Answer:
k = - 
, k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2
12 pieces i think sorry for the uncertainty
Answer:
33 children
62 adults
Step-by-step explanation:
Set up 2 equations (a=adults c=children)
The first equation will be 3.25(a)+3 = 300.5
The second equation will be a + c = 95
Subtract c from both sides to get:
a = 95 - c
Replace c in the 1st equation to get:
3.25(95-c) + 3c = 300.5
Distribute 3.25 to 95 and -c:
308.75 - 3.25c + 3c = 300.5
Subtract 308.75 from both sides:
-3.25c + 3c = 300.5 - 308.75
Combine like terms:
-0.25c = -8.25
Divide by -0.25
children = 33
Subtract 33 from 95 to get
adults = 62
Answer:
The $2,000 decrease in Carlos's taxable income will save him
Step-by-step explanation:
i) Carlos is in the 12% tax bracket.
ii)The $2,000 decrease in Carlos's taxable income will save him
Answer:
6
Step-by-step explanation:
2 x 3 = 6
