Answer:
Lines are parallel if the sum of external angles of same side is 180°.
Step-by-step explanation:
Let one of the external angle is α°.
and other external angle is β° which is equal to α°/11. (∵ Given on is 11 times smaller than the other.)
Also β° = 1/6 of the right angle = (1/6)×90° = 15°.
β° = α°/11 , ⇒ α° = 11×β° = 11×15° = 165°.
α°+β° = 165° + 15° = 180°.
Here, sum of the two external angles = 180° ⇔ the given lines are parallel.
Answer:
The dimensions of the yard are W=20ft and L=40ft.
Step-by-step explanation:
Let be:
W: width of the yard.
L:length.
Now, we can write the equation of that relates length and width:
(Equation #1)
The area of the yard can be expressed as (using equation #1 into #2):
(Equation #2)
Since the Area of the yard is
, then equation #2 turns into:

Now, we rearrange this equation:

We can divide the equation by 5 :

We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since
and
. The equation factorised looks like this:

Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:

Therefore, the dimensions of the yard are W=20ft and L=40ft.
Answer:
(x+10)+(×+50)=180(exterior co- interior angel
2x+60=180
2×=180-60
×=120/2
×=60
(6x+3)=(7x-12)(corresponding angle )
3+12=7×-6×
x=15
4x-2=3x-19(vertically opposite angle)
4x-3×=-19+2
x=-17
Answer:

Explanation:
You are comparing irrational numbers.
By inspection, i.e. at first sight you can only compare
because they have the same radicand.
You can order: 
You can introduce the 2 inside the radical by squaring it:

Since 5 is between 3 and 12, you can order:
Which is:
You must know that π ≈ 3.14.
5 is less than 9 and the square root of 9 is 3; hence,
and 
Now you must determine whether π is less than or greater than 
Using a calculator or probing numbers between 3 and 4 you get 
Hence, the complete order is:
Answer: he had 68 cherries in the start
Step-by-step explanation: