Step-by-step explanation:
For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,
b^2 - 4ac must be positive.
b^2 - 4ac > 0
(k - 3)^2 - 4(3 - 2k) > 0
k^2 - 6k + 9 - 12 + 8k > 0
k^2 + 2k - 3 > 0
I’m not sure about number 1 but the answer for number 2 is
-4 1/2, -4.2, -4, ,0, 4
To solve this, you will have to set up your equation as fractions:
X is to 4 as 4 is to 4+3, or 7
X/4 = 4/7
You will then cross multiply
7x = 4•4
7x = 16
Divide.
X = 2.285714...
Round to the nearest hundredth.
2.29
Answer:
Step-by-step explanation:
Since there's no one one number you can add to one number in the sequence to get to the next number, this is not arithmetic. It must be geometric. We need then to find the common ratio. Let's start with the first 2 numbers, find a ratio, and then use it to test for accuracy.
10x = 15 and
x = 
If this is in fact a geometric sequence witha common ratio of 3/2, we should be able to multiply 15 by 3/2 to get to the next number in the sequence. Let's try it out:
Good. So the common ratio is 3/2. The formula for an explicit geometric formula is
where a1 is the first number in the sequence and r is the common ratio. Filling in:
