Answer:
1-i and -1+i
Step-by-step explanation:
We are to find the square roots of [tex]z=0-2i[/tex]. First, convert from Cartesian to polar form:
[tex]r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2[/tex]
[tex]\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}[/tex]
[tex]z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})[/tex]
Next, use the formula [tex]\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr][/tex] where [tex]\displaystyle k=0,1,2,...\:,n-1[/tex] to find the square roots:
When k=1
[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr][/tex]
[tex]\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr][/tex]
[tex]\sqrt{2}\biggr(cis\frac{7\pi}{4}\biggr)[/tex]
[tex]\sqrt{2}(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4})\\ \\\sqrt{2}(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)\\ \\1-i[/tex]
When k=0
[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr][/tex]
[tex]\sqrt{2}\biggr(cis\frac{3\pi}{4}\biggr)[/tex]
[tex]\sqrt{2}(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})\\ \\\sqrt{2}(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\-1+i[/tex]
Thus, the square roots of -2i are 1-i and -1+i
express the following rational algebraic expression to its simple form.show your solution
5. ײ+5×-14/ײ-4
Answer
[tex] \frac{ \times -+7}{×+2} [/tex]
5. Look at the figure in the graph below. If a figure congruent to this one were drawn, which statement must be TRUE?
Answer:
C. by a facotor of 3
Step-by-step explanation:
The approximate value of the figure in the graph is [tex]\sqrt{3[/tex]
So if you were to draw a figure that is congruent to the one drawn it would be C. by a factor of 3.
What is the measure of \angle D∠Dangle, D?
Answer:
74⁰
Step-by-step explanation:
As in cyclic quadrilateral sum of opposite angles us equal to 180⁰
explain why the other expressions do not have like terms A. 14m + mn B. 2y + 2x + 4 C. -3/4m + 8m + m D. 4 - 3p E. 5.75t + 7.75t - t F. 8xy - 6xy
How many lines of symmetry does the following figure have?
1
3
4
5
Answer:
1
Step-by-step explanation:
It has 1 lines of symmetry
Hopes this helps
#ViolentJax
I need help please and thank you and show work
Answer:
Ivy is correct
Step-by-step explanation:
the perimeter of a parallelogram can be written as P= 2(a+b), where a and b are the lengths of the sides of the parallelogram.
since the parallelogram has been dilated by a scale factor of 0.6, we multiple the original side lengths by 0.6.
12 × 0.6 = 7.2
16 × 0.6 = 9.6
Plug into the equation
P=2(7.2+9.6)
P=2(16.8)
P= 33.6
You can also solve by plugging in the original values and multiplying the answer by 0.6.
P=2(12+16)(0.6)
P=2(28)(0.6)
P=(56)(0.6)
P=33.6
find the measures of
Find the measure of
Find the measure of
Answer:
15.
If we look at angle BOD, that would form a right angle (90°), given that one part of that whole angle is 30°, the other would be;
30° + x = 90°
-30 -30
x = 60°, therefore ∠BOC = 60°.
If we take a look at angle EOC, we can see that that angle is a straight angle (180°), we can also see that a right angle (90°) is a part of that angle alongside the angle we just previously found (60°). So all of those angles plus the unknown angle (AOE) which we will consider 'x' summed up would result in 180 degrees.
Now we set up the equation;
90° + 60° + x = 180°
150 + x = 180
-150 -150
x = 30°, therefore ∠AOE = 30°.
16.
The sum of the interior angles in a triangle will always equal 180°. (We can also confirm this using the formula (n - 2) x 180.)
Given two of the angles, we must add them and the unknown angle(D) which we will consider 'x' to make it result in 180°.
Now we set up the equation;
55° + 18° + x = 180°
73 + x = 180
-73 -73
x = 107°, therefore ∠EDF = 107°.
17.
To find angle P, we must first find the supplement of 34° because 34° and the angle beside forms a straight angle (180°).
Set up an equation;
34 + x = 180
-34 -34
x = 146°, now that we've found the supplement, we add this supplement with the other given angle (23°) because all three angles (unknown angle which we will consider x + 23 + 146) will equal 180°(sum of interior angles of triangle).
146° + 23° + x = 180°
169 + x = 180
-169 -169
x = 11°, therefore ∠QPR = 11°.
18.
Seeing that the bigger triangle has a 90° angle (indicated with a square), and two other equal angles(indicated with the two lines on both legs of the big triangle), we solve for those two missing equal angles in the bigger triangle which we will then use to solve for the smaller triangle's angle.
2x + 90° = 180°
-90 -90
2x = 90
/2 /2
x = 45°, so now we know the two angles in the bigger triangle excluding the right angle.
One of those equal angles is vertical to the smaller triangle, and vertical angles are congruent.
Hence, the angle vertical to the bigger triangle in the smaller triangle will be 45°.
Now we solve for ∠CDE.
Add the two angles and the missing angle to equal 180°.
Set up the equation;
86° + 45° + x = 180°
131 + x = 180
-131 -131
x = 49°, so ∠CDE = 49°.
Given m|n, find the value of x.
