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Anon25 [30]
3 years ago
10

Kellys bathroom is 6feet wide and 8 feet long. she will cover the floor with 4-inch square tiles. how many tiles does kelly need

?
Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
7 0
She need 432 tiles because 6 feet is 72 inches and 8 feet equals 96 inches so we divide 72 by 4 to get 18 and 96 by 4 to get 24 the since there are 18 rows of ties with each row containing 24 tiles we multiply 24 by 18 and get 432 which means she will need 432 4 inch tiles. i really hope this helps.
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Which of the following is not one of the 8th roots of unity?
Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1.  Since z=1=1+0\cdot i, then

Rez=1,\\ \\Im z=0

and

|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.

This gives you \varphi=0.

Thus,

z=1\cdot(\cos 0+i\sin 0).

2. The 8th roots can be calculated using following formula:

\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.

Now

at k=0,  z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;

at k=1,  z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};

at k=2,  z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;

at k=3,  z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};

at k=4,  z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;

at k=5,  z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};

at k=6,  z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;

at k=7,  z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};

The 8th roots are

\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.

Option C is icncorrect.

5 0
3 years ago
LC Motor Sales conducted a survey to find out why people who bought cars at the dealership did not use it for ongoing service. T
Alenkasestr [34]

Answer: D

Step-by-step explanation:

42+23+102+124+17+26 = 334 total responses

LC Motors charged too much = 102

102/334 = .305..

Move the decimal 2 places to the right = 30.5

Rounds to 31%

8 0
3 years ago
Tell whatever the ordered pair is a solution of the given system.
bagirrra123 [75]
1. No 2. Yes 3. No
I’m pretty sure
5 0
3 years ago
Jessie recently drove to visit her parents who live 240240 miles away. On her way there her average speed was 2525 miles per hou
dusya [7]

Answer:

The speed/rate to her parent's house is x = 75 mph

The speed/rate from her parent's house is y = 50 mph

Step-by-step explanation:

Given;

Distance to her parent's house = 240 miles

Total distance travelled (to and fro) = 240×2 = 480 miles

Total time taken t = 8 hours

On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weather)

Let x and y represent her speed to and from her parent's house respectively.

x = y+25 ......1

The time taken to her parent's house is;

time = distance/velocity

t1 = 240/x = 240/(y+25)

The time taken from her parent's house is;

time = distance/velocity

t2 = 240/y

Total time taken t = t1 +t2

t = 240/(y+25) + 240/y = 8

Solving for y ;

(240y + 240(y+25))/(y^2 +25y) = 8

Cross multiply;

240y + 240y+6000 = 8y^2 + 200y

480y +6000 = 8y^2 + 200y

8y^2 + 200y -480y -6000 = 0

8y^2 - 280y - 6000 = 0

Divide through by 8;

y^2 - 35y - 750 = 0

Solving the quadratic equation;

y = 50

or

y = -15

Velocity cannot be negative, so y = 50mph

From equation 1;

x = y+25

Substituting y =50

x = 50 + 25

x = 75 mph

The speed/rate to her parent's house is x = 75 mph

The speed/rate from her parent's house is y = 50 mph

3 0
3 years ago
If f(x)=-x+7 and g(x)=x-3 what is (f g)(4)
bogdanovich [222]

Answer:

fg(4) = 6

Step-by-step explanation:

f(x) = -x + 7

g(x) = x - 3

fg(x) = -(x-3) + 7

= -x + 3 + 7

fg(4) = -4 + 10

= 6

6 0
3 years ago
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