Answer:
75
Step-by-step explanation:
<em><u>Refer to attachment</u></em>
As the first step extending the segment BC until intersection with AD.
Since ∠A + ∠B = 90° we get right triangle by extending CB
Naming the segments a, b, c, d as pictured
<u>The are of (ABCD) is equal to sum of areas of two right triangles:</u>
<u>Substitute d with a-c as a = c+d, then:</u>
- Area = 1/2(ac+bc) + 1/2b(a-c) = 1/2(ac + bc + ab - bc) = 1/2(ab + ac)
- Area = 1/2(ab+ac)
<u>Applying Pythagorean to small triangle:</u>
- 10² = b² + (a-c)²
- 100 = b² + a² - 2ac + c²
<u>Applying Pythagorean to bigger triangle:</u>
- 20² = (a+b)² + c²
- 400 = a² + 2ab + b² + c²
<u>Subtracting equations we got:</u>
- 400 - 100 = a² + 2ab + b² + c² - (b² + a² - 2ac + c²)
- 300 = 2ab + 2ac
<u>This gives us the 4 times of the area which is 1/2(ab + ac), so the area is </u>
Area of a trapezoid is found with the formula, A=(a+b)/2 x h.
Answer:
30% x 350000 + 105000
Step-by-step explanation:
30
100
(350000)
=(
30
100
)(
350000
1
)
=(
3
10
)(
350000
1
)
=
(3)(350000)
(10)(1)
=
1050000
10
=105000
Answer:
A.6
Step-by-step explanation:
Step 1: Do the parenthesis first, 4+2 = 6
Step 2: Multiply: 6 x 1/6 = 1
Step 3: 1 + 5 = 6, So the answer is A. 6
The value of <em>x</em> where by exterior angles theorem, ∠DCO equals 2·x, 69° equals the sum of ∠DCO and x° is <em>x </em>= 23°
<h3>What is the exterior angles theorem?</h3>
The exterior angles theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
The given parameters are;
Points on the circle are; ABCD
Straight lines = AOBE and DCE
Segment CO = Segment CE
∠AOD = 69°
∠CEO = x°
∠OCD = ∠ODC base angles of isosceles triangle
69° = ∠x° + ∠ODC exterior angle of a triangle
∠DOC = 180 - 2×∠ODC (Angle sum property of a triangle)
180 - 2×∠ODC + x° + 69° = 180° (Sum of angles on a straight line are supplementary)
x° + 69° - 2×∠ODC = 0
∠ODC = 2·x° (exterior angle of a triangle is equal to the sum of the opposite interior angles)
69° = x° + ∠ODC = x° + 2·x° = 3·x° (substitution property of equality)
69° = 3·x°
x = 69° ÷ 3 = 23°
Learn more about angles in a triangle here:
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