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3 years ago

Calculate the area of the square shown below (HARD)

Mathematics

1 answer:

sergey [27]3 years ago

7 0

Check the picture below.

recall that in a square, all sides are equal, so if we make b = a, then we get that for one side, also recall that the area of a rectangle is length*width, so in this case,

$\bf \stackrel{\textit{area of the square}}{\stackrel{length}{5\sqrt{2}}\cdot \stackrel{width}{5\sqrt{2}}}\implies 25(\sqrt{2})^2\implies 25\cdot 2\implies 50$

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Gregory knows that Triangle A B C is reflected onto Triangle A prime B prime C prime. Which statement about the figures is true?

ziro4ka [17]

Answer: if Gregory draws the segment with endpoints A and A’, then the midpoint will lie on the line of reflection.

Explanation:

Given that a triangle ABC is reflected in triangle A'B'C'

Here reflection is done on a line

If you imagine the line as a mirror then ABC will have image on the mirror line as A'B'C'

Recall that in a mirror the object and image would be equidistant from the mirror and also the line joining the image and object would be perpendicular to the mirror

But note that corresponding images will only be perpendicular bisector to the line

So A and A' only will be corresponding so AA' will have mid point on line

Option 1 is right

5 0

3 years ago

if the diagonals of a quadrilateral biscects each other, then the quadrilateral is a parallelogram. true or false

Irina-Kira [14]

Answer:

true

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Suppose $12000 is invested into a savings account for 23 years. The interest on the account is conpounded continuously. How much

KATRIN_1 [288]

I'm guessing to probably divide $45,000 by 23 and then multiply that answer by $12,000. I hope this helps

5 0

3 years ago

What is (2-2i√3)4 equivalent to?

maxonik [38]

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

<h3>What are complex numbers?</h3>

Complex numbers are numbers of the form z = x + iy

<h3>a. Complex numbers in polar form</h3>

Complex numbers in polar form z = r(cosθ + isinθ) where

r = √(x² + y²) and
θ = tan⁻¹(y/x)

Given that z = (2 - 2i√3)⁴ =

So,

x = 2 and
y = -2√3

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

<h3>Powers of complex numbers</h3>

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

<h3>b. Complex numbers in rectangular form</h3>

The complex number z = r(cosθ + isinθ) in rectangular form is z = x + iy where

x = rcosθ and
y = rsinθ

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y = rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

Learn more about complex numbers in polar form here:

brainly.com/question/9678010

#SPJ1

7 0

2 years ago

Ms.Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs sold this week. Ms.Kitts sold a total

Gre4nikov [31]

Number of CDs Kitts sold last week = x = 84

Number of CDs she sold this week = y = 26

Hope this helps :DD !!

6 0

3 years ago