Write | √3 - 2i | in a + bi form.

Answers

Answer 1

keeping in mind that, an absolute value expression is in effect a piece-wise, then

[tex]\bf |\sqrt{3}-2i|\implies \begin{cases} +(\sqrt{3}-2i)\\ -(\sqrt{3}-2i) \end{cases}\implies \begin{cases} \sqrt{3}-2i\\ -\sqrt{3}+2i \end{cases}[/tex]

Related Questions

The sum of the digits of a certain number is 12. When you reverse its digits you decrease the number by 36. Find the number

Answers

x+y=12

x*y =36

8+4=12, so make the digits 84, reverse to make it 48

84-48=36

the numbers are 8 & 4

Solve the equation: 2.6 = -0.2t

Answers

2.6 = -0.2t...divide both sides by -0.2
2.6 / -0.2 = t
-13 = t <==

2.6=-0.2t
T=2.6/-0.2=-13

T= -13

Hope this helps!

A wire is first bent into the shape of a rectangle with width
4in and length 14in. Then the wire is unbent and reshaped into a square. What is the length of a side of the square?

Answers

First find the perimeter of the rectangle: 2w+2l which is 8+28=36. Then find the square root of 36 which is 6 so that is the answer.

First you have to find the area of the wire
Area of a rectangle=L*W= 14*4=56
Then divide that by 4 since a square has 4 equal sides
56/4=14
The length of a side of a square is 14 in

Ryan spent $3.25 on lunch every day, Monday through Friday. If he had $20 at the start of the week, how much money will he have left after Friday?

Answers

$3.75

it's pretty simple you multiply $3.25 times the amount of days he spent the money so 5 which gives you $16.25 then subtract that out of $20 and you'll have $3.75 (:

The amount of money left after Friday is $3.75.

What is unitary method?

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Amount of money spent for the lunch every day is $3.25.

Total amount of money Ryan have is $20.

Now, number of total days from Monday to Friday is 5.

So,

The amount spent for lunch for 5 days by Ryan

= 5 × $ 3.25 = $16.25 (by unitary method)

Therefore,

The amount of money left after Friday

[tex]\$20 - \$16.25\\= \$3.75[/tex]

Hence, the amount of money left after Friday is $3.75.

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Determine the standard variation of the data below. (1, 2, 3, 4, 5)

Answers

Calculate for the mean/ average of the given numbers:

μ = (1 + 2 + 3 + 4 + 5) / 5 = 3

Then, we calculate for the summation of the squares of differences of these numbers from the mean, S

S = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
S = 10

Divide this summation by the number of items and take the square root of the result to get the standard deviation.

SD = sqrt (10 / 5) = sqrt 2
SD = 1.41

Thus, the standard deviation of the given is equal to 1.41.

Answer:

So basically sqrt of 2...

Step-by-step explanation:

Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Answers

check the picture below.

[tex]\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)} \\\\\\ \cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\ -------------------------------\\\\ \begin{cases} d=10\\ e=18\\ f=22 \end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D[/tex]

[tex]\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D[/tex]

30 POINTS!!!!!!!
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 99m long and 72m wide.
Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

You need to add the area of a rectangle which is 99 by 72, and the area of a circle with a diameter of 72
99 * 72 = 7128
3.14 * (72/2)^2
3.14 * 36^2
3.14 * 1296
4069.44
7128 + 4069.44 = 11197.44

Answer:

1273 hola aaaaa oigan busco novia

A farmer had 17 sheep. all but 9 died. how many live sheep were left

Answers

all but 9 have died so he has 9 alive.

9 all BUT 9 died. I have to write 20 character for it to be "explained well" These words are basically fluff. my answer is in the first sentence.

I don't understand this and would appreciate an explanation as well :)
Solve for the variable in the equations below.
Round your answers to the nearest hundredth.
Do not round any intermediate computations.

e^x = 6

4^(y+3) = 3

[tex]e^x = 6[/tex]
[tex]4^y^+^3 = 3 [/tex]

Answers

We want to solve the two equations
[tex]e^{x}=6[/tex]
and
[tex]4^{y+3}=3[/tex]

First equation.
Take natural log of each side.
[tex]ln(e^{x})=ln(6)\\xln(e)=ln(6)\\ x=ln(6)=1.7918[/tex]
Note that ln(e) = 1 by definition.
Answer: x = 1.79 (nearest hundredth)

Second equation.
Take natural log of each side.
[tex]ln(4^{y+3})=ln(3)\\ (y+3)ln(4)=ln(3)\\ y+3= \frac{ln(3)}{ln(4)} =0.7925\\y=0.7925-3=-2.2075[/tex]
Answer: y = -2.21 (nearest hundredth)

Identify a semicircle that contains C.

A.ABC
B.AC
C.CB
D. ACB

Answers

A semicircle that contains C is ACB.