Rt
(6x+9)
(4x-19)
11
Answer:
x = 19
Step-by-step explanation:
See attched image.
15. Graph the line 3 y - 2x = 3 on the axes provided. At what value of x does the line you graphed intersect the line y = 5. Show how you determined your answer. th 6 noints
Answer:
x=6
Step-by-step explanation:
3*5-2x=3
15-2x=3
15-3=2x
12=2x
6=x
Find the area of the figure. Use 3.14 as π.
area triangle:
b×h/2
= 11 in×10 in/2
=55 in²
area half-circle:
pi×r² /2
= 3.14×5in² /2
=78.5in² /2
=39.25 in²
Total area: area triangle+ area half-circle
= 55 in²+39.25 in²
=94.25 in²
-3(2x+2)<10 thank you in advance
[tex]-3(2x+2) < 10\\\\\implies -6x -6 < 10\\\\\implies -6x < 10 +6\\\\\implies -6x < 16 \\\\\implies x > -\dfrac{16}6\\\\\implies x > -\dfrac{8}3[/tex]
Which expressions are equivalent to 4^-2 x 7^-2
Answer:
[tex]\frac{1}{784}[/tex]
Step-by-step explanation:
4⁻² * 7⁻²
Use the Negative Exponent Property: x⁻ⁿ = [tex]\frac{1}{x^n}[/tex]
[tex]4^{-2}*7^{-2}\\\\ \frac{1}{4^2}*\frac{1}{7^2}\\\\ \frac{1}{16}*\frac{1}{49}\\\\ \frac{1}{784}[/tex]
Hope this helps!
Factor the following:
y^2-3y-40
3x62+10x+3
Answer:
Below in bold.
Step-by-step explanation:
y^2 - 3y - 40
To factor this we need 2 numbers whose product is -40 and whose sum is -3. These are -8 and +5. so the factors are:
(y - 8)(y + 5).
3x^2 + 10x + 3
To factor this we need 2 numbers whose product is (3*3) = +9 and whose sum is +10. These are +9 and +1 so we write:
3x^2 + 9x + x + 3
Factor by grouping:
= 3x(x + 3) + 1(x + 3)
= (3x + 1)(x + 3).
What is the volume of the right prism
A. 1275
B. 600
C. 1020
D. 680
Answer:
B
Step-by-step explanation:
The face of the prism is the right triangle closest to us.
The area of the right triangle is 15 * 8 = 120 / 2 = 60 The general formula for a triangle's area is 1/2 * B * h.
B = 8
h = 15
The volume in general is B*h.
The height in this case is 10 (the height in this case is perpendicular to the surface containing the right triangle).
Volume = B * h
Volume =60 * 10
Volume = 600
What is the value of x?
Enter your answer in the box.
units
Answer:
x=27
Step-by-step explanation:
the attached photo might help you
find variables x, y, and z
Answer:
Step-by-step explanation:
plsss need help nowwww
Answer:
49/12
Step-by-step explanation:
1 ⅓ can be written as 1 + 1/3
1 ⅓
= 1 + 1/3
LCM = 3
= 3/3 + 1/3
= ( 3 + 1 )/3
= 4/3
2 ¾
= 2 + 3/4
LCM = 4
= 8/4 + 3/4
= ( 8 + 3 )/4
= 11/4
1 ⅓ + 2 ¾
= 4/3 + 11/4
LCM = 3 x 4 = 12
4/3 x 4/4
= ( 4 x 4 )/( 3 x 4 )
= 16/12
11/4
= 11/4 x 3/3
= ( 11 x 3 )/( 4 x 3 )
= 33/12
16/12 + 33/12
= ( 16 + 33 )/12
= 49/12
Answer:
I don’t know if it correct, but when I solved it I got 4 1/12
Step-by-step explanation:
(1+2) (1/3 + 3/4)
3 + 13/12
3 + 1 1/12
3 + 1 + 1/12
4 + 1 /12
4 1/12
What is the slope of the given line? (Use only whole numbers or fractions to answer)
What is the y-intercept of the given line? (Put your answer as the y-intercept point with no spaces)
Answer:
Slope m= -12/5
Step-by-step explanation:
Slope Solution
m=riserun=ΔyΔx
m=y2−y1x2−x1
m=−9−37−2
m=−125
m=−125
In decimals:
m = -2.4
Point Slope Form
y−y1=m(x−x1)
y−3=−125(x−2)
In decimals:
y−3=−2.4(x−2)
Slope Intercept Form
Find the Equation of the Line:
y=mx+b
by solving for y using the Point Slope Equation.
y−y1=m(x−x1)
y−3=−125(x−2)
y−3=−125x−(−125×2)
y−3=−125x−−245
y−3=−125x+245
y=−125x+245+3
y=−125x+395
m=−125
b=395
In decimals:
y=−2.4x+7.8
Standard Form of a Linear Equation
Ax+By=C
Starting with y = mx + b
y=−125x+395
Multiply through by the common denominator, 5, to eliminate the fractions:
5y=−12x+39
Then rearrange to the Standard Form Equation:
12x+5y=39
A=12
B=5
C=39
y-Intercept, when x = 0
y=mx+b
y=−125x+395
When x = 0
y=−125×0+395
y=395
y-intercept=395
(x,y)=(0,395)
In decimals:
(x,y)=(0,7.8)
x-Intercept, when y = 0
y=mx+b
y=−125x+395
When y = 0
0=−125x+395
125x=395
x=395×512
x=3912
x=134
x-intercept=134
(x,y)=(134,0)
In decimals:
(x,y)=(3.25,0)
is 627 divisible by 3
Answer:
yes.
