is it 6, 9, 18, or 8?

Given:

The statement is

[tex](1+i)^2=2i[/tex]

To prove:

The given statement [tex](1+i)^2=2i[/tex].

Solution:

We have,

[tex](1+i)^2=2i[/tex]

Taking LHS, we get

[tex]LHS=(1+i)^2[/tex]

[tex]LHS=(1)^2+2(1)(i)+(i)^2[/tex]         [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]LHS=1+2i+(-1)[/tex]         [tex][\because i^2=-1][/tex]

On further simplification, we get

[tex]LHS=1+2i-1[/tex]

[tex]LHS=2i[/tex]

[tex]LHS=RHS[/tex]

Hence proved.

Answer:

1. The breadth is 4 cm

2. The perimeter is 32 cm

Step-by-step explanation:

From the question given above, the following data were obtained:

Length (L) = 12 cm

Area (A) = 48 cm²

1. Determination of the breadth.

Length (L) = 12 cm

Area (A) = 48 cm²

Breadth (B) =?

A = L × B

48 = 12 × B

Divide both side by 12

B = 48 / 12

B = 4 cm

Thus, the breadth is 4 cm.

2. Determination of the perimeter

Length (L) = 12 cm

Breadth (B) = 4 cm

Perimeter (P) =?

P = 2(L + B)

P = 2(12 + 4)

P = 2(16)

P = 32 cm

Thus, the perimeter of the rectangle is 32 cm

Answer:

1/28 of a cup of sugar would be in each glass

Step-by-step explanation:

1/7 x 4

1/7 x 1/4      

1/28

Answer:

[tex](2a -b)^2[/tex]

Step-by-step explanation:

Answer:

The given exponential functions f(x) and g(x) will be equal for the value of x as 4.1466.

Step-by-step explanation:

We need to give exponential function to the given constraints.

since f(x) is a decreasing function so

f(x) = [tex]a(1-r)^x[/tex]

where

a = Initial value

r = rate at which function is decreasing

as we are given the values of a and r such as a = 800 and r = 12%

upon substituting these values in the equation we get

f(x) = [tex]800(1-0.12)^x[/tex]

      = [tex]800(0.88)^x[/tex]

similarly we will do for g(x) but the only difference in f(x) and g(x) will be that f(x) in a decreasing exponential function whereas g(x)  is an increasing function.

g(x) = [tex]a(1-r)^x[/tex]

where a is initial value and r is the rate at which the function is increasing so upon substituting these values we get.

g(x) = [tex]20(1+0.12)^x[/tex] = [tex]20(1.12)^x[/tex]

Now,

we need to find the value of x for which f(x) and g(x) will be equal.

so  

[tex]800 (0.88)^x = 20(1.12)^x[/tex]

[tex]40(0.88)^x = (1.12)^x[/tex]

x will be approximately 4.1466

Therefore the given exponential functions f(x) and g(x) will be equal for the value of x as 4.1466.

Answer

(3x-3)

Step-by-step explanation:

Answer:

The answer would be 22x^2-x+17 so the answer is C.

Step-by-step explanation:

I'm pretty sure this is correct. Good luck lol

Answer:

?

Step-by-step explanation:

?

Answer:

5/144

Step-by-step explanation:

Answer:

B.     A = {G2, G4, R2, R4}

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Formula for area of a triangke is;

A = ½bh

Where;

b is base

h is height

From the triangle diagram given;

b = x + 6

h = x

Thus;

A = ½(x + 6)x

A = ½x² + 3x

Now we are told that the area is 108 m², Thus;

½x² + 3x = 108

Multiply through by 2 to get;

x² + 6x = 216

x² + 6x - 216 = 0

Using quadratic formula, we arrive at;

x = -18 or 12

x can't be negative, thus; x = 12

Answer:

x=8.16

Step-by-step explanation:

x=the money before

2x=doubled

3x=24.50

x=8.16

Answer:

The answer would be...

Step-by-step explanation:

$12.25 Because if you divide $24.50 by 2 then you would get the amount of money William had before he got doubled which would be $12.25.

Hope this helped

:)

Answer:

b^3 + c^2

Step-by-step explanation:

23

.

.

.

.

.

.

.

I hope it's helpful for you dude

Answer:23

Step-by-step explanation:

Answer:

48.75

Step-by-step explanation:

The salesmen makes a commission of 3.25%. So to get the percent into a usable form for this take 3.25 and divided by 100. You get 0.0325.

Now you take the 0.0325 and mutliply it by the 1500. This gives you 48.75

Answer:

A: 6

B: 16

C: 2

D: -12

Step-by-step explanation:

They are asking you to multiply the equations:

(3x^2 + 2x - 3)(2x + 4)

Distribute and you should get:

6x^3 + 16x^2 + 2x - 12

The Coefficients A,B,C, and D are 6, 16, 2, and -12.

Answer:

x=2

Step-by-step explanation:

Answer: Y=1/3   X=2

Step-by-step explanation: Have a brilliant day mate- Lily (^_^)

Plzz mark brainliest if this helped you.

Answer:

3.707, 3.71, 3.8, 3.809, 3.83, 3.83, 3.89

Step-by-step explanation:

3.707, 3.71, 3.8, 3.809, 3.83, 3.83, 3.89

Answer:

c

Step-by-step explanation:

because im smart :)

Answer:

I'm sorry that your frog is dead, at least now we can fry his legs ~~tasting like chicken ~~~~~~flavor ain't missing

Answer:

false

Step-by-step explanation:

you have to order them from least to greatest in order to find the answer

Answer:

[tex]y=3x+5[/tex]

Step-by-step explanation:

Parallel lines have the same slope.

This means that we would only have to change the y-intercept to get our new line.

We are asked to write an equation of a parallel line with the y-intercept of five.

Rewrite the infomation to create the new equation. Note that parrarell lines have the same slope.

[tex]y = 3x + 2\rightarrow\boxed{y=3x+5}[/tex]

Hope this helps.

Answer:

should be 107

Step-by-step explanation:

Answer:

107

Step-by-step explanation:

Since x is the 107 angle on the opposite side, it is the same

Answer:

I would say it's the first one correct me if I'm wrong but I hope I helped

Answer:

Addition Property of Equality

Step-by-step explanation:

Hope this helps.

Answer:

18 girls

Step-by-step explanation:

6:9

6+9 = 15

we multiply each part of the ratio by 3

6*3 = 18 girls

9*3 = 27 boys

Answer:

a+a

Step-by-step explanation:

a+a

Answer:

89.1

Step-by-step explanation:

Mass= Density *Volume

9.86 g/cm3 *150 cm3 =1479g

1479 g to kilograms

1479g= x

1000g = 1 kg

x = 1479 g / 1000 x = 1.479 kg.

Answer:

55

Step-by-step explanation:

Answer:

8:12

Step-by-step