a + b ≥ 30, b ≥ a + 10, the system of inequalities could represent the values of a and b
option A
<u>Step-by-step explanation:</u>
Here we have , The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, We need to find which system of inequalities could represent the values of a and b . Let's find out:
Let two numbers be a and b where b>a . Now ,
- The sum of two positive integers, a and b, is at least 30
According to the given statement we have following inequality :
⇒ ![a+b\geq 30](https://tex.z-dn.net/?f=a%2Bb%5Cgeq%2030)
- The difference of the two integers is at least 10
According to the given statement we have following inequality :
⇒ ![b-a\geq 10](https://tex.z-dn.net/?f=b-a%5Cgeq%2010)
⇒ ![b-a+a\geq 10 +a](https://tex.z-dn.net/?f=b-a%2Ba%5Cgeq%2010%20%2Ba)
⇒ ![b\geq 10 +a](https://tex.z-dn.net/?f=b%5Cgeq%2010%20%2Ba)
Therefore , Correct option is A) a + b ≥ 30, b ≥ a + 10
The slope of KH is 1
The slope of GJ is -1
The product of the slopes of the diagonals is -1
Therefore, KH is perpendicular to GJ
I think it's 20 because 5 feet times 4 more times equals 20.
5*4=20
So 20 feet?
I think that's right, and I hope it helps :)
THE Answer is 34.6153846154%
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