1. true.
2. false.
3. false.
4. true.
these should be correct.
Answer:
All points on line CD are equidistant from A and B
Step-by-step explanation:
Given that point A is the center of circle A and point B is the center of circle B, and the circumference of circle A passes through the center of circle B which is point B and vice versa.
Therefore we have;
The radius of circle A = The radius of circle B
Which gives;
The distance of the point C to the center A is equal to the distance of the point C to the center B
Similarly, the distance of the point D to the center A is equal to the distance of the point D to the center B
So also the distances of all points on the line from the center A is equal to the distances of all points on the line from the center B.
We have three similar triangles, let's see if we can get this right, right vertex first, then other vertex from small side:
EDF ~ GDE ~ GEF
As ratios that means
ED:DF:EF = GD:DE:GE = GE:EF:GF
x:20:y = 5:x:GE = GE:y:15
Since we're after y we choose
20/y = y/15
20(15) = y²
y² = 300
y = 10√3
y ≈ 17.32
Answer:10 gallons of 30% solution and 30 gallons of 70% solution should be mixed.
Step-by-step explanation:
Let x represent the number of gallons of the 30% solution that should be mixed.
Let y represent the number of gallons of the 70% solution that should be mixed.
The total number of gallons of the mixture to be made is 40. This means that
x + y = 40
The 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. This means that
0.3x + 0.7y = 0.6 × 40
0.3x + 0.7y = 24- - - - - - - - - - - - - -1
Substituting x = 40 - y into equation 1, it becomes
0.3(40 - y) + 0.7y = 24
12 - 0.3y + 0.7y = 24
- 0.3y + 0.7y = 24 - 12
0.4y = 12
y = 12/0.4
y = 30
x = 40 - y = 40 - 30
x = 10
