Well, there are different ways to do this if you are really familiar with fractions, but "officially" :P
1) convert mixed numbers to improper fractions.
rule: a b/c = (ac+b)/c
2) make all fractions have a common denominator...
a/b+c/d
(a/b)(d/d)+(c/d)(b/b)
(ad/bd)+(cb/bd)
3)
The simplify your final answer with greatest common denominator or convert back to mixed number if needed...
Let's to the first example:
f(x) = x^2 + 9x + 20
Ussing the formula of basckara
a = 1
b = 9
c = 20
Delta = b^2 - 4ac
Delta = 9^2 - 4.(1).(20)
Delta = 81 - 80
Delta = 1
x = [ -b +/- √(Delta) ]/2a
Replacing the data:
x = [ -9 +/- √1 ]/2
x' = (-9 -1)/2 <=> - 5
Or
x" = (-9+1)/2 <=> - 4
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Already the second example:
f(x) = x^2 -4x -60
Ussing the formula of basckara again
a = 1
b = -4
c = -60
Delta = b^2 -4ac
Delta = (-4)^2 -4.(1).(-60)
Delta = 16 + 240
Delta = 256
Then, following:
x = [ -b +/- √(Delta)]/2a
Replacing the information
x = [ -(-4) +/- √256 ]/2
x = [ 4 +/- 16]/2
x' = (4-16)/2 <=> -6
Or
x" = (4+16)/2 <=> 10
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Now we are going to the 3 example
x^2 + 24 = 14x
Isolating 14x , but changing the sinal positive to negative
x^2 - 14x + 24 = 0
Now we can to apply the formula of basckara
a = 1
b = -14
c = 24
Delta = b^2 -4ac
Delta = (-14)^2 -4.(1).(24)
Delta = 196 - 96
Delta = 100
Then we stayed with:
x = [ -b +/- √Delta ]/2a
x = [ -(-14) +/- √100 ]/2
We wiil have two possibilities
x' = ( 14 -10)/2 <=> 2
Or
x" = (14 +10)/2 <=> 12
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To the last example will be the same thing.
f(x) = x^2 - x -72
a = 1
b = -1
c = -72
Delta = b^2 -4ac
Delta = (-1)^2 -4(1).(-72)
Delta = 1 + 288
Delta = 289
Then we are going to stay:
x = [ -b +/- √Delta]/2a
x = [ -(-1) +/- √289]/2
x = ( 1 +/- 17)/2
We will have two roots
That's :
x = (1 - 17)/2 <=> -8
Or
x = (1+17)/2 <=> 9
Well, this would be your answers.
(x-3) *squared* + (y + 2) *squared* = 6
The total amount of calories burnt in jogging 2 miles = 185 calories
We have to determine the number of calories burned in jogging 3 miles.
Firstly, we will determine the amount of calories burnt in jogging 1 mile. We will use unitary method to evaluate this.
So, the total amount of calories burnt in jogging 1 mile = 
= 92.5 calories
So, the amount of calories burnt in 3 miles = 
= 277.5 calories
Therefore, 277.5 calories are burned in jogging 3 miles.
Answer:
The answer to your question is speed = 81.5 mi/h
Step-by-step explanation:
Data
distance = 230 ft
time = 1.932 s
speed = ? mi/h
Process
1.- Convert the distance to mi
1 mile ----------------- 5280 ft
x ----------------- 230 ft
x = (230 x 1) / 5280
x = 0.044 mi
2.- Convert time to hours
1 h ------------------ 3600 s
x ------------------ 1.932 s
x = (1.932 x 1) / 3600
x = 0.00054 h
3.- Calculate the speed
speed = distance / time
-Substitution
speed = 0.044/ 0.00054
-Result
speed = 81.5 mi/h
