we are given
![f(x)=2x^4-x^3+x-2](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E4-x%5E3%2Bx-2)
we can check each options
option-A:
-1,1
we can plug x=-1 and x=1 and check whethet f(x)=0
At x=-1:
![f(-1)=2(-1)^4-(-1)^3+(-1)-2](https://tex.z-dn.net/?f=f%28-1%29%3D2%28-1%29%5E4-%28-1%29%5E3%2B%28-1%29-2)
![f(-1)=0](https://tex.z-dn.net/?f=f%28-1%29%3D0)
At x=1:
![f(1)=2(1)^4-(1)^3+(1)-2](https://tex.z-dn.net/?f=f%281%29%3D2%281%29%5E4-%281%29%5E3%2B%281%29-2)
![f(1)=0](https://tex.z-dn.net/?f=f%281%29%3D0)
so, this is TRUE
option-B:
0,1
we can plug x=0 and x=1 and check whethet f(x)=0
At x=0:
![f(0)=2(0)^4-(0)^3+(0)-2](https://tex.z-dn.net/?f=f%280%29%3D2%280%29%5E4-%280%29%5E3%2B%280%29-2)
![f(0)=-2](https://tex.z-dn.net/?f=f%280%29%3D-2)
At x=1:
![f(1)=2(1)^4-(1)^3+(1)-2](https://tex.z-dn.net/?f=f%281%29%3D2%281%29%5E4-%281%29%5E3%2B%281%29-2)
![f(1)=0](https://tex.z-dn.net/?f=f%281%29%3D0)
so, this is FALSE
option-C:
-2,-1
we can plug x=-2 and x=-1 and check whethet f(x)=0
At x=-2:
![f(-2)=2(-2)^4-(-2)^3+(-2)-2](https://tex.z-dn.net/?f=f%28-2%29%3D2%28-2%29%5E4-%28-2%29%5E3%2B%28-2%29-2)
![f(-2)=36](https://tex.z-dn.net/?f=f%28-2%29%3D36)
At x=-1:
![f(-1)=2(-1)^4-(-1)^3+(-1)-2](https://tex.z-dn.net/?f=f%28-1%29%3D2%28-1%29%5E4-%28-1%29%5E3%2B%28-1%29-2)
![f(-1)=0](https://tex.z-dn.net/?f=f%28-1%29%3D0)
so, this is FALSE
option-D:
-1,0
we can plug x=-1 and x=0 and check whethet f(x)=0
At x=-1:
![f(-1)=2(-1)^4-(-1)^3+(-1)-2](https://tex.z-dn.net/?f=f%28-1%29%3D2%28-1%29%5E4-%28-1%29%5E3%2B%28-1%29-2)
![f(-1)=0](https://tex.z-dn.net/?f=f%28-1%29%3D0)
At x=0:
![f(0)=2(0)^4-(0)^3+(0)-2](https://tex.z-dn.net/?f=f%280%29%3D2%280%29%5E4-%280%29%5E3%2B%280%29-2)
![f(0)=-2](https://tex.z-dn.net/?f=f%280%29%3D-2)
so, this is FALSE
Answer:
20
Step-by-step explanation:
Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, etc. Each multiple is created by multiply 5 times some other number.
Answer:
D. Opposite angles are congruent
With option A, we can see that it is clearly wrong, in a parallelogram, only the opposite sides are congruent, if all of the sides are congruent then the shape is more likely to be a square or a rhombus.
With option B, only the opposites angles are congruent. If all four angles are congruent, that will be more likely to be true when we consider a square or a rectangle.
With option C, it is also wrong, unless the shape is a rhombus, square or rectangle.
That leaves us with the last option which is D.
Answer:
a. 3 ways: -3 and -1; -2 and -2; -1 and -3
b. 5 ways: -2 and 2; -1 and 1; 0 and 0; 1 and -1; 2 and -2
c. 6 ways: -3 and 2; -2 and 1; -1 and 0; 0 and -1; 1 and -2; 2 and -3
d. A sum of -1 would (probabilistically) be the most popular. There are 36 (6 x 6) possible outcomes every time you roll two 6-sided dice. In this case, the possible outcomes are:
-6: 1 way
-5: 2 ways
-4: 3 ways
-3: 4 ways
-2: 5 ways
-1: 6 ways
0: 5 ways
1: 4 ways
2: 3 ways
3: 2 ways
4: 1 way
So -1 is the most likely sum since it can be rolled 6 different ways, which is more ways than any other sum. A sum of -1 will be rolled 6/36 (or 1/6) of the time.