write 1+√-32/4 as a complex number in the form a + bi, where a and b are real numbers.
a. 1/4+1/2√2i
b. 1/4+1/4√2i
c. 1/4+√2i
d. 1/4+4√2i

Answers

Answer 1
Answer: Choice C

Work Shown:

[tex]\frac{1+\sqrt{-32}}{4}\\\\\frac{1+\sqrt{-1*16*2}}{4}\\\\\frac{1+\sqrt{-1}*\sqrt{16}*\sqrt{2}}{4}\\\\\frac{1+i*4*\sqrt{2}}{4}\\\\\frac{1+4i*\sqrt{2}}{4}\\\\\frac{1}{4}+\frac{4i*\sqrt{2}}{4}\\\\\boldsymbol{\frac{1}{4}+i\sqrt{2}}\\\\[/tex]

This matches with choice C. The imaginary 'i' term is not under the square root.


Related Questions

The ratio of boys to girls in a group is 2:1. If there are 26 more boys than girls, work out how many boys there are.

Answers

Answer : 52 boys : 26 girls

Step - by - step explanation :

Now we can guess, whatever number we put HAS to be 26 more boys than girls and it has to follow the 2 boys : 1 girl ratio . . .

26 boys : 13 girls <-- this follows the 2:1 ratio but is NOT 26 more boys than girls

52 boys : 26 girls <-- this follows the 2:1 ratio and has 26 more boys than girls ! :D

please help!!! Anyone know this? Thanks!!!!!!!

Answers

Answer:

[tex]i\sqrt4 ~ \text{and} ~ 2i[/tex]

Step-by-step explanation:

[tex]\sqrt{-4}\\\\=\sqrt{-1} \sqrt4\\\\=i\sqrt4\\\\=2i[/tex]


If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?

Answers

Answer:

23 days

Step-by-step explanation:

Given,

No. of days taken by Jenny to read 7 books

= 8

So,

No. of days taken by her to read 1 book

[tex] = \frac{8}{7} [/tex]

Therefore,

No. of days taken by her to read 20 books

[tex] = \frac{8}{7} × 20 [/tex]

[On Simplification]

[tex] = \frac{160}{7} [/tex]

[On dividing]

= 22.85.....

[On approximating]

= 23 days (approx. )

Hence,

Jenny will take 23 days to read 20 books (Ans)

Question:-

If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?

Answer:-

22.85714 or 23 days

Explanation:-

[tex]GIVEN,[/tex]

Number of books Jenny can read in 8 days = 7

[tex]NOW,[/tex]

Number of days taken by Jenny to read 1 book = [tex] \frac{8}{7} [/tex]

Number of days taken by her to read 20 books =

→ [tex]20 \times \frac{8}{7} [/tex]

→ [tex] \frac{160}{7} [/tex]

22.85714 or 23 days

Each side of the triangle is represented by an expression. Find the value of x is the triangle has a perimeter of 73.

Answers

Answer:

Step-by-step explanation:

The answer is 27

The value of x is 4.

What is the perimeter of a triangle?

The perimeter of a polygon is the total length of the boundary. For a triangle, we can find it by adding the lengths of its three sides. We can find the length of the fencing required for a triangular park by finding the perimeter of the triangle.

The triangle has a perimeter of 73.

[tex]7x-2+3x+9+8x-6=73\\18x+1=73\\18x=72\\x=4[/tex]

Learn more about triangles here https://brainly.com/question/2938476

#SPJ2


Serious help needed what is the domain and range

Answers

Answer:

domain: all real numbersrange: -1 ≤ y ≤ 5   or   -1 ≤ y < ∞

Step-by-step explanation:

The arrows on the ends of the graph mean the graph extends indefinitely left and right. The domain is the horizontal extent of the graph, so it extends from -∞ to +∞, all real numbers.