Answer: The correct option is (D). ACB.

Step-by-step explanation: We are given to identify a semi-circle that contains the point 'C'.

As shown in the figure, AB is the diameter of the circle with center 'O'.

So, there are two congruent semi-circles made by the diameter AB.

The point 'C' lies on the upper semi-circle made by the diameter AB.

Since the upper semi-circle contains the point 'C', so it is named as the semi-circle ACB.

Thus, the semi-circle ACB contains the point 'C'.

Option (D) is correct.

A school director must randomly select 6 teachers to participate in a training session. There are 34 teachers at the school. In how many different ways can these teachers be selected, if the order of selection does not matter?

Answers

The selection of r object out of n, is carried out in C(n, r) many ways,

where [tex]C(n, r)= \frac{n!}{r!(n-r!)} [/tex]

n! meaning 1*2*3*....*(n-1)*n

According to this, the selection of 6 teachers out of 34, can be carried out in C(34, 6) many different ways.

[tex]C(34, 6)= \frac{34!}{6!(34-6!)}=\frac{34!}{6!(28!)}= \frac{34*33*32*31*30*29*28!}{6!28!}= \frac{34*33*32*31*30*29}{6!}[/tex]

[tex]=\frac{34*33*32*31*30*29}{6*5*4*3*2*1}= 34*11*4*31*29=1,344,904[/tex]

In which case would it be best to use the “Factoring Method” to solve the trinomial equation?
x^2 + 4x = -5
4.3x^2 + 2.4x - 3 = 0
x^2 - 4x + 3 = 0

Answers

The best case would be to use factoring in the last equation because it has whole numbers that are "factorable," meaning that its c value has factors that evenly add up to its b value.
In this case, (x-3)(x-1). -1*-3=3 and -1+-3=-4

The sum of three consecutive odd integers is 18 less than 5 times the middle number. Find the 3 integers. Use an algebraic solution

Answers

X +(x+2) + (x+4) = 5(x+2)-18

3x+6 = 5x+10-18

3x+6 = 5x-8

3x=5x-14

-2x=-14

x=7

(x+2) =9

(x+4) =11

7 + 9+ 11 =27

5(9)-18 =45-18 =27

3 numbers are 7, 9 & 11

For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?

Answers

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

x-------> the pressure in PSI

y------> the volume of the gas in cubic inches

In this problem we have the point [tex](30,600)[/tex]

[tex]x=30\ psi\\y=600\ in^{3}[/tex]

Find the constant k

[tex]y*x=k[/tex]

substitute the values of x and y

[tex]600*30=k[/tex]

[tex]k=18,000\ lb*in[/tex]

the equation is

[tex]y=18,000/x[/tex]

therefore

the answer is

[tex]y=18,000/x[/tex]

Answer:

[tex]y=\frac{18000}{x}[/tex]

Step-by-step explanation:

Let the volume of gas be y

Let the pressure be x

Since we are given that the volume of the gas is inversely proportional to its pressure.

⇒[tex]y \propto \frac{1}{x}[/tex]

Let the proportionality be k

So, [tex]y=\frac{k}{x}[/tex] ---A

Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches

So, substitute x = 30

y = 600

[tex]600=\frac{k}{30}[/tex]

[tex]600 \times 30=k[/tex]

[tex]18000 =k[/tex]

Substitute the value of k in A

So, [tex]y=\frac{18000}{x}[/tex]

Hence function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is [tex]y=\frac{18000}{x}[/tex]

Which is a sum of cubes? a3 + 18 a6 + 9 a9 + 16 a12 + 8
a3 + 18
a6 + 9
a9 + 16
a12 + 8

Answers

Answer: [tex]a^{12}+8[/tex]

Step-by-step explanation:

let's check all the expressions

1. [tex]a^3+18[/tex]

here 18 is not a perfect cube.

2. [tex]a^6+9[/tex]

here 9 is not a perfect cube.

3.[tex]a^9+16[/tex]

here 16 is not a perfect cube.

4.[tex]a^{12}+8[/tex]

here 8 is a perfect cube, thus we can write above expression by using laws of exponents as

[tex](a^4)^3+2^3[/tex]

Thus, [tex]a^{12}+8[/tex] is a sum of cubes.

Julio paid 1.3 times his normal hourly rate for each he works over 31 hours in a week. Last week he worked 35 hours and earned $448.88. What is julios normal hourly rate ?

Answers

Hi, Globabypatricia! :)

All the time worked past 31 hours gets paid 1.3 times.
He worked 4 hours at such a rate.

31+4(1.3)
31+5.2
=36.2
Paid as if he worked 36.2 at a normal rate.

To find his normal wage, divide 448.88 by 36.2
448.88/36.2
=12.40

His normal wage is $12.40.

