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
Answer:
-8 ≤ y ≤ 8
Step-by-step explanation:
Subtract 7 from the first one:
y ≥ -8
Subtract 3 from the second one, then multiply by 4.
y/4 ≤ 2
y ≤ 8
Now, you can write these as a compound inequality:
-8 ≤ y ≤ 8
_____
<em>Additional comment</em>
You basically solve these the same way you would an equation. The only difference is that multiplying or dividing by a negative number will reverse the inequality symbol:
2 > 1
-2 < -1 . . . . . multiplied above by -1.
Answer:
1/12
Step-by-step explanation:
Is the answer I'm bro
The confidence interval would be
.
We use the formula
, where
, with p being the sample proportion and N being the sample size.
First we find the z-score associated with this level of confidence:
Convert 95% to a decimal: 95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975
Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.
Since 578/720 said yes, this gives us p=0.80:
This gives us
<em>Answer:</em>
There is 1 liter in 100 centiliters
<em>Step-by-step explanation:</em>
<em>1 liter = 100 centiliters</em> !
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