Answer: Angle XCB = 46 degrees ( ∠XCB = 46°)
Step-by-step explanation: Please refer to the picture attached for details.
A rhombus basically is a parallelogram with a diamond shape. All four sides have equal length, opposite sides are parallel and opposite angles are