__

The upward slant of the graph at the ends is ambiguous regarding the vertical extent of the graph. It could mean either of ...

the graph oscillates indefinitely between the values -1 and +5, orthe graph continues upward toward +∞

We expect the latter case would be drawn with the ends of the arrows above the peak value shown. However, oscillation tends to involve a certain symmetry, and the graph has no symmetry about the local minimum points. In short the usual clues to the vertical extent are missing. Your guess is as good as mine.

The range could be [-1, 5], or it could be [-1, ∞). We cannot tell from this graph.

_____

Additional comment

The shape of the graph does not seem to match that of a 4th-degree polynomial, so we're not at all certain what sort of function is being plotted here. (A 4th-degree polynomial gets steeper beyond the outside zeros, rather than flatter, as shown here.) A couple of different functions with the approximate characteristics shown are graphed in the attachment.

is y=3x^2+2 a linear function

Answers

Answer: No!

Step-by-step explanation: This is a parabola. The graph for this function is not straight. We can also tell this is not a linear function because the degree of the function is 2.

Hope this helps :)

No.

y = 3x² + 2 has a degree of 2. So, it'll not make a graph which is a straight line. It's NOT a linear function. Linear functions have a degree of 1 or 0.

This is a quadratic polynomial (degree = 2) & when drawn on a graph, it'll make a parabola.

_____

Hope it helps ⚜

X-Y=9 and 2X+5Y=4 solve by substitution

Answers

Answer:

(7,-2)

Step-by-step explanation:

Answer:

(7, - 2 )

Step-by-step explanation:

x - y = 9 ( add y to both sides )

x = y + 9 → (1)

2x + 5y = 4 → (2)

Substitute x = y + 9 into (2)

2(y + 9) + 5y = 4 ← distribute parenthesis and simplify left side

2y + 18 + 5y = 4

7y + 18 = 4 ( subtract 18 from both sides )

7y = - 14 ( divide both sides by 7 )

y = - 2

Substitute y = - 2 into (1)

x = - 2 + 9 = 7

solution is (7, - 2 )

equivalent expression for: 3(1-7)

Answers

Answer:

Multiply the number in the parantheses by 3. Then subtract them.

Step-by-step explanation:

Hellp! To get points!

Answers

Answer:

your answer would be B.

Step-by-step explanation:

for this fraction equation all you need to do is round the 2 up to a 8 putting it at 4/8, round the 4 up to a 8 putting it at 2/8, and keep the 1/8 the same. then add them all together and you would get 7/8

Answer:

b 7/8

Step-by-step explanation:

your gonna change everything to eights

Write an equation of the line that passes through the points (3,6) and (4,9)

Answers

Answer:

y=3x-3

Step-by-step explanation:

slope = change in y/change in x

slope = 3/1 = 3

y-intercept = y value when x=0

 go 3u left, 3x3 = 9 so 9u down

 (0,-3)

slope = m = 3

y-int = b = -3

y=mx+b

y=3x-3

The 13th arithmetic sequence of whose common difference is d=7 and first term is A1=3

Answers

Answer:

87

Step-by-step explanation:

difference = 7

A1 = 3

so let's imagine this arithmetic sequence as

3, 10, 17, 24 etc....

mathematically the sequence can be described as

An = a1 + (n - 1) d

A13 = 3 + (13 - 1) 7 = 3 + 12*7 = 87

Can u please help answer 9 and 10 please

Answers

Answer:

  9. 23

  10. D

Step-by-step explanation:

9.

In order to make the equation true, the blank must contain 23.

That statement, however, is an example of the commutative property of addition. The symmetric property says if a = b, then b = a.

__

10.

Your calculator can tell you which expressions are equivalent to 25·18. Clearly, the sum in choice D is not a product that will be equivalent.

