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Taya2010 [7]
3 years ago
12

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
3 0

Answer:

A) -2 - i√3 , -2 + i√3

Step-by-step explanation:

Solve using quadratic formula

x² + 4x + 7 = 0

The Almighty Formula

= -b ± √b² - 4ac/2a

Where ax + bx² + c = 0

From the above question

a = 1, b = 4, c= 7

Hence,

-4 ± √4² - 4 × 1 × 7/2 × 1

-4 ± √16 - 28/2

=( -4 ± √-12)/2

Since

b² - 4ac < 0

We have two complex roots

Simplifying

( -4 ± √-12)/2

= -4/2 ± √-12/2

= -2 ± 2√3i/2

= -2 ± √3i

Therefore,

-2 - √3i , -2 + √3i

or

-2 - i√3 , -2 + i√3

Option A , is the correct answer

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Kobotan [32]

f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}

This is because

h(x)=\sqrt x

g(x)=x-1

\implies g(h(x))=\sqrt x-1

(that is, replace any instance of <em>x</em> in the definition of <em>g</em> with √<em>x</em> )

and

f(x)=x^4+4

\implies f(\sqrt x-1)=(\sqrt x-1)^4+4

(replace any <em>x</em> in <em>f</em> with √<em>x</em> - 1)

Also acceptable:

(\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4

=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}

(assuming <em>x</em> is not negative)

6 0
3 years ago
How many black keys would you expect to find on a keyboard with 72 keys in all? Show your work.
Black_prince [1.1K]

Answer:

50 black keys

Step-by-step explanation:

for every set of 7 white keys there are 5 black keys

72/7 = 10

so there is a total of 10 full sets of keys

then you have 2 white keys remaining but that doesn't matter because they will just be on the dies and already have a black key next

so this means that you only have to calculate the number of 10 sets of black keys and thats 5 x 10.

hope this helps : )

4 0
3 years ago
Using the number 0,4,9 what is the smallest number you can create
ryzh [129]
9-4=-5 would be the smallest answer
5 0
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vredina [299]

Answer:

A= $0.60

B= $5.62

Step-by-step explanation:

A: If you do 1.5*0.10, the product will be 0.15. If you do 1.5*0.50, the product would be 0.75. So, 0.75-0.15 is 0.6.

B: 2.5*0.50 is 1.25 and 1.25*0.10 is 0.125. So, if you add the products together, you would get 1.375 but because it's money, you have to round it to $1.38 and $7-$1.38 is $5.62.

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4 years ago
a person ate 2000 calories in a day of those calories 35% were from fat how many calories are from fat​
Nata [24]

Answer:

700

Step-by-step explanation:

6 0
3 years ago
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