To check:
12.40*31=384.40
12.40*1.3=16.12
16.12*4=64.48

384.40+64.48
=$448.88

Hope this helps.
-Benjamin

Good question

Let his hourly rate is x

then:

31x + (35-31)*1.3x = 448.88

solve for x:

31 x + 5.2x = 448.88

36.2 x =448.88

x = 12.4$

not fair hourly rate by the way ;)

I need to find the answer to these questions in about 10 minutes or I'm screwed. please help me out.

Answers

For the first figure, the geometric figure used in the construction that is shown is the intersection of the angle bisectors of the triangle is the center of the inscribed circle.

For the second figure, the construction of the above figure in the circle represents how to find the intersection of the perpendicular bisectors of triangle ABC.

For the third figure, the statement that is demonstrated in the in line P intersecting line m perpendicularly is the set of points equidistant from the endpoints of a line segment is the perpendicular bisector of the segment.

Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two. what is the value of x?

Answers

3(x - 7) = 23 - (3x + 2) =
3x - 21 = 23 - 3x - 2 =
3x - 21 = -3x + 21
3x + 3x = 21 + 21
6x = 42
x = 42/6
x = 7 <==

The required value of x is 7.

What are linear equation?

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now the given statement is,

Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two.

So converting them into numerical form,

the difference of a number x and seven = x - 7

∴ Three times the difference of a number x and seven = 3(x - 7)

Similarly,

the sum of three times a number x and two = 3x + 2

∴ Twenty-three minus the sum of three times a number x = 23 - (3x + 2)

Therefore, the required equation is,

3(x - 7) = 23 - (3x + 2)

Expanding the brackets we get,

3x - 21 = 23 - 3x - 2

or, 3x - 21 = 21 - 3x

Taking alike terms together,

3x + 3x = 21 + 21

or, 6x = 42

Dividing both side by 6 we get,

x = 7

which is the required value of x.

Thus, The required value of x is 7.

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What is the missing step in this proof?

Answers

The answer is the third choice..
Statement: Angle 1 and angle 4 are congruent, and angle 3 and angle 5 are congruent.
Reason: Alternate Interior Angles Theorem

Hope this helps!

The missing step in the proof is;

Statement: ∠1 ≅ ∠4 and ∠3 ≅ ∠5Reason: Alternate interior angle theorem.

The correct answer choice is option C.

What is alternate interior angles theorem?

Alternate angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior or exterior angles are congruent.

It is used to prove that alternate interior angles are equal if two parallel lines are cut by a transversal,

Hence, angle 1 is congruent to angle 4 and angle 3 is congruent to angle 5.

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In triangle PQR, C is the centroid.

A. If CY = 10, find PC and PY
B. If QC = 10, find ZC and ZQ
C. If PX = 20, find PQ

Answers

Because point C is the centroid of the triangle, therefore:

Segments PZ = ZR; RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:

PC = 20

PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:

ZC = 5

ZQ = 15

C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:

PQ = 40

HELPPP Plzzzzzzzzzz ASAP
Use Addition of Composite Figures to find the total shaded regions.

1) Find the shaded area. Round your answer to the nearest tenth, if necessary.

Answers

12*6 = 72 - (3*4) = 60 - (4*5) = 40

Come on, Queen. You can do this. It's a square sitting on top of a long skinny rectangle. The rectangle is 12 wide and 2 high. It's area is 12x2=24. The only tough part is figuring out the width of the block sitting on it. The width of the block is what's left after you subtract the 5 and the 3 from the 12. That's (12-5-3)=4. Whaddaya know ! The block is 4 wide and 4 high ... It's a square ! Its area is 4x4=16. Add that to the area of the rectangle and you have the answer.

5v + 7f =28.70 if f is 2.85

Answers

5v+7(2.85)=28.70

5v+19.95 = 28.70

5v = 8.75

v = 1.75

Hey!

First, let's write the problem.
[tex]5v+7\left(2.85\right)=28.7[/tex]
Multiply [tex]7[/tex] with [tex]2.85[/tex].
[tex]5v+19.95=28.7[/tex]
Subtract [tex]19.95[/tex] from both sides.
[tex]5v+19.95-19.95=28.7-19.95[/tex]
[tex]5v=8.75[/tex]
Divide both sides by [tex]5[/tex].
[tex]\frac{5v}{5}=\frac{8.75}{5}[/tex]
[tex]v=1.75[/tex]

Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish

What is 5 plus 5 minus 5 divided by 5 and then multiplied by 5?

Answers

With the order of operations first, you multiply and divide from left to right:

So you have 5+5-5/5(5)

We will divide first:
5+5-1(5)

Then multiply:
5+5-5

Then add and subtract from left to right:
10-5=5

Hope that helps.