Sally's Stuffed Animal Company charges $0.75 per pound to ship stuffed animals. Part A: Write an equation to determine the total cost, c, to ship p pounds of stuffed animals. Use your equation to determine the cost of shipping 2 pounds of stuffed animals. (6 points) Part B: If the company reduces the cost to ship the stuffed animals by $0.05 per pound, write an equation to determine the total cost, c, to ship p pounds of stuffed animals with the reduced cost. (4 points)

Answers

Part A :

Rate of shipping per pound of stuffed animal = $0.75

Therefore total cost for P pounds = C = 0.75 P

Cost of shipping 2 pounds of stuffed animals = 0.75*2 = $1.50

Part B :

If the cost is reduced by $0.05 per pound then the reduced cost per pound = 0.75 - 0.05 = $0.70

Therefore total reduced cost for P pounds = C = 0.70 P

Answer:

i think the person on top of me is correct :)

Step-by-step explanation:

What type of triangle is this?
5
7
8
acute
obtuse

Answers

Answer:

Acute

Step-by-step explanation:

The triangle is is acute

I need to find the missing angles

Answers

Can you explain well

I need help with this is dont really understand it

Answers

Answer:

y = 10x + 6.

Step-by-step explanation:

y = mx + c

Here  the slope m = 10 and c = 6 ( the y-intercept)

It's 6 because the point (0, 6) lies on the y-axis (where x = 0).

Please help me, you can see the parabola down below. Please.

Determine the equation of the parabola in Vertex Form. Work must be shown.

Answers

Answer:

let me check....

Step-by-step explanation:

how many 2 digit combos can you make with numbers 1, 2, and 3?

Answers

Answer:

9 i believe

Step-by-step explanation:

11

12

13

21

22

23

31

32

33

8[tex]x^-{4/3}[/tex]

Answers

Answer:

6

Step-by-step explanation:

8x

[tex] 8x - \frac{4}{3} = 0 \\ 8x = \frac{4}{3} \\ 24x = 4 \\ x = 6[/tex]

Mrs. Palmer's famous peanut butter cookies call for 1 cup of peanut butter for every
1
2
of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?

Answers

Answer:

2 cups

Step-by-step explanation:

if she uses 1/2 cup of oil per 1 cup of peanut butter

then she should use the ratio PB(peanut butter)= 2O(oil)

so if oil is 1 then PB must be 2 cups

c. The height h of a diver over the water is modeled by the equation h = 5t^2 + 8t + 3 where h denotes the height of the diver over the water (in meters) and t is time measured in seconds. Rewrite this equation, finding t in terms of h.

Answers

Answer:

steps below

Step-by-step explanation:

h = 5t² + 8t + 3

5t² + 8t + (3-h) = 0

** ax²+bx+c=0       x= (-b±√b²-4ac)/2a

[tex]t=\frac{-8+\sqrt{64-4*5*(3-h)} }{10\\}\\ =\frac{-8+\sqrt{4+20h} }{10}\\ = -0.8 +0.2* \sqrt{1+5h}[/tex]   ..... h≥3 to make t≥0

Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.

Answers

Both still have the same profit. $2 for sandwiches and $3 for wraps. The only reason why there is a difference in the total amount is the change in number of sandwich or wrap sold in a given month. Therefore, next month's total sale is higher than last month's total sale making it safe to assume that the sale of sandwich or wrap is higher than last month's sale.

{hope this helps}

Solve the inequality:
12+x≥3(x-6)​

Answers

Hello there! :)

The first step is to use the Distributive Property.

It states that

a(b+c)=ab+ac

Let's distribute 3, using this property:

3(x-6)=3x-18

Now, our inequality looks like so:

12+x≤3x-18

The next step is to move the variables to the left, using the opposite operation:

12+x-3x≤-18

12-2x≤-18

Now, move all the numbers to the right, using the opposite operation:

-2x≤-18-12

-2x≤-30

Divide both sides by -2 to isolate x.

