Answer: for a sum of 7 would either be 6 and 1, 5 and 2 or 4 and 3. you can roll a double 1,2,3,4,5,6. the sum of 8 would be 2 and 6, 3 and 5 and a double 4,
Step-by-step explanation:
well the there are six sides on a die so 6 x 2 is 12 so the max sum you can get is 12. So you take 7 and you start adding up to 7, same thing for sum of 8. since there is 6 sides and a pair of dices you will roll six doubles
D. All irrational numbers are rational numbers.
I attached the diagram my teacher showed us when we learned about this. I think it makes it a lot less confusing.
Hope this helps :)
Answer:
Length = 18.099 ft
Width = 11.049 ft
Step-by-step explanation:
let the length of the field be x ft
and the width be y ft
as per the condition given in problem
x=2y-4 -----------(A)
Also the area is given as 200 sqft
Hence
xy=200
Hence from A we get
y(2y-4)=200
taking 2 as GCF out
2y(y-2)=200
Dividing both sides by 2 we get
![y(y-2)=100](https://tex.z-dn.net/?f=y%28y-2%29%3D100)
![y^2-2y=100](https://tex.z-dn.net/?f=y%5E2-2y%3D100)
subtracting 100 from both sides
![y^2-2y-100=0](https://tex.z-dn.net/?f=y%5E2-2y-100%3D0)
Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Here in our case
a=1
b=-1
c=-100
Putting those values in the formula and solving them for y
![y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%28-2%29%2B%5Csqrt%7B%28-2%29%5E2-4%20%5Ctimes%20%28-1%29%20%5Ctimes%20100%7D%7D%7B2%20%5Ctime%201%7D)
![y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%28-2%29-%5Csqrt%7B%28-2%29%5E2-4%20%5Ctimes%20%28-1%29%20%5Ctimes%20100%7D%7D%7B2%20%5Ctime%201%7D)
Solving first
![y=\frac{2+\sqrt{4+400}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%2B%5Csqrt%7B4%2B400%7D%7B2%7D)
![y=\frac{2+\sqrt{404}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%2B%5Csqrt%7B404%7D%7B2%7D)
![y=\frac{2+20.099}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%2B20.099%7D%7B2%7D)
![y=\frac{22.099}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B22.099%7D%7B2%7D)
![y=11.049](https://tex.z-dn.net/?f=y%3D11.049)
Solving second one
![y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-%28-2%29-%5Csqrt%7B%28-2%29%5E2-4%20%5Ctimes%20%28-1%29%20%5Ctimes%20100%7D%7D%7B2%20%5Ctime%201%7D)
![y=\frac{2-\sqrt{4+400}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2-%5Csqrt%7B4%2B400%7D%7B2%7D)
![y=\frac{2-\sqrt{404}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2-%5Csqrt%7B404%7D%7B2%7D)
![y=\frac{2-20.099}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2-20.099%7D%7B2%7D)
![y=\frac{-18.99}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-18.99%7D%7B2%7D)
![y=-9.045](https://tex.z-dn.net/?f=y%3D-9.045)
Which is wrong as the width can not be in negative
Our width of the field is
y=11.099
Hence the length will be
x=2y-4
x=2(11.049)-4
x=22.099-4
x=18.099
Hence our length x and width y :
Length = 18.099 ft
Width = 11.049 ft
Their family drove 7,305 miles that year. Hope this helps!!