Shivani had 3/10 of a pound of blueberries. Shivani let her friend Rosa eat 1/4 of the

Solve for x 6(x+5)-3(x-2)=12x+18

serg [7]

6x +30 -3x +6 =12x +18

3x +36 =12x +18

3x-12x = 18 -36

-9x = -18 | -1

9x =18

x= 18/9

x=2

7 0

3 years ago

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Express the fifth roots of unity in standard form a + bi. with 1 + 0i

marishachu [46]

Answer:

For K=0

$cos(\frac{0+2\pi 0}{5})+isin(\frac{0+2\pi 0}{5})\\cos(0)+isin(0)=1+i0$

For K=1:

$cos(\frac{0+2\pi 1}{5})+isin(\frac{0+2\pi 1}{5})\\cos(2\pi/5)+isin(2\pi/5)=0.3090+i0.9510$

For K=2:

$cos(\frac{0+2\pi 2}{5} )+isin(\frac{0+2\pi 2}{5} )\\cos(4\pi/5)+isin(4\pi/5)=-0.809+i0.587$

For K=3:

$cos(\frac{0+2\pi 3}{5} )+isin(\frac{0+2\pi 3}{5} )\\cos(6\pi/5)+isin(6\pi/5)=-0.809-i0.587$

For K=4:

$cos(\frac{0+2\pi 4}{5} )+isin(\frac{0+2\pi 4}{5} )\\cos(8\pi/5)+isin(8\pi/5)=0.3091-i0.9510$

Step-by-step explanation:

Fifth Root is given by:

$\sqrt[5]{z}=1+0i$

The above equation will become:

$z=(1+0i)^5$

It can be written as:

$z=[cos(0)+isin(0)]^5$

|z|=1,

According to De-moivre's Theorem:

$z=cos(\frac{0}{5})+isin(\frac{0}{5})\\ z=cos(0)+isin(0)$

Now, Fifth Roots of unity in standard form a + bi :

$\sqrt[5]{z}=[{cos(0+2\pi k)+isin(0+2\pi k)}]^{1/5}$

k=0,1,2,3,4

For K=0

$cos(\frac{0+2\pi 0}{5})+isin(\frac{0+2\pi 0}{5})\\cos(0)+isin(0)=1+i0$

For K=1:

$cos(\frac{0+2\pi 1}{5})+isin(\frac{0+2\pi 1}{5})\\cos(2\pi/5)+isin(2\pi/5)=0.3090+i0.9510$

For K=2:

$cos(\frac{0+2\pi 2}{5} )+isin(\frac{0+2\pi 2}{5} )\\cos(4\pi/5)+isin(4\pi/5)=-0.809+i0.587$

For K=3:

$cos(\frac{0+2\pi 3}{5} )+isin(\frac{0+2\pi 3}{5} )\\cos(6\pi/5)+isin(6\pi/5)=-0.809-i0.587$

For K=4:

$cos(\frac{0+2\pi 4}{5} )+isin(\frac{0+2\pi 4}{5} )\\cos(8\pi/5)+isin(8\pi/5)=0.3091-i0.9510$

6 0

3 years ago

The length of a rectangle picture frame is 2 centimeters more than twice it’s width. If the area of the frame is 364 square cent

sergeinik [125]

Answer:

Length:28 cm

Width: 13 cm

Step-by-step explanation:

Let

x ---> the length of a rectangle picture frame

y ---> the width of a rectangle picture frame

we know that

The area of a rectangle picture frame is equal to

$A=xy$

we have

$A=364\ cm^2$

so

$364=xy$ ----> equation A

The length of a rectangle picture frame is 2 centimeters more than twice it’s width

so

$x=2y+2$ ---> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (28,13)

see the attached figure

therefore

Length:28 cm

Width: 13 cm

5 0

3 years ago

which set of side lengths form a right side?a) 3ft,6ft,5ft b)50 in,48in,14in c)53m,48m,24m d)8cm,17cm,14cm

muminat

Answer:

Step-by-step explanation:

If a ≤ b < c form of a right side, then a² + b² = c²

a) 3ft, 6ft, 5ft

3² + 5² = 6²

9 + 25 = 36

34 = 36 FALSE

b) 50in, 48in, 14in

14² + 48² = 50²

196 + 2304 = 2500

2500 = 2500 CORRECT :)

c) 53m, 48m, 24m

24² + 48² = 53²

576 + 2304 = 2809

2880 = 2809 FALSE

d) 8cm, 17cm, 14cm

8² + 14² = 17²

64 + 196 = 289

260 = 289 FALSE

3 0

3 years ago

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Choose the formula for the volume of a rectangular box, V = lwh written in terms of w.

lilavasa [31]

The width of the rectangular box will be 8cm

Given that the formula for calculating the volume of a rectangular box is expressed as:

$V=lwh$

L is the length

w is the width

h is the height

Get the "value of "w

$V = lwh\\w=\frac{V}{lh}$

Given the following parameters

Length l = 3 cm

Volume V = 120cm³

Height = 5cm

Get the width of the box as shown:

$w=\frac{V}{lh}\\w=\frac{120}{3\times 5}\\w=\frac{120}{15}\\w= 8cm$

Hence the width of the rectangular box will be 8cm

Learn more here: brainly.com/question/20415942

4 0

3 years ago