Step-by-step explanation:
If you divide 627 by 3, you get 209 which is a whole number.
Hope this helped! Have a nice day!
Please give Brainliest when you can!
-Jaron
Answer:
technically speaking, yes. but if you don't want any remainders, (or decimals) then no.
Step-by-step explanation:
7 isnt divisable by anything, unless you have remanders or decimals, fractions ext. so yeah.
Write an expression that is equivalent to 1.5a +4.7+0.25a-0.3-0.5a
Answer:
1.25a-4.4
Step-by-step explanation:
you take :1.5a+0.25a-0.5a=1.25
then:4.7+0.3=4.4
1.25a-4.4
but am not sure sorry
Answer:
1.25a + 4.4Step-by-step explanation:
Collect like terms and simplify
1.5a +4.7 + 0.25a - 0.3 - 0.5a = a(1.5 + 0.25 - 0.5) + (4.7 - 0.3) = 1.25a + 4.4if 7 notebooks $3.85,what is the unit price of the notebooks
Answer:
0.55
Step-by-step explanation:
I think you would just divide the numbers
Is the number -243 an integer?
Answer:
yes
Step-by-step explanation:
Yes it is because it is a whole number and rational
Please mark this as brainliest and I hope this helps you
What is the area, in square units, of the shaded part of the rectangle below?
Answer:
10 units²
Step-by-step explanation:
Area = bh/2
b = 4
h = 5
A = (4 x 5)/2 = 10 units²
I hope this helps!
Please help me please
Answer: x is 125
Step-by-step explanation: Angles P and S are also consecutive angles, adding up to 180 degrees. 180-55 = 125, so adding the two angles together is 180 degrees. Thus, x is 125.
A pair of shoes usually sells for $63. If the shoes are 40% off, and a sales tax of 7% is applied to
the discounted cost, what is the total price of the shoes, including tax? Round your answer to
the nearest penny
A.$37.08
B.$40.45
C.$40.82
D.$42.2
Answer: 40.45 or B
Step-by-step explanation:
63 x 0.6(100%-40%) = 37.8
37.8 x 1.07 = 40.446
40.446 rounded is
40.45
The measures of the interior angles of a quadrilateral are 2x + 10, 3x, 3x + 5, and 5x + 20. What is the measure of the largest angle?
Answer:
Step-by-step explanation:
Finding the angles of quadrilateral:
Sum of all angles of quadrilateral = 360
2x + 10 + 3x + 3x + 5 + 5x +20 =360
2x + 3x + 3x + 5x + 10 + 5 + 20 = 360
Combine like terms
13x + 35 = 360
Subtrace 35 from both sides
13x = 360 - 35
13x = 325
Divide both sides by 13
x = 325/13
x = 25
5x +20 = 5*25 +20
= 125 +20
= 145°
Measeure of largest angle : 145°
80 wpm how many words typed while typing 12 hours straight
Answer:
57600 words in 12 hours.
Step-by-step explanation:
80 wpm means 80 words per minute.
We need to know how many minutes are in a 1 hour which is 1 hour is 60 minutes.
We want to know how much words in 12 hours.
Given:
[tex]\frac{80 word}{1 min}, \frac{60 min}{1 hour},\frac{12 hour}{1}[/tex]
[tex]\frac{80 word}{1 min} *\frac{60 min}{1 hour} *\frac{12 hour}{1} =[/tex] 57600 words in 12 hours.
Answer: 57,600
Step-by-step explanation:
80 × 60 = 4800 in 1hr
4800 ×12 = 57, 600 in 12hrs
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
6/5 or A. 1 1/5
Step-by-step explanation:
Hey there!
In order to simplify this, you need to add the numerators but not the denominators since they are the same
4+2=6
So this shows that the answer is 6/5 or 1 1/5
Answer:
6/5 or 1 1/5 or A
Step-by-step explanation:
In order to simplify this, you need to add the numerators but not the denominators since they are the same
4+2=6
So this shows that the answer is 6/5 or 1 1/5
Expand and simplify (x+6)(x−11)
Answer:
x^2 - 5x - 66
Step-by-step explanation:
1. Distrubute the x to the x and -11 so you will get x^2 - 11x
2. Distrubute the 6 to x and -11 and you get 6x - 66
3. Combine like terms (x^2 - 11x + 6x - 66) you will get x^2 - 5x - 66
what are the missing reasons in the proof?
Answer:
Step-by-step explanation:
3) Opposite sides of a parallelogram are parallel
4) Alternate interior angles theorem
5) Reflexive property
6) ASA
