9514 1404 393
Answer:
∠4 = 100°
Step-by-step explanation:
This has nothing to do with parallel lines.
Angles 1 and 4 are "vertical angles", hence congruent.
∠1 = ∠4 = 100°
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Vertical angles are on opposites sides of the intersection where lines cross.
Problem 1)
AC is only perpendicular to EF if angle ADE is 90 degrees
(angle ADE) + (angle DAE) + (angle AED) = 180
(angle ADE) + (44) + (48) = 180
(angle ADE) + 92 = 180
(angle ADE) + 92 - 92 = 180 - 92
angle ADE = 88
Since angle ADE is actually 88 degrees, we do NOT have a right angle so we do NOT have a right triangle
Triangle AED is acute (all 3 angles are less than 90 degrees)
So because angle ADE is NOT 90 degrees, this means
AC is NOT perpendicular to EF-------------------------------------------------------------
Problem 2)
a)
The center is (2,-3) The center is (h,k) and we can see that h = 2 and k = -3. It might help to write (x-2)^2+(y+3)^2 = 9 into (x-2)^2+(y-(-3))^2 = 3^3 then compare it to (x-h)^2 + (y-k)^2 = r^2
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b)
The radius is 3 and the diameter is 6From part a), we have (x-2)^2+(y-(-3))^2 = 3^3 matching (x-h)^2 + (y-k)^2 = r^2
where
h = 2
k = -3
r = 3
so, radius = r = 3
diameter = d = 2*r = 2*3 = 6
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c)
The graph is shown in the image attachment. It is a circle with center point C = (2,-3) and radius r = 3.
Some points on the circle are
A = (2, 0)
B = (5, -3)
D = (2, -6)
E = (-1, -3)
Note how the distance from the center C to some point on the circle, say point B, is 3 units. In other words segment BC = 3.
Using the midpoint formula, the coordinates of the endpoint X, are calculated as: X(6, -12).
<h3>How to Apply the Midpoint Formula?</h3>
The midpoint formula is expressed as: M(x, y) = [(x_1 + x_2)/2, (y_1 + y_2)/2].
We are given the following:
Line XY has a midpoint with the coordinates: (3, -5)
It has one endpoint: Y(0, 2)
To find the coordinates of the other endpoint, X, let:
X(?, ?) = (x_1, y_1)
Y(0, 2) = (x_2, y_2)
M (x, y) = (3, -5)
Plug in the values into the midpoint formula
M(3, -5) = [(x_1 + 0)/2, (y_1 + 2)/2]
Isolate and solve each variable
3 = (x_1 + 0)/2
6 = x_1
x_1 = 6
-5 = (y_1 + 2)/2
-10 = y_1 + 2
-10 - 2 = y_1
y_1 = -12
Therefore, the coordinates of the endpoint X, are: X(6, -12).
Learn more about the midpoint formula on:
brainly.com/question/13115533
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Answer:
<h2>x = 5</h2>
Step-by-step explanation:

Answer:
The total volume is 41.1 cubic meters.
Step-by-step explanation:
Volume of the platform is:
1.8m * 1.8m * 10m = 32.4 m^3
Volume of the ramp is half of a prism with same dimensions as that ramp:
0.5 * 6m * 1.8m * 1.8m = 9.7 m^3
Total: (32.4 + 9.7) m^3 = 41.1m^3