Answer:
Step-by-step explanation:
Let points D, E and F have coordinates 
and 
1. Midpoint M of segment DF has coordinates
2. Midpoint N of segment EF has coordinates
3. By the triangle midline theorem, midline MN is parallel to the side DE of the triangle DEF, then points M and N are endpoints of the midsegment for DEF that is parallel to DE.
<u>Answers:</u>
These are the three major and pure mathematical problems that are unsolved when it comes to large numbers.
The Kissing Number Problem: It is a sphere packing problem that includes spheres. Group spheres are packed in space or region has kissing numbers. The kissing numbers are the number of spheres touched by a sphere.
The Unknotting Problem: It the algorithmic recognition of the unknot that can be achieved from a knot. It defined the algorithm that can be used between the unknot and knot representation of a closely looped rope.
The Large Cardinal Project: it says that infinite sets come in different sizes and they are represented with Hebrew letter aleph. Also, these sets are named based on their sizes. Naming starts from small-0 and further, prefixed aleph before them. eg: aleph-zero.
1/4n-8=1/4 would be first because it says less than so you switch it. then you put the 8 since it's in the same subtraction problem. Then the word "is" indicates the equal sign. and the n represents "a number" since it is unknown.
X=pounds of coffee bean ($0.20 per pound)
y=pounds of coffee bean ($0.68 per pound )
We can suggest this system of equations:
x+y=120
(0.20x+0.68 y) / (x+y)=0.54 ⇒ (0.2x+0.68y)=0.54(x+y)
We can solve this system by substitution method.
x+y=120 ⇒ y=120-x
0.2x+0.68(120-x)=0.54[x+(120-x)]
0.2x+81.6-0.68x=0.54(120)
-0.48x+81.6=64.8
-0.48x=64.8-81.6
-0.48x=-16.8
x=-16.8/-0.48
x=35
y=120-x=120-35=85
Answer: the coffee mixture has 35 pounds of coffee beans sold to $0.2 a pound, and 85 pounds of coffee beans sold to $0.68 a pound, the solutions is reasonable because the price of a coffee mixture ($0.54 a pound) is greater than $0.2 and smaller than $0.68.
Answer:
Step-by-step explanation:
Explanation:
First, find two points on the line if you change the inequality to an equation.
For
x
=
0
:
0
+
2
y
=
4
2
y
=
4
2
y
2
=
4
2
y
=
2
or
(
0
,
2
)
For
y
=
0
:
x
+
0
=
4
x
=
4
or
(
4
,
0
)
We can plot these two points and draw a line through them to get the border of the inequality:
graph{(x^2+(y-2)^2-0.075)((x-4)^2+y^2-0.075)(x+2y-4)=0}
The line will be solid because the inequality operator has a "or equal to" clause in it. We can now shade the area to the right of the line because the inequality has a "great than" clause in it.
graph{(x+2y-4)>=0}
