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

Answer:

Step-by-step explanation:

#a

[tex]\\ \sf{:}\dashrightarrow -2(-4.5)=9.0[/tex]

#b

[tex]\\ \sf{:}\dashrightarrow (-8.7)(-10)=8.7[/tex]

#c

[tex]\\ \sf{:}\dashrightarrow (-7)(-2)=14[/tex]

#d

[tex]\\ \sf{:}\dashrightarrow (-9)(-10)=90[/tex]

Answer:

-4

Step-by-step explanation:

let the number be x

6x+(x+6)=-30-2x

7x+6=-30-2x

9x=-36

x=-4

Answer: there you go

Step-by-step explanation:

Answer:

50h+25.5=154

Step-by-step explanation:

Answer:

0.5%

Step-by-step explanation:

The equilibrium constant of the reaction is 0.0030.

The equation of the reaction is given as;

N2(g) + 3H2(g) ⇆ 2NH3 (g)

We have the following information at equilibrium;

[NH3] = 0.105 M

[N2] = 1.1 M

[H2] = 1.50 M

Hence, we can calculate the equilibrium constant using the relation;

K = [NH3]^2/ [N2]  [H2]^3

Substituting values;

K = [0.105]^2/[ 1.1] [1.50]^3

K =0.011025 /3.7125

K= 0.0030

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10101₂ = 1×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰

10101₂ = 16 + 0 + 4 + 0 + 1

10101₂ = 21

Here see below

[tex]\\ \sf\Rrightarrow (10101)_2[/tex]

[tex]\\ \sf\Rrightarrow 1\times 2^0+0\times 2^1+1\times 2^2+0\times 2^3+1\times 2^4[/tex]

[tex]\\ \sf\Rrightarrow 1+4+16[/tex]

[tex]\\ \sf\Rrightarrow (21)_{10}[/tex]

Answer:

Step-by-step explanation:

Answer:

Perhaps 270 mm^2, if it is a box.

Step-by-step explanation:

What shape is this?  A box?

If a box:

There are 6 faces:

1.   2 ends:  7mm x 4mm  = 28 mm^2/end

2.  2 sides:  10mm x 7mm  = 70 mm^2/side

3.   top and bottom:  10mm x 4 mm = 40 mm^2/each

====

Totals:

1.    56 mm^2

2.  140 mm^2

3.   80 mm^2

Total  270 mm^2

Here are ur answer.......

Answer:

Step-by-step explanation:

Using PRT/100, let's find the interest.

Conclusion:

Therefore, the interest plus principle is 2,000 + 800, which is $2,800.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

4/5

Step-by-step explanation:

Sin = Opposite / Hypotenuse

Note that hypotenuse = longest side

We want to find sinФ

The opposite side length of angle "Ф" has a length of 8 and the longest side or hypotenuse has a length of 10

So sinФ would equal 8/10 which can be simplified to 4/5

Answer:

= 24/7

Step-by-step explanation:

1. Find common denominator

2. Combine fractions with common denominator

3. Re-order terms so constants are on the left

137 - 16X = Y

Since Lorraine is picking blackberries in her backyard at a rate of 15 berries per minute, and after 16 minutes of picking, there are still 137 blackberries left to pick, to determine an equation that models how many berries are left (y) after x minutes of picking, the following calculation must be performed:

137 - 16X = Y

Thus, for example, after 5 minutes the calculation would be as follows:

Learn more about maths in https://brainly.com/question/25989509

Answer:

1/3

Step-by-step explanation:

the y increases by 3 in the line while at the same time x is increased by 1. x/y for slope, so itd be 1/3

Step-by-step explanation:

you can't find that out ?

either simplify the expressions and then insert the values for x, or simply insert the values for x and see.

6 - 5x < 27 + 5x < x + 35

6 < 27 + 10x < 6x + 35

-21 < 10x < 6x + 8

it is then

-21 < 10x

-2.1 < x

and

10x < 6x + 8

4x < 8

x < 2

-2.1 < x < 2

therefore, B is the right answer.

-2, -1, 0, 1

-3 would be too small, and 2 is blocked by the right "<" sign.

