Step One
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Find the length of FO (see below)
All of the triangles are equilateral triangles. Label the center as O
FO = FE = sqrt(5) + sqrt(2)
Step Two
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Drop a perpendicular bisector from O to the midpoint of FE. Label the midpoint as J. Find OJ
Sure the Pythagorean Theorem. Remember that OJ is a perpendicular bisector.
FO^2 = FJ^2 + OJ^2
FO = sqrt(5) + sqrt(2)
FJ = 1/2 [(sqrt(5) + sqrt(2)] \
OJ = ??
[Sqrt(5) + sqrt(2)]^2 = [1/2(sqrt(5) + sqrt(2) ] ^2 + OJ^2
5 + 2 + 2*sqrt(10) = [1/4 (5 + 2 + 2*sqrt(10) + OJ^2
7 + 2sqrt(10) = 1/4 (7 + 2sqrt(10)) + OJ^2 Multiply through by 4
28 + 8* sqrt(10) = 7 + 2sqrt(10) + 4 OJ^2 Subtract 7 + 2sqrt From both sides
21 + 6 sqrt(10) = 4OJ^2 Divide both sides by 4
21/4 + 6/4* sqrt(10) = OJ^2
21/4 + 3/2 * sqrt(10) = OJ^2 Take the square root of both sides.
sqrt OJ^2 = sqrt(21/4 + 3/2 sqrt(10) )
OJ = sqrt(21/4 + 3/2 sqrt(10) )
Step three
find h
h = 2 * OJ
h = 2* sqrt(21/4 + 3/2 sqrt(10) ) <<<<<< answer.
Answer:
Approximately 7.8 units
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
From the graph, we can see that A is (0,0). Let's let this be x₁ and y₁.
B is (-5,6). Let's let this be x₂ and y₂. So, substitute:
Simplify:
Square:
Add:
Take the square root. Use a calculator:
So, the distance between them is about 7.8 units.
And we're done!
9514 1404 393
Answer:
y = 3x
Step-by-step explanation:
A proportional relation has the equation ...
y = kx
To write the desired equation, you need to know the value of k. That can be found from the given information:
for x = 2, y = 6
6 = k·2
3 = k . . . . divide by 2
Now, we know the equation can be written ...
y = 3x
A slope intercept form: y = mx + b where m = slope and b = y -intercept
A slope of 3/2 is given
So y = 3/2 x + b
To find b:
b = y - mx
A line passes through the point (4, -6)
b = -6 - (3/2)(4)
b = -6 - 6
b = - 12
Answer
Equation in slope intercept form: y = 3/2 x - 12
