Evaluate Vb2 - 4ac when a = -2, b = 8 and c = 1/2 Write your answer in simplest form and in decimal form rounded to the
nearest hundredth
Simplest form:
Decimal form:

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].

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Answer:

(x-3^2+y+2^2 =25

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

The length of the actual car is 600.

Scale factor is that it is a number that multiplies times a given quantity to produce a smaller or larger version of the original number. The ratio of any two corresponding lengths in two similar geometric figures.

For the given situation,

The scale factor of a model car = 2

The length of the model car = 300

The length of the actual car = [tex]300(2)[/tex]

⇒ [tex]600[/tex]

Hence we can conclude that the length of the actual car is 600.

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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:

[tex]\huge\boxed{x=-15}[/tex]

Step-by-step explanation:

[tex]-18=-3+x\qquad|\text{add 3 to both sides}\\\\-18+3=-3+3+x\\\\-15=x\to x=-15[/tex]

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: XD that was great

Answer: 15

Hope this helps!

Heres some info i learend

s but its not complete maybe i guess

Terms. We combine em by adding. The numbers or subtracting the numbers that are multiplied times the radicals.

Answer:

hmm,,,,,,

Step-by-step explanation:

Answer:

0.0425

Step-by-step explanation:

Answer:

0.0425

Step-by-step explanation:

Answer:

65.12 mm

Step-by-step explanation:

Circumference of semicircle = 8π mm

Perimeter = (40 + 8π) = 65.12 mm

Answer:

3.125 miles

Step-by-step explanation:

5 × 0.625 = 3.125 miles

Answer:

[tex]y = \sqrt{ {14}^{2} - {10}^{2} } \\ y = \sqrt{96} \\ y = 9.8[/tex]

Answer:

Step-by-step explanation:

using pythagoras theorem

h^2=p^2+b^2

14^2=10^2+b^2

196=100+b^2

196-100=b^2

96=b^2

[tex]\sqrt{96}[/tex] =b

4[tex]\sqrt{6}[/tex] =y

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:

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

Step-by-step explanation:

Answer:

6 crickets

Step-by-step explanation:

First day:  20% of 10 is (.20)(10) = 2, so there were 10 - 2 = 8 crickets left.

Second day: 25% of 8 is (.25)(8) = 2, so there were 8 - 2 = 6 crickets left.

Answer:

hi how are you doing today Jasmine

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: i cant see the picture can you send it to me please

Step-by-step explanation:

Answer:

Vajsjke

Step-by-step explanation:

ggzodxkdfdjhs

Answer:

A

Step-by-step explanation:

In A, the number of bags that had more than 19 skittles is 7 and the number of bags that had less than 19 skittles is 16, so A is true.

In B, the median package contained 18 candies.

In C, 5 bags contained 18 candies, while there were 8 bags in total for the 17 and 20 bags.

In D, the range is the highest value minus the lowest, so it's 22-12=10.

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

Answer:

15.87%

Step-by-step explanation:

We start with getting the z score

Mathematically , we have this as;

z-score = (x-mean)/SD

where x = 114

z-score = (114-100)/14 = 14/14 = 1

So we want to calculate the probability values that are greater than 1

We can use the standard normal distribution table

so we have P(z> 1) = 0.15866

in percentage, we multiply by 100 and that gives 15.866 which is 15.87 people

Answer:

Rhombus

Step-by-step explanation:

Answer:

The answer is a rhombus

Hope this helps!

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