Austen needs to buy a bathroom mirror that is 2 feet wide and 3 feet long. If the mirror
sells for $5.00 per square foot, what will the total cost of the mirror be?

Answer:

Hello! I know I am late but here is the answer for anyone else who might need it.

D. 1/2-i√3/2

Step-by-step explanation:

I got it right on edge. Hope this helps!

The value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].

What is binomial theorem?

The expression of the form (a+b)^n is expand by binomial theorem.

The expansion is [tex](a+b)^{n}=\sum_{r=0}^{n}{ }^{n} C_{r} a^{n-r} b^{r}[/tex].

Use a=1/2 and b=[tex]b=\frac{i\sqrt{3} }{2}[/tex] into the expansion of binomial.

[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\sum_{k=0}^{5}\left(\begin{array}{l}5 \\k\end{array}\right)\left(\frac{1}{2}\right)^{5-k}\left(\frac{\sqrt{3} i}{2}\right)^{k}[/tex]

When k=0 then, [tex]\left(\begin{array}{l}5 \\0\end{array}\right)\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{5 !}{(5-0) ! 0 !}\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{1}{32}[/tex]

When k=1 then, [tex]\left(\begin{array}{l}5 \\1\end{array}\right)\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 !}{(5-1) ! 1 !}\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 \sqrt{3} i}{32}[/tex]

When k=2 then, [tex]\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=\frac{5 !}{(5-2) ! 2 !}\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=-\frac{15}{16}[/tex]

When k=3 then, [tex]\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=\frac{5 !}{(5-3) ! 3 !}\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=-\frac{15 \sqrt{3} i}{16}[/tex]

When k=4 then, [tex]\left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{5 !}{(5-4) ! 4 !}\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{45}{32}[/tex]

When k=5 then, [tex]\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{5 !}{(5-5) ! 5 !}\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{9 \sqrt{3} i}{32}[/tex],

Now we will add all the results to get the expansion of given expression,

[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{32}+\frac{5 \sqrt{3} i}{32}-\frac{15}{16}-\frac{15 \sqrt{3} i}{16}+\frac{45}{32}+\frac{9 \sqrt{3} i}{32}[/tex]

On simplifying,

[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex]

Therefore, the value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].

Learn more:https://brainly.com/question/13672615

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Answer:

[tex]t=3.142sec[/tex]

Step-by-step explanation:

From the question we are told that:

Speed of ball [tex]V=35m/s\approx 80 mph[/tex]

Length of field [tex]l=110m[/tex]

Generally the equation for Time taken [tex]t[/tex] is mathematically given by

 [tex]t=m/V[/tex]

 [tex]t=110/35[/tex]

 [tex]t=3.142sec[/tex]

 [tex]t \approx \frac{3.142}{60}[/tex]

 [tex]t \approx 0.05hrs[/tex]

Therefore it will take the ball to get from one end of the field to the other

[tex]t=3.142sec[/tex]

Answer:

a = 40π

Step-by-step explanation:

a = (∅/360) * πr²

a = (144/360) * π(10)²

a = 40π

Answer:

6%

Step-by-step explanation:

for this is divided the fee by the price of the item.

Answer: 15

Hope this helps!

Answer:

12.60

Step-by-step explanation:

give brainliest and 5 star and thank!

Answer:

3.125 miles

Step-by-step explanation:

5 × 0.625 = 3.125 miles

Answer:

[tex] \frac{9}{w} = \frac{15}{5} \\ w = 45 \div 15 = 3[/tex]

Answer:

hmm,,,,,,

Step-by-step explanation:

Answer:

The value of 1 tenth is less than the value of 1 ten.

Step-by-step explanation:

Answer:

Because 3 x 1/10 = 3/10

whereas 3 x 10 = 30

and 3/10 < 30

Also b/c 1/10 < 10 and they are multiplied by the same value (3)

Step-by-step explanation:

Answer:

one board game cost 15 dollars

75/5=15

15y

y = number of board games and 15= the price of each board game

so to calculate any number of board games bought just input the number of board games bought for y in the expression 15y and you will get the price.

