Show that ( 1 +i )2 = 2i

Answer:

6) x^2+6x+8

7) x^2+3x-10

Step-by-step explanation:

Answer:

[tex]\frac{3^{n} }{3^{2(n-1)} }[/tex]

Step-by-step explanation:

3²⁻ⁿ is the simplification of  3ⁿ/9ⁿ⁻¹ in powers of 3.

An expression is combination of variables, numbers and operators.

The given expression is  3ⁿ/9ⁿ⁻¹

three power n divided by nine power n minus one.

To express to the power of 2, we have few properties of exponentials.

aˣ/aⁿ=aˣ⁻ⁿ

aˣ.aⁿ=aˣ⁺ⁿ

The given expression is

3ⁿ/9ⁿ⁻¹

3ⁿ/(3²)ⁿ⁻¹

3ⁿ/3²ⁿ⁻²

3ⁿ.3⁻²ⁿ⁺²

When bases are same then we will add the powers

3ⁿ⁻²ⁿ⁺²

3²⁻ⁿ

Hence 3²⁻ⁿ is the simplification of  3ⁿ/9ⁿ⁻¹ in powers of 3.

To learn more on Expressions click:

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Answer:

the third option

Step-by-step explanation:

x= 13

[tex] {y}^{2} = {13}^{2} + {13}^{2} \\ {y}^{2} = 338 \\ y = \sqrt{338} = 18.38 = 13 \sqrt{2} [/tex]

Answer:

h = 215/f

Step-by-step explanation:

Answer:

Step-by-step explanation:

The difference in the cost:

Tax on the difference:

Answer:

94

Step-by-step explanation:

If you add them all together, you get 266. You subtract that from 90*4= 360

you get 94

Answer:

2

Step-by-step explanation:

a = (-1 x 4) + 6

a = -4 + 6

a = 2

Answer:

n = 6

Step-by-step explanation:

To isolate n, subtract 1 from both sides:

4n + 1 = 25

4n = 24

Then divide by 4 on both sides:

4n = 24

n = 6

Hope this helped :)

Answer:

6

Step-by-step explanation:

4n+1= 25

or,4n= 25- 1

or,4n=24

or,n=24/4

so n= 6

Answer and Step-by-step explanation: Distributive Property describes how to solve expressions like a(b +c). According to the property, multiplying the sum of two or more numbers by a number will result in the same as multiplying each number and then add the products. For example:

                 11(2 + 4)

11(6) = 66                 22 + 44 = 66

So, for the expression that represents the area:

5.5(7.5 + x) = 41.25 + 5.5x

As the expression has non-numerical terms, the distributive property will be multiply each term and then add the products.

The expressio for area of a rectangular mural is 41.25 + 5.5x.

Answer:

30

Step-by-step explanation:

The angle for BOF is going to be 180.

So if the angle for COF is 150, then COB is going to be the complement angle.

This means it's 180 - 150 = 30.

Given:

The expression is

[tex]\dfrac{2}{a-2}-\dfrac{8}{a^2-4}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{2}{a-2}-\dfrac{8}{a^2-4}[/tex]

It can be written as

[tex]=\dfrac{2}{a-2}-\dfrac{8}{a^2-2^2}[/tex]

[tex]=\dfrac{2}{a-2}-\dfrac{8}{(a-2)(a+2)}[/tex]            [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

Taking LCM, we get

[tex]=\dfrac{2(a+2)-8}{(a-2)(a+2)}[/tex]

[tex]=\dfrac{2a+4-8}{(a-2)(a+2)}[/tex]

[tex]=\dfrac{2a-4}{(a-2)(a+2)}[/tex]

[tex]=\dfrac{2(a-2)}{(a-2)(a+2)}[/tex]

Cancel out the common factors.

[tex]=\dfrac{2}{a+2}[/tex]

Therefore, the simplified form of the given expression is [tex]\dfrac{2}{a+2}[/tex].

Answer:

81

Step-by-step explanation:

sq rt 81 = 8.94

8.94 is between 8 and 9

20-8.94 = 11.06   rounds to 11

Answer:x=6

Step-by-step explanation:

Answer: A

Step-by-step explanation:

For every 3 cups she need 7 cups of white paint.

answer a displays that with 3*2=6 and 7*2=14

Answer:

A

Step-by-step explanation:

I did the math

Answer: The distance between the ring and the coin = 15 units.

Step-by-step explanation:

Distance between two points (a,b) and (c,d) is given by :-

[tex]D=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Location of rine = (-2,-6)

Location of the coin = (7,6)

Then, the distance between the ring and the coin [tex]=\sqrt{(6-(-6))^2+(7-(-2))^2}[/tex]

[tex]=\sqrt{(12)^2+(9)^2}\\\\=\sqrt{144+81}\\\\=\sqrt{225}=15[/tex]

Hence, the distance between the ring and the coin = 15 units.

Step-by-step explanation:

First I had to find 60% of 220.

220 × .60 = 132.

132 people are in favor so I have to subtract that number from 220 to find how many people were against.

220-132 = 88

88 people were against changing the mascot.

Answer:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(0,2)

Equation Form:x=0, y=2

Answer:

(0,2)

Step-by-step explanation:

Multiply each equation by the value that makes the coefficients of  y  opposite.

3*2x-y=3*-2

Simplify

6x-3y=-6

Add the two equations

10x = 0

Divide both by 10 and simplify

x=0

Substitute x into the equations.

4*0+3y=6

3y=6

2

y=2

Answer: B=3+.11m

18.73=3+.11m

-3    -3

15.73=.11m

143=m

Step-by-step explanation:

Answer:

I believe it’s 65

Step-by-step explanation:

Not fully sure

Answer:

D 8m(4 + 7p)

Step-by-step explanation:

The GCF of 32 and 56 is 8.

m and mp have m in common, so you can factor out 8m.

32m + 56mp = 8m(4 + 7p)

Answer: D 8m(4 + 7p)

Answer: D, 8m(4+7p)

Step-by-step explanation:

8m times 4=32m

8m times 7p=56mp

Answer:

C. F(3) = 7

Step-by-step explanation:

You have to to substitute the value of the function into each equation.

So...

A. 7+4 does not equal 7

B. 3+4 does not equal 3

C. 3+4 DOES equal 7

Answer:

C

Step-by-step explanation:

Answer:

number 3 is B and number 4 is C

Step-by-step explanation:

7n-1

the 5th term of the sequence 4n+1

Answer:

5n -5

Step-by-step explanation:

7n +2 –(2n +7)

7n +2 -2n -7

5n -5

Answer:

The area is 120

The perimeter is 78

Step-by-step explanation:

To find area you have to multiply length x width.

(8x5)

To find perimeter you have to find the length of all the sides and add them

together. To find perimeter of a shape you do length x2 + width x2

(8x2 + 5x2)

Then you need to find the scale factor.

A scale factor of 3 is 3x the size of the original shape

Remember to press Thanks

Answer:

0.375

Step-by-step explanation:

3/8 = 0.375

Answer:

The correct explanation is option B;

B. ∠L ≅ ∠L  By Reflexive Prop. ≅.

Since [tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex], ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6

Step-by-step explanation:

The given parameters are;

[tex]\overline {LP}[/tex] = 5

[tex]\overline {NP}[/tex] = 10

[tex]\overline {LN}[/tex] = [tex]\overline {LP}[/tex] + [tex]\overline {NP}[/tex] = 15

[tex]\overline {OP}[/tex] = x - 3

[tex]\overline {MN}[/tex] = x + 1

A two column proof is presented as follows;

Statement    [tex]{}[/tex]      Reason

∠L ≅ ∠L     [tex]{}[/tex]        By Reflexive property of congruency

[tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex]     [tex]{}[/tex]     Given

∠LOP ≅ ∠LMN [tex]{}[/tex]  By the Corresponding angles Postulate

Therefore

ΔLOP ~ ΔLMN [tex]{}[/tex]  By AA similarity Postulate

Where we have that ΔLOP and ΔLMN, we get;

[tex]\overline {OP}[/tex]/[tex]\overline {MN}[/tex]  = [tex]\overline {LP}[/tex]/[tex]\overline {LN}[/tex] = 5/15 = 1/3

∴ (x - 3)/(x + 1) = 1/3

3·(x - 3) = 1·(x + 1)

3·x - 9 = x + 1

3·x - x = 1 + 9 = 10

2·x = 10

x = 10/2 = 5

x = 5

[tex]\overline {OP}[/tex] = (x - 3) = 5 - 3 = 2

[tex]\overline {OP}[/tex] = 2

[tex]\overline {MN}[/tex] = x + 1 = 5 + 1 = 6

[tex]\overline {MN}[/tex] =  6

Therefore, the correct option is ∠L ≅ ∠L  By Reflexive Prop. ≅.

Since [tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex], ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.

Answer:

67,600 possible outcomes

Step-by-step explanation:

In total, it's a four digit password.

For the first digit, which is a letter, there are 26 possibilities. The same goes for the second digit, so first multiply 26 x 26 (because that's the number of possibilities for the first two digits alone).

! if the letters have to be different then it would be 26 x 25 because there's one less letter for the second digit.

Next, 2 one digit numbers. There are 10 individual digits: 0,1,2,3,4,5,6,7,8,9, so after 26 x 26 x 10 x 10 for the total number of possibilities. If the numbers have to be different (and the letters too) then it'd be 26 x 25 x 10 x 9

so 26 x 26 x 10 x 10 = 67,600

hope this helps!