Answer:

Step-by-step explanation:

[tex](5+5-5:5)\cdot5\\\\\text{Use PEMDAS}\\\\\text{P Parentheses first}\\\text{E Exponents}\\\text{MD Multiplication and Division (left-to-right)}\\\text{AS Addition and Subtraction (left-to-right)}\\\\=(5+5-1)\cdot5\\\\=(10-1)\cdot5\\\\=9\cdot5\\\\=45[/tex]

An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.

Answers

Final answer:

To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula: inradius = (area of the triangle) / (semiperimeter of the triangle). First, we need to find the area and semiperimeter of the triangle. Then, we can calculate the inradius and find the radius of the circle.

Explanation:

To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula:

inradius = (area of the triangle) / (semiperimeter of the triangle)

First, we need to find the area of the triangle. Since it is an isosceles triangle with equal sides of 5 inches, we can split it into two congruent right triangles. The height of each right triangle can be found using the Pythagorean theorem:

height = sqrt(5^2 - (6/2)^2) = sqrt(25 - 9) = sqrt(16) = 4 inches

Now, we can find the area of the triangle:

area = (1/2) * base * height = (1/2) * 6 * 4 = 12 square inches

Next, we need to find the semiperimeter of the triangle:

semiperimeter = (5 + 5 + 6) / 2 = 16 inches

Finally, we can calculate the inradius:

inradius = 12 / 16 = 3/4 inches

Therefore, the radius of the circle is 3/4 inches.

Solve the equation: h/9 = 7. A. h = 1 2/7 B. h = 63 C. h = –63 D. h = 7/9

Answers

I did this on a calculator so i'm 100% sure it's correct.

The answer is: B. h= 63

Well, just times 7 and 9 since if you times 9 on both side, h will be alone. Then just times 7 and 9 and will get 63, which is B.

How do you get rid of an exponent on a variable?

Answers

To get rid of an exponent to do the inverse function which is to take the root, or you can expand it.

Final answer:

To get rid of an exponent on a variable, apply the inverse operation of the exponent such as division or root operations.

Explanation:

To get rid of an exponent on a variable, you need to apply the inverse operation of the exponent. If the exponent is multiplication, you use division, and if the exponent is an exponentiation, you use a root operation. For example, to get rid of a squared variable, you take the square root of the variable. If you have a variable raised to the third power, you take the cube root of the variable.

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State the Midpoint formula?

How are the midpoint formula and the Distance formula alike? How are they different?

Give a real-world example that could be addressed using the distance formula.

Give a real-world example that could be addressed using the midpoint formula.

Answers

Let point A (x₁, y₁) and point B (x₂, y₂)

Mid-point formula is given by: [tex][ \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}] [/tex]

The distance formula is given by: [tex] \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]

The two formula are alike because they both need the information of two coordinate points

They are different because the mid point formula is adding up then divide by two, whereas the distance formula is subtracting then square the answer.

--------------------------------------------------------------------------------------------------------------
Real life problem involving distance formula:

Plane A is spotted on a radar with cartesian coordinate (450, 640).
Plane B is spotted on the same radar with cartesian coordinate (350, 540)

Work out the distance between plane A and plane B.
--------------------------------------------------------------------------------------------------------------
Real life problem involving mid point formula

Ms. Holland arranges a treasure hunt for a group of scouts. She marks two points, C and D, with cartesian coordinate (-5, 6) and (7, 10) respectively. The clue is that the treasure is buried in the middle point between C and D. Work out the coordinate where the treasure is buried.

a triangle has two sides of the lengths 8 and 10 what value could the length of the third side be

Answers

The last side could be 6 making it a right triangle.
Pythagorean theorem proof: 6^2+8^2=10^2, or 36+64=100

Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event

Answers

The possible outcomes for 1 HEAD and 3 TAILS are

HTTT
THTT
TTHT
TTTH

Assuming the coin is a fair coin, we have:
Probability of tossing head is 0.5
Probability of tossing tail is 0.5

Probability of tossing the coin four times for each outcome combination listed above is

HTTT = 0.5×0.5×0.5×0.5 = 0.0625
THTT = 0.5×0.5×0.5×0.5 = 0.0625
TTHT = 0.5×0.5×0.5×0.5 = 0.0625
TTTH = 0.5×0.5×0.5×0.5 = 0.0625

Hence, probability of getting three tails and one head from 4 tossing is
4×0.0625 = 0.25

Answer: False

Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.

A. True

B. False

Which rate is the lowest price?
$6.30 for 9
$5.50 for 5
$4.20 for 7
$0.80 each

Answers

Answer: $4.20 for 7
This problem can be solved by dividing the pay by the number of items.

$6.30 / 9 = $0.70
$5.50 / 5 = $1.10
$4.20 / 7 = $0.60
$0.80 / 1 = $0.80

This shows that for the third option, $4.20 for 7, the rate per item is the lowest.

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