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3 years ago

Complex numbers simplify square roots of negative numbers

Mathematics

2 answers:

sergey [27]3 years ago

8 0

Step-by-step explanation:

√-100

√-(10)²

√10²√-1

10i

0+10i

Bogdan [553]3 years ago

3 0

Lets do

$\\ \sf\longmapsto \sqrt{-100}$

$\\ \sf\longmapsto \sqrt{-(10)^2}$

$\\ \sf\longmapsto \sqrt{10^2}\sqrt{-1}$

$\\ \sf\longmapsto 10i$

Write in standard form

$\\ \sf\longmapsto 10i$

$\\ \sf\longmapsto \boxed{0}+\boxed{10}i$

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An ongoing promotion at a department store gives customers 20\%20%20, percent off the portion of their bill that is over \$100$1

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The equation best models the situation 100 + 0.8(x - 100) = 250.

The correct option is (D)

<h3>What is equation?</h3>

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The complete question is:

An ongoing promotion at a department store gives customers 20% off the portion of their bill that is over $100. Ruby's total bill at the department store after the promotion has been applied is $250. If x represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?

A. 0.2x + 100 = 250

B. 0.8x + 100 = 250

C. 100 + 0.2(x - 100) = 250

D. 100 + 0.8(x - 100) = 250

Given:

Department store gives 20 % off the portion of the bill that is over 100 dollars.

Total bill = 250

let x is the amount of money she would have spent without the promotion.

Then, cost after discount applies = 0.8 ( x - 100 ).

Hence, the equation is 100 + 0.8 (x - 100) = 250.

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2 years ago

The net of a rectangular prism is shown below. What is the total surface area of the rectangular prism represented by this net?

Finger [1]

Answer:

150.88 cm²

Step-by-step explanation:

A rectangular prism also known as cuboid is a three dimensional object with six rectangular faces and eight vertices. It is a prism because it has the same cross section along the length. It is called a rectangular prism because its cross section is rectangular.

The opposite faces of a rectangular prism are equal to each other.

The total surface area (TSA) of a rectangular prism is:

TSA = 2(wl + wh + lh)

where w is the width of the base, l is the length of the base and h is the height of the prism.

From the question, we can see that:

w = 5 cm, l = 7.4 cm and h = 3.1 cm. therefore:

TSA = 2(wl + wh + lh) = 2[(5 * 7.4) + (5 * 3.1) + (7.4 * 3.1)] = 2(37 + 15.5 + 22.94)

TSA = 2(75.44)

TSA = 150.88 cm²

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