Answer:
H
Step-by-step explanation:
Once graphed, the line passes through (-4,2) while the others do not
Answer:
A
Step-by-step explanation:
Given
20 - || - 13 | + 17 |
Note the absolute value function always returns a positive value, that is
| - a | = | + a | = a, thus
= 20 - | | - 13 |+ 17 |
= 20 - | 13 + 17 |
= 20 - | 30 |
= 20 - 30
= - 10 → A
Answer:
Roots are not real
Step-by-step explanation:
To prove : The roots of x^2 +(1-k)x+k-3=0x
2
+(1−k)x+k−3=0 are real for all real values of k ?
Solution :
The roots are real when discriminant is greater than equal to zero.
i.e. b^2-4ac\geq 0b
2
−4ac≥0
The quadratic equation x^2 +(1-k)x+k-3=0x
2
+(1−k)x+k−3=0
Here, a=1, b=1-k and c=k-3
Substitute the values,
We find the discriminant,
D=(1-k)^2-4(1)(k-3)D=(1−k)
2
−4(1)(k−3)
D=1+k^2-2k-4k+12D=1+k
2
−2k−4k+12
D=k^2-6k+13D=k
2
−6k+13
D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))
For roots to be real, D ≥ 0
But the roots are imaginary therefore the roots of the given equation are not real for any value of k.
Answer:
x-3
Step-by-step explanation:
f(x) = 3x-2
g(x) = 2x + 1
(f-g)(x) = 3x-2 - (2x+1)
Distribute the minus sign
=3x-2-2x-1
Combine like terms
= 3x-2x-2-1
=x-3
