Answer:
d) geometric; r = 4
Step-by-step explanation:
Differences of adjacent terms are not constant (they are 1.2, 4.8, 19.2, ...), so the sequence is NOT ARITHMETIC.
Ratios of adjacent terms are constant (they are 1.6/0.4 = 6.4/1.6 = 25.6/6.4 = 4), so the sequence is geometric with a common ratio of 4.
To find out which equation has no real solutions, we need to calculate the discriminant for each of these given equations.
For calculating the discriminant, we need to first compare these equations with the general formula which is <u>ax²+bx+c.</u>
So, let's get started.
1) x² + 4x + 16 = 0
a=1, b=4, c=16
D = b²-4ac
= (4)² - 4(1)(16)
= 16-64
= -48
√D = √-48
2) 4x² + 4x - 24 = 0
a=4, b=4, c=-24
D = b²-4ac
= (4)² - 4(4)(-24)
= 16 - 16(-24)
= 16 + 384
= 400
√D = √400 = +20 or -20
3) 5x² + 3x - 1 = 0
a=5, b=3, c=-1
D = b²-4ac
= (3)² - 4(5)(-1)
= 9 + 20
= 29
√D = √29
4) 2x² - 4x + 4 = 0
a=2, b=-4, c=4
D = b²-4ac
= (-4)² - 4(2)(4)
= 16 - 32
= -16
√D = √-16
Now from all these above calculations, we can see that discriminant was negative in first equation and in last equation.
If D<0 then roots does not exist, as the square root can not contain a negative value or the equation does not have any real solutions.
Roots in such case can be calculated but those roots are known as imaginary roots, which is a higher concept.
So Final answer is,
Equation 1 => x² + 4x + 16 = 0
and
Equation 4 => 2x² - 4x + 4 = 0
has no real solutions.
Answer:
8.005 km
Step-by-step explanation:
There are 1000 meters in a kilometer, so:
5/1000 = 1/200 = 0.005
8 km + 0.005 km = 8.005 km
28. This equation satisfies the condition
-x - 10 = -17
29. You can use this equation
x/5 + 5 = 0
30. The error is dividing the equation first by 3. The solution should have been
3x + 2 = 15
3x = 15 - 2
3x = 12
3x/3 = 12/3
x = 4
31.
x/4 - 6 = 2
x/4 = 2 + 6
x/4 = 8
x = 8(4)
x = 32
The first step was the combine the like terms; in this example he is subtracting the 3x on both sides of the =.
If you were to solve the equation it would look like this:
2x+6=3x-8
-3x -3x
-x+6=-8
-6 -6
-x=-14
/-1 /-1
x=14