Remember that when we divide by a negative variable, we change the inequality sign:

x≥15

Therefore, x≥15

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

Which expression is equivalent to 10 ( – 5 x + 3) – 2x

Answers

Step-by-step explanation:

well, we just do the multiplication and simplify by combining terms with the same base :

10(-5x + 3) - 2x = -50x + 30 - 2x = -52x + 30

Answer:-52x + 30 is the evaluated expression.Step-by-step explanation:10(-5x + 3) - 2x=> -50x + 30 - 2x=> -52x + 30Conclusion:

Hence, -52x + 30 is the evaluated expression.

Hoped this helped.

WILL GIVE BRAINLIEST!! ILL GIVE LINK IF YOU NEED IT

Answers

Answer: As x increases, the slope of the graph increases.

I will Need the link

Help with number 3 please

Answers

Answer:

A biconditional statement is a combination of a conditional statement Its converse written in the if and only form

Calculate 18.75 x 11.54 a) exact value b. corrected to 1 d.p c. corrected to 2 s.f

Answers

Step-by-step explanation:

18.75 x 11.54

= 216.375

216.375 is the correct answer

If y varies directly as x, and y = 12 when x = 72, then what is the value of x when y = 3 ?

18

2

1 half

1
6

Answers

Answer:

x = 18

Step-by-step explanation:

difference between y = 12, x=72 is 6

so if y = 3 then multiply 3×6 = 18

Answer:

18

Step-by-step explanation:

can anybody help me with this?​

Answers

Answer:

a) 3.6 × 10²

Time = distance / speed

So time = 1.08 × 10⁸ / 3 × 10⁸

= 1.08 × 10¹¹ / 3 × 10⁸ ( converted 10⁸ km to meter )

= 1.08 × 10³ / 3

= 0.36 × 10³

. = 3.6 × 10²

Time = 3.6 × 10²

x−6y=−13
7x+2y=41
find the x and y value

Answers

Answer:

X=5

Y=3

(5,3)

Step-by-step explanation:

Solve using substitution

Other Questions
Jeremy brought a sandwich and a drink that cost him $7. His drink cost $1.75. Solve the equation 7=s + 1.75 to find s, the cost of Jeremys sandwich. I need helpppoppppppppppppp What health concern might roquefort blue cheese help alleviate? what is an example of imagery in the passage? One method used by some analysts to estimate the future value of a stock is the dividend growth model. This model would probably be most useful in the case of A) a small-cap stock B) a AAA corporate bond C) a preferred stock D) a large-cap stock What are the three layers that make up the body of a Cnidarian?A. endoderm, mesoderm, ectodermB. endoderm, mesoglea, ectodermC. ectoderm, mesoderm, mesogleaD. endoderm, mesoglea, epidermis 14x-21yfactorise this equation Do you believe its important for humans to continue to explore space? Which text features are included in this text? Check all that apply. A title a subtitle headings a callout illustrations a sidebar. what is an equation in slope-intercept form for the line (-5, 2) and (5,-3)? A 32 year old female presents to her primary care physician complaining of frontal headaches for over one week. She states the location of her pain to be on top of her eyebrows with radiation to the top of her head. She states she has been more fatigued than usual and has some minor nose congestion. She denies any visual disturbances, nausea, vomiting, cough or fever. You should: a) Send her to the emergency room for emergent evaluation as she may be having a brain bleedb) Advise rest and fluids with an anti-inflammatory such as Advil and reassure her she most likely has a viral sinus infectionc) Do nothingd) Send her for a CT of the head and give steroids Conner earns 24$ working every 1.5 12 blank Can someone plz help me? After moving down a group in the periodic table, the number of valence electrons Correct one mistake in each sentence. Snow on the ground prevents polar climate systems from gaining heat by what mechanism?Question 7 options:Heating by greenhouse gasesSnow reflecting solar radiationHeat spread from the equatorRelease of heat from Earth's core Need Some Photography help which of these is a form of narrative From what you read in the Content, who is the college student that wanted to createa tutoring app?VickyXavierIsaiahLisa Why do you want to be a bank manager?