Answer:
x = 10
Step-by-step explanation:
1) Subtract x from both sides.
4x − x = 30
2) Simplify 4−x to 3x
3x = 30
3) Divide both sides by 3
x =
4) Simplify to 10
x = 10
Solve by additionmethod3x - 84 = 3
1 answer:
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Answer:
0.98 $/cup
Step-by-step explanation:
The final answer asks for price/cup, as "per" means "divided by".
So, our final units will be in $/cup.
We are given that for every 2 gallons, it will cost $31.36.
In order to get from gallons to cups, we need to convert units.
In 1 gallon, there are 16 cups.
So, our conversion factor will be 16 cups/1 gallon.
$/cup
Important things to note:
- With these types of problems, it makes it much easier if you just figure out what units you need in the final answer, and then use conversions and dimensional analysis to get the answer
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