let's call G the intersection point of EF & BC.
according to the thales' theorem:
and EF= EG+GF=EG+3
length of the altitude of △AED=EF
EF=EG+GF=1.5+3=4.5
Answer: x = 40
Step-by-step explanation:
these two angles are vertical angles, they will equal each other
therefore, move numbers and variables to the opposite sides of the = sign to isolate the X
3x-10 = 2x + 30
+10 +10 move the -10 by doing opposite
_____________
3x = 2x + 40
-2x -2x move -2x by doing opposite
____________
x = 40
you can check your work by substituting 40 in place of x
3(40) - 10 = 2(40) +30
120-10 = 80 + 30
110 = 110
answer is correct
Answer: height of the tower is 1064 feet
Step-by-step explanation:
We want to determine the height of the tower.
Assuming her line of sight of the top of the tower is a straight line, then a right angle triangle is formed. The height, h of the tower represents the opposite side of the triangle. Her distance from the foot of the tower represents the adjacent side of the triangle.
To determine h, we would apply the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side
Therefore,
Tan 85.7 = h/80
h = 80tan 85.7
h = 1064 feet
Answer:
Step-by-step explanation:
A. Directrix: y = 4-6 = -2
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B. Axis of symmetry: x = 6
Axis of symmetry intersects directrix at (6,-2)
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C . Vertex is halfway between focus and directrix, at (6,1)
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D. The focus lies above the directrix, so the parabola opens upwards.
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E. Focal length p = 1/(4×0.5)
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F. p = 0.5
::::
G. y = 0.5(x-6)² + 1
4 quarts per gallon
<span>10 gallons: 4x10 = 40 quarts. </span>
<span>Add the 11 quarts to get 51 quarts. </span>
<span>51 divided by 3 = 17 quarts, or 4 gallons + 1 quart.</span>
