Answer:
Step-by-step explanation:
<u>Given</u>
<u>Substitute and solve for n:</u>
- 42 = n² + n
- n² + 2*1/2n + 1/4 = 42.25
- (n + 0.5)² = 42.25
- n + 0.5 = √42.25
- n + 0.5 = 6.5
- n = 6
Correct option is C
Answer:
x = 1 ±2sqrt(5)
Step-by-step explanation:
2x^2-4x-9=29
Add 9 to each each side
2x^2-4x-9+9=29+9
2x^2-4x=38
Divide by 2
2/2x^2-4/2x=38/8
x^2 -2x =19
Complete the square
x^2 -2x + (-2/2)^2 = 19 +(-2/2)^2
x^2 -2x +1 = 19+1
(x-1)^1=2 = 20
Take the square root of each side
sqrt((x-1)^2) = ±sqrt(20)
x-1 = ±sqrt(20)
Add 1 to each side
x-1+1 = 1 ±sqrt(20)
x = 1 ±sqrt(20)
Simplifying the square root of 20
x = 1 ±sqrt(4)sqrt(5)
x = 1 ±2sqrt(5)
Answer:
Rocco mowed 1 lawn a week.
Step-by-step explanation:
If Carly mowed 18 lawns in six weeks that’s 3 lawns a week and 3-2=1.
Thus Rocco mowed 1 lawn a week.
Mike age is 3 less then twice the age of his brother nuke.
M = Mike's age now
N = Nuke's age now
M = 2N - 3
Ten years ago, four times nuke's age was one more mike's age.
M-10 = Mike's age 10 years ago
N-10 = Muke's age 10 years ago
4(N - 10) = 1 + M -10
what are their present ages
find M and N
substitute M = 2N - 3 into 4(N - 10) = 1 + M -10:
4(N - 10) = 1 + [2N - 3] - 10
4N - 40 = 2N - 12
2N = 28
N = 14
M = 2(14) - 3 = 28 - 3 = 25
Mike is 25 and Nuke is 14.
check:
4(14 - 10) = 4(4) = 16 = 26 -10 = 1 + 25 - 10
