Answer:
Step-by-step explanation:
x = 0.8 + 0.2y
Answer:
- ∠CDE ↔ 50°
- ∠FEG ↔ 75°
- ∠ACB ↔ 55°
Step-by-step explanation:
To solve angle problems like this, you make use of three relations:
- linear angles have a sum of 180°
- angles in a triangle have a sum of 180°
- vertical angles have the same measure
The attached diagram shows the measures of all of the angles of interest in the figure. The ones shown in blue are the ones that have the measures and names on the list of answer choices.
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A good place to start is with the linear angle pair at A. Since the sum of the two angles is 180°, the angle at A that is inside the triangle will be ...
180° -130° = 50°
Then the missing angle in that triangle at C will have the measure that makes the sum of triangle angles be 180°:
∠ACB = 180° -50° -75° = 55° . . . . . this is one of the angles on your list
Similarly, the angle at E inside triangle FEG will have a measure that makes those angles have a sum of 180°:
∠FEG = 180° -60° -45° = 75° . . . . . this is one of the angles on your list
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The two angles whose measures we just found are vertical angles with the base angles in triangle CDE, so that triangle's angle D will have a measure that makes the total be 180°.
∠CDE = 180° -55° -75° = 50° . . . . . this is one of the angles on your list
Since the dimensions are 40 ft by 60 ft, and 16 ft high, I assume the floor of the room is shaped like a rectangle.
Each wall is a rectangle. Two walls measure 40 ft by 16 ft, and two walls measure 60 ft by 16 ft.
lateral area = 40 ft * 16 ft * 2 + 60 ft * 16 ft * 2
lateral area = 1280 ft^2 + 1920 ft^2
lateral area = 3200 ft^2
EF = 12
Step-by-step explanation:
Step 1 :
The square of side 18 in is divided into 3 parts of equal area by the polygonal chain
So we have
Area of the figure ABCE = Area of the figure AECF = Area of the figure AFCD
Step 2 :
Area of figure ABCE is Area of the triangle AME + Area of the trapezium EMBC
Area of triangle AME = 1/2(ME )(AM) where ME is the base and AM = 9 is the height of the triangle ( AM = 9 since M is the midpoint of AB)
Area of triangle AME = 1/2(ME )9 = 9/2(ME)
Area of the trapezium EMBC = 1/2(ME +BC)(MB) Where ME and BC are the 2 parallel sides and MB is the distance between them
Area of the trapezium EMBC = 1/2(ME+18)9 = 9/2(ME+18)
Therefore
Area of figure ABCE = 9/2(ME) + 9/2(ME+18)
= 9/2(ME +ME+18)
But we know that the area of this figure is 1/3 of the area of the square = 1/3(18*18) = 108
So, 9/2(ME +ME+18) = 108 => 2 ME + 18 = 24 = > ME = 3
Step 3 :
Using the same procedure as above we get, FN = 3
Also we have
ME + EF + FN = 18 ( side of the square)
3 + EF + 3 = 18 => EF = 12
Answer:
13/15
Step-by-step explanation:
Solve using implicit differentiation:
First take derivative:
6y
-3
-10x+7 = 0
Next isolate the
:
6y
-3
= 10x-7
(6y-3) = 10x-7
= 
Finally plug in the point (2,3):