Step-by-step explanation:

Answer:

4550

Step-by-step explanation:

Answer:

Step-by-step explanation:

18.2% of 25000 = 4550

Answer:

this triangle is "obtuse

Step-by-step explanation:

Since sides 14 and 16 add up to 30, which is more than the third side, 27, we DO have a triangle here.  The sides of lengths 14 and 16 form an angle greater than 90 degrees, and so this triangle is "obtuse."  It's not a right triangle either, because the Pythagorean Theorem is not satisfied:  14^2 + 16^2 = 452, which is NOT 27^2.

Answer:

not sure no attachments but i think its 49 or 37 or both together 88

Step-by-step explanation:

Answer:

TQ=SR [since it is isosceles trapezoid]

6x+1.2=9x-48

48+1.2=9x-6x

3x=49.2

x=49.2/3=16.4

now

QR=3×16.4+2.5=51.7

SR=9×16.4-48=99.6

ST=4×16.4-2=63.6

TQ=6×16.4+1.2=99.6

As it's isosceles trapezoid

Now

QR=3(2)+2.5=8.5

RS=9(2)-4.8=13.2

ST=4(2)-2=6

QT=6(2)-1.2=10.8

Answer: all you have to do is times length times width

which is 1 1/2x4 1/2 and then make it a decimal

Answer:

the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2006053?

Answer:

2,000 + 600 + 50 + 3 = 2,653

Step-by-step explanation:

Answer:

please apply the formula of distance

l think but not sure

Answer:

man you still have to use IXL

Step-by-step explanation:

Answer:

the answer is B.(-1,-2)

Step-by-step explanation:

please give brainliest

Answer: $285

Step-by-step explanation:

Given

A trip costs [tex]\$319.19[/tex] after-tax inclusion

The rate of tax is 12%

Suppose x is the amount of charge before tax inclusion

We can write

[tex]\Rightarrow x+12\%x=319.19\\\Rightarrow x(1+0.12)=319.19\\\\\Rightarrow x=\dfrac{319.19}{1.12}\\\\\Rightarrow x=\$284.99\approx \$285[/tex]

The amount before tax inclusion is $285

Answer:

The 16oz is a better deal

Step-by-step explanation:

32 = 2 * 16

buying 2 packages of 16 oz cost

0.79 * 2 = 1.58

1.58 < 2.09

The 16oz is a better deal

Answer:

The 16 oz package.

Step-by-step explanation:

Make the 16 oz a 32 oz so we can compare the prices

Mutiply 0.79 X 2 = 1.58

The 16 oz is because you can buy it twice making it a 32 oz for less than the orginal 32 oz.

(Compared side by side)

2.09 > 1.58

hope this helped!

Answer:

(-3, -2)

Step-by-step explanation:

To find the solution of two functions, you need to know at which x and y value they are equal. So solve for x and y when 1/3x - 1 = 2x + 4

1/3x - 1 = 2x + 4

First, subtract 2x from both sides.

-5/3x - 1 = 4

Add one to both sides.

-5/3x = 5

Multiply both sides by the reciprocal of -5/3 (3/-5)

x = -3

Then, substitute x into one of the equations to get y.

1/3(-3) - 1

-1 - 1 = -2

So drag the dot to the point (-3, -2)

Answer: i took a screen shot of the answer hope this helped

plz make brainly

Step-by-step explanation:

Answer:

d and e

Step-by-step explanation:

Answer:

Substraction

Step-by-step explanation:

Given that  

The amount paid in the year 2018 is $3,200

And, in the year 2019 the amount paid is $3,516'

We need to find the differnece between two years so how we can find

Basically we need to subtract the amount i.e.

= $3,516 - $3,200

= $316

hence, the difference is of $316 from 2018 to 2019