Answer: $8 21 quarters

Step-by-step explanation:

20 quarters is $5 plus another is $5.25

8 dollars is $8 plus the $5.25 = $13.25

Have a nice day, and if you could be so kind as to give me a brainliest

Answer:

I think the correct answer is D since the arrows go infinite ways. Let me know if im right. :)

Step-by-step explanation:

A (1,3) is a solution to the system of inequalities

Answer:

The first one:

Equation n+(n+1) +(n+2)=36

3n+3=36

the numbers are 11, 12,13

Step-by-step explanation:

So if you plug ll for n you get 36

So if you plug 12 in for in u get 39

Then in you plug 13 in for n u get 41

I hoped that helped

Answer: First option

The numbers are 11, 12, 13

11+12+13 = 36

===============================

Explanation:

Here's one way to solve for n

n+(n+1)+(n+2) = 36

3n+3 = 36

3n = 36-3

3n = 33

n = 33/3

n = 11

That leads to n+1 = 11+1 = 12 and n+2 = 11+2 = 13

So the three numbers are 11,12,13

11+12+13 = 23+13 = 36 which confirms the answer

-------------

For the second option, it's not clear how the student got n = 15. If I had to guess, they probably divided both sides by 3, then added 3 to both sides.

As a quick check, 15+16+17 = 31+17 = 48 which doesn't match up with the 36.

Or you could note that the units digits add to 5+6+7 = 11+7 = 18. That 8 doesn't match with the 6 in 36. So this is an even quicker way to rule out the second option.

Answer:

4) a₁₅ = 128

5) B. [tex]a_n=a_{n-1}+6[/tex]

Step-by-step explanation:

4)

This is an arithmetic sequence, where all terms have a common difference:

[tex]a_n=a_1+(n-1)d[/tex]

Here, the common difference is 9.

[tex]11-2=9\\20-11=9[/tex]

Use that to write the equation and solve for a₁₅:

[tex]a_n=2+(n-1)9\\\\a_{15}=2+(15-1)9\\a_{15}=2+(14)9\\a_{15}=2+126\\a_{15}=128[/tex]

5)

This is also an arithmetic sequence, but it is a recursive arithmetic sequence in the form of:

[tex]a_n=a_{n-1}+d[/tex]

This simply states that each term is d more than the term before it.

Here, the common difference is 6:

[tex]2--4=6\\8-2=6\\14-8=6[/tex]

And the equation for this is B. [tex]a_n=a_{n-1}+6[/tex]

Answer:

7,15,20

Step-by-step explanation:

Triangle side rule : The sum of the two shorter sides must be greater than the length of the largest side.

7 , 15 and 20

7 + 15 must be greater than 20 in order for 7,15 and 20 to be sides of a triangle

7 + 15 = 22

22 > 20 is true so this might be the answer but lets check the other answer choices just in case.

( we do this same process to the other answer choices )

11 , 22 and 35

11 + 22 must be greater than 35 in order for these to be side lengths of a triangle

11 + 22 = 33

33 is not greater than 35 therefore these sides lengths can not represent sides of a triangle

7, 16 and 23

7 + 16 must be greater than 23

7 + 16 = 23

23 > 23 , this is not true so this can't be the answer.

5 + 17 must be greater than 22

5 + 17 = 22

22 > 22 this is not true so this can't be the answer.

The answer is 7,15,20

The pre-sale price of the wedding gown is £224.

A reduction decreases the price of an item. As a result of the reduction, the wedding gown would be sold cheaper. The wedding gown would cost  pay 75%(100 - 25%) of the pre-sale price.

This equation can be used to determine the pre-sale price of the wedding gown:  discounted price / 75%

£168  / 0.75 = $224

To learn more about how to determine the price of an item, please check: brainly.com/question/25717996

Answer:

3.25

Step-by-step explanation:

13÷4=3.25

Everyone gets 3.25 kg of chocolate

Answer:

3 1/4 kilograms

Step-by-step explanation:

13 ÷ 4 = 3.25 = 3 1/4

Answer:

64

Step-by-step explanation:

8^9/8^7

Subtract the 9 and 7 which equals 2

Which is 8^2

8^2 is 64

Thus the answer is 64

Hope this helps!

Answer:

  x = -2, x = 2

Step-by-step explanation:

The denominator factors as ...

  x^2 -4 = (x -2)(x +2)

The numerator has no factors that cancel either of these, so the function will have vertical asymptotes where the denominator is zero: at x = -2 and x = 2.

Answer:

Step-by-step explanation:

Dimensions given:

A small cube has side of 1/4 ft

Find the number of small cubes can fit in each dimension of the prism.

Length

Width

Height

Part A

Number of small cubes would be:

Part B

Each small cube has volume:

The volume of the prism in terms of small cubes is 180 as we found above.

The volume in terms of unit cube:

Multiply length of track by number of times run:

8 x 400 = 3,200 meters

1 km = 1000 meters

3200 meters / 1000 = 3.2 kilometers

Answer: 3.2 kilometers