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stiks02 [169]
3 years ago
12

Simplify the expression 2+3i/4+3i Please help

Mathematics
1 answer:
rjkz [21]3 years ago
7 0

Answer:

17+6i

-----------

25

Step-by-step explanation:

2+3i

---------

4+3i


We want to multiply by the complex conjugate of the denominator

4+3i has a complex conjugate of 4-3i

2+3i             4-3i

--------- * --------------

4+3i           4-3i


Lets multiply the numerator

(2+3i) ( 4-3i)

2*4 +4*3i -3i*2 - 3i*3i =

8 +12i -6i - 9i^2

Remember i^2 = -1

8 +6i -9(-1)

17 +6i


Lets multiply the denominator

(4+3i) ( 4-3i)

4*4 +4*3i -3i*4 - 3i*3i =

16 +12i -12i - 9i^2

Remember i^2 = -1

16 -9(-1)

25

Putting numerator over denominator

17+6i

-----------

25

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Sally bought 124 sheets of stickers. Each sheet had 14 stickers. She gave away 204 stickers to her family and friends on Christm
frez [133]

Answer:

Sally has 1,532 stickers remaining.

Step-by-step explanation:

First, you have to determine the total amount of stickers Sally bought by multiplying the number of sheets she bought for the number of stickers in each sheet:

124*14=1,736

Now, you have to subtract the number of stickers Sally gave away to her family and friends from the total amount of stickers she bought:

1,736-204=1,532

According to this, the answer is that Sally has 1,532 stickers remaining.

6 0
3 years ago
The sides of the rectangle are in the ratio of 4:7. If its length is 31.5 in., find the width, the perimeter, and the area of th
AveGali [126]
Let \ell the length and w the width. By the ratio of the sides:

\dfrac{w}{\ell}=\dfrac{4}{7}\Longrightarrow \dfrac{w}{31.5}=\dfrac{4}{7}\Longrightarrow w=\dfrac{4\cdot31.5}{7}\Longrightarrow \boxed{w=18~in.}

Now, we'll find the perimeter p. We'll use the formula below:

p=2(\ell+w)\\\\
p=2(31.5+18)\\\\
p=2\cdot49.5\\\\
\boxed{p=99~in.}

The area of a rectangle is S=w\cdot\ell. Then:

S=w\cdot\ell\\\\
S=18\cdot31.5\\\\
\boxed{S=567~in.^2}
8 0
3 years ago
Read 2 more answers
X + 9x + 5 = 35 . Find value of x.
otez555 [7]

Answer:

x = 3

Step-by-step explanation:

x + 9x + 5 = 35

=> x + 9x = 35 - 5

=> x + 9x = 30

=> 10x = 30

=> x = 30/10

=> x = 3

8 0
3 years ago
Read 2 more answers
I AM CALLING ALL ACES, EXPERTS, SMARTY PANTS, ETC!!! :)) (MATH 50 POINTS)
8_murik_8 [283]

10. The volume of the triangular prism is V=A_{base}\cdot H=\dfrac{1}{2} height \cdot base\cdot H, then

V=\dfrac{1}{2} \cdot 4\cdot 3.5\cdot 3.3=23.1.

11. The volume of the triangular pyramid is V=\dfrac{1}{3}A_{base}\cdot H=\dfrac{1}{3}\cdot \dfrac{1}{2} height \cdot base\cdot H, then

V=\dfrac{1}{3}\cdot \dfrac{1}{2} \cdot 4\cdot 3.5\cdot 3.3=7.7.

12. They have common base (common triangle). y=7.7, r=23.1, then r:y=23.1:7.7=3.

13. See 10 and 11 for notations in symbols.

6 0
3 years ago
Please Solve for n and thank you
kotegsom [21]

To solve for n, you are trying to get n by itself on one side of the equation.

n/5 + 0.6 = 2

Subtract 0.6 on both sides

n/5 = 1.4

Multiply 5 on both sides to get n by itself

n = 7

8 0
3 years ago
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