² + 2ab
Answer:
a) g(3) = 9
b) g(-1) = 1
c) g(-x) = x²
d) g(2y) = 4y²
e) g(1+h) = 1 + 2h + h²
Step-by-step explanation:
a) when x = 3 ,
g(3) = 3² = 9
b) when x = -1 ,
g(-1) = (-1)² = 1
c) when x = -x ,
g( -x ) = (-x)² = x²
d) when x= 2y ,
g( 2y ) = (2y)² = 4y²
e) when x = 1 + h ,
g( 1 + h ) = ( 1 + h )² = 1 + 2h + h²
If the equation to calculate the time it takes
your account balance to double is 72/6, what
is the interest rate of that investment?
Answer:
12%
Step-by-step explanation:
well when you get 72/6 and to make it into a easier full number/ (not a fraction) you get 12 then you put the % behind it and now you have 12%
Christopher's car can drive 230 miles on a full tank of gas. He plans to drive with a full tank from Austin to Dallas, which is 195 miles. How many miles will be left once he arrives in Dallas?
Answer:
35 miles
Step-by-step explanation:
Total Miles driven at full tank = 230 miles
Miles drive at full tank from Austin to Dallas = 195 miles
How many miles will be left once he arrives in Dallas?
Number of miles remaining at full tank = Total Miles driven at full tank - Miles drive at full tank from Austin to Dallas
= 230 miles - 195 miles
= 35 miles
A square and an equilateral triangle have the same perimeter. The length of the side of the square os x+10. The length of the side of the triangle os 4x. What is the length of the triangle side
Answer:
20
Step-by-step explanation:
the perimeter of the square and the triangle are the same
4×(x + 10) = 3×4x
4x + 40 = 12x
40 = 8x
x = 5
=>
a triangle side is 4x = 4×5 = 20
rization
Vhat is the prime factorization of 180?
Select a composite number to break into factors. Continue
factoring until all factors are prime.
22•2•3•3.5
2.2.45
2.3.3.5
480
2.9.5
Answer:
5 3 3 2 2
Step-by-step explanation:
180
90 2
45 2 2
15 3 2 2
5 3 3 2 2
Answer:
180 = 5 × 3² × 2²
Step-by-step explanation:
Starting with 180, the prime factors are in bold
180 = 90 × 2
= 45 × 2 × 2
= 15 × 3 × 2 × 2
= 5 × 3 × 3 × 2 × 2
Then
180 = 5 × 3 × 3 × 2 × 2 = 5 × 3² × 2²
If an item weighs 45kilograms what is its weight in pounds
A new hospital tracked the number of births during its first 6 months of operation, as shown in the table.
A 2-column table with 6 rows. The first column is labeled month with entries 1, 2, 3, 4, 5, 6. The second column is labeled number of births with entries 137, 110, 93, 70, 65, 77.
Find a quadratic function that models the data. Round numerical values to the nearest whole number
Answer:
y = 4x² - 43x + 178
Step-by-step explanation:
Given that data:
1 __ 137
2 __ 110
3 __ 93
4 __ 70
5 __ 65
6 __ 77
Usibg technology, the quadratic regression equation obtained is written in the form:
Ax² + Bx + C
A = 4.34 = 4 ( nearest whole number)
B = - 43.46 = - 43 (nearest whole number)
C = 178.3 = 178 ( nearest whole number)
Hence, the quadratic model is
y = 4x² - 43x + 178
By rounding the coefficients to the nearest whole number, the quadratic function that models the data is[tex]f(x) = 5x^2 - 42x + 174[/tex]
How to Find a quadratic function that models the data.To find a quadratic function that models the data, use a quadratic equation of the form:
[tex]f(x) = ax^2 + bx + c[/tex]
Let's use the given data points to form a system of equations and solve for the coefficients a, b, and c.
Using the first data point (month 1 with 137 births):
[tex]f(1) = a(1)^2 + b(1) + c = 137[/tex]
a + b + c = 137 (Equation 1)
Using the second data point (month 2 with 110 births):
[tex]f(2) = a(2)^2 + b(2) + c = 110[/tex]
4a + 2b + c = 110 (Equation 2)
Using the third data point (month 3 with 93 births):
[tex]f(3) = a(3)^2 + b(3) + c = 93[/tex]
This simplifies to:
9a + 3b + c = 93 (Equation 3)
Solve this system of equations will give us the values of a, b, and c.
Subtract Equation 1 from Equation 2
3a + b = -27 (Equation 4)
Subtract Equation 1 from Equation 3
8a + 2b = -44 (Equation 5)
Now solve Equations 4 and 5 simultaneously.
Multiply Equation 4 by 2 and subtracting it from Equation 5:
8a + 2b - (6a + 2b) = -44 - (-54)
2a = 10
Divide both sides by 2:
a = 5
Now substitute the value of a back into Equation 4:
3(5) + b = -27
15 + b = -27
Subtract 15 from both sides:
b = -42
Finally, substitute the values of a and b into Equation 1
5 + (-42) + c = 137
-37 + c = 137
Add 37 to both sides:
c = 174
Therefore, the quadratic function that models the data is:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Rounding the coefficients to the nearest whole number, the quadratic function becomes:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
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3 miles. 128 yards. Converted to feet
what single transformation maps triangle ABC onto A’B’C?
Answer:
the answer is rotation hope it helps ahhaha
please help ASAP
-
-
-
-
Answer:
The answer is A.
How I got it:
Formula of finding a triangle: 1/2 bh.
In this case, the base is R and the Height is X.
1/2rx.
What is the word form of 1.604
Answer:
one point 4 inchs
Step-by-step explanation: yessuh
Answer:
one and six hundred four thousandths
Factor 140c + 28 -14a to identify the equivalent expressions.
Step-by-step explanation:
140c+28-14a14(10c+2-a)hope it helps
stay safe healthy and happy...Can someone help me with this math homework please!
The distance traveled depends on the amount of time Marlene rides her bike
The function f(t) = 16t represents the scenario
Answer:
options (2), (3) and (5)
Step-by-step explanation:
2.
the distance traveled depends upon the amount of time she rides her bike.
as she travels 16 miles in 1 hr. she'll ride 32 miles in 2 hrs. so all values of distance traveled by her depends upon the time she takes.
3.
yes the initial is 16 miles per hour as the output of 1hr will be 16 and that's what the initial value is 16 miles for one hour. or 16 miles per hour.
5.
f(t) = 16t represents the scenario
where f(t) will be the output of the function that is d, distance when the output is t that is time.
whch of the following can be usefiul when finding the vaue of a variable
Answer:
i don't see anything so i cant help you sorry
Step-by-step explanation:
Celsius to Fahrenheit
Step-by-step explanation:
149......hshdbhdhsbhsjsusvshhs
