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Sladkaya [172]
3 years ago
6

Select the correct answer.

Mathematics
1 answer:
stiks02 [169]3 years ago
8 0

Answer:

\dfrac{31}{2}+\dfrac{27}{2}i

Step-by-step explanation:

The given complex number is:

z=\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}

Firstly we can solve (2+3i)(4-7i)(1+i)

= 2(8)+2(-7i)+4(3i)+3i(-7i²)× (1+i)

= (16-14i+12i-21i²i)× (1+i)

Since, i² = -1

= (16-14i+12i-21(-1)i)× (1+i)

= (16-14i+12i+21)× (1+i)

= (29-2i)(1+i)

= 31+27i

Denominator : (1-i²)

= (1-(-1))

= 2

\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}=\dfrac{31+27i}{2}\\\\=\dfrac{31}{2}+\dfrac{27}{2}i

Hence, the correct answer is \dfrac{31}{2}+\dfrac{27}{2}i.

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Macie Andersen earns $9.75 an hour working at the local bookstore. Last week she worked 17 hours. This week she worked 25 hours.
vovangra [49]

Answer:

$407.50

Step-by-step explanation:

take 9.75 × 17=165.75

take 9.75 × 25=243.75

add 165.75 and 243.75=407.50

turn into dollars $407.50

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3 years ago
What is the surface area of the cylinder? Use three and fourteen-hundredths for pi and round to the nearest hundredth. Enter you
nadya68 [22]

Answer:

954.56 cm²

Step-by-step explanation:

Firstly i would calculate the circumference of the circles on top of the cylinders:

Circumference of circles = \pi d or 2\pi r

d = diameter

r = radius

I will use 2\pi r

circumference = 2 x 3.14 x 8 = 50.24 cm

⇒ This would help me to find out the surface area of the side of the cylinder

50.24 x 11 = 552.64 cm²

⇒ This is the surface are of the sides

Now we have to find the are of the two circles on the top and the bottom:

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200.96 x 2 = 401.92

Add all the values up:

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I hope this helps!

3 0
2 years ago
Solve the square root of 2x-5=x-4​
Varvara68 [4.7K]
Answer:

Simplifying
2x + -5 = x + -4

Reorder the terms:
-5 + 2x = x + -4

Reorder the terms:
-5 + 2x = -4 + x

Solving
-5 + 2x = -4 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.
-5 + 2x + -1x = -4 + x + -1x

Combine like terms: 2x + -1x = 1x
-5 + 1x = -4 + x + -1x

Combine like terms: x + -1x = 0
-5 + 1x = -4 + 0
-5 + 1x = -4

Add '5' to each side of the equation.
-5 + 5 + 1x = -4 + 5

Combine like terms: -5 + 5 = 0
0 + 1x = -4 + 5
1x = -4 + 5

Combine like terms: -4 + 5 = 1
1x = 1

Divide each side by '1'.
x = 1

Simplifying
x = 1
8 0
3 years ago
A newspaper used a chart resembling the one to the right to illustrate the rising amounts that a video rental company spends to
Dmitry [639]

This question is incomplete- no bar chart was included.  

The complete question was gotten from google.

A newspaper used a chart resembling the one to the right to illustrate the rising amounts that a video rental company spends to provide streaming content online. Is this the bar chart of a categorical​ variable, or is it a timeplot that uses bars to show the​ data?

Open the attachment below to see the bar chart'

Answer:

A newspaper used a chart resembling the one to the right to illustrate the rising amounts that a video rental company spends to provide streaming content online. Is this the bar chart of a categorical​ variable, or is it a time plot that uses bars to show the​ data? It is a time plot that uses bars to show the data; because it graphs a series of data recorded over time; presenting the values in sequential order.

Step-by-step explanation:

The chart used in the newspaper to illustrate the rising amounts that a video rental company spends to provide streaming content online is a time plot that uses bars to show the data; because it graphs a series of data recorded over time; presenting the values in sequential order.

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