I think Lin is trying to convince Andre that all circles are similar by saying all the circles are similar with math.
Set up a system of equations and say green route is x and blue route is y
This will give you
Monday 6x + 5y= 52
Tuesday 12x + 13y = 119
Solve by multiplying the top equation by two to get
12x + 10y= 104
Since you have 12x in both equations, these cancel out when you subtract the bottom from the top. This leaves you with
-3y=-15
Y=5
The blue route is 5 miles, but they want to know the green route. Fill in the y value in either one of your equations. Let’s use the one from Tuesday
12x + 13 (5) = 119
12x= 54
X= 4.5
This means that the answer is B, 4.5 miles
The midpoints of the sides are:
M ( (2a+0)/2 , (2b+0)/2 ) = ( a , b )
N ( (-2a+0)/2 , (2b+0)/2 ) = ( - a, b )
P ( (-2a+0)/2, ( -2b+0)/2 ) = ( - a, - b )
Q ( (2 a+0)/2) , (-2b+0)/2 ) = ( a , - b )
The midpoints of a rhombus determine a rectangle.
Let x be the number Henry is thinking of.
The number is doubled and got an answer of 4.
That means:
2 · x = 4
or
2x = 4
This is the equation when Henry doubled the number and got 4 as an answer.
Solve it by dividing both sides by 2.
2x ÷ 2 = 4 ÷ 2
x = 2
The original number Henry was thinking was 2.
Cheers!
