Answer :
1) If x = 6
Substitute 6 for x in the expression.
a) 5x-9
5(6)-9
30-9
21
b) 2x-7
2(6) -7
12-7
5
c) 8x+5
8(6)+5
48+5
53
d) 4(x+3)
4(6+3)
4(9)
36
e) x²-(-4)
6²-(-4)
36+4
40
f) 3x²+1
3(6²)+1
3(36) +1
108+1
109
2) Solve
a) 54 = 3x
Divide both sides by 3.
54/3 = 3x/3
x = 18
b) x-9 = -3
Add 9 to both sides.
x-9+9 = -3+9
x = 6
c) x/7 = 140
Express the 140 over 1 and cross multiply.
x/7 = 140/1
x = 140×7
x = 980
d) x/8 = 72
Express the 72 over 1 and cross multiply.
x/8 =72/1
x = 72×8
x = 576
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.
Factors of six would be 1*6 and 2*3
Answer:
360
Step-by-step explanation:
multiply 90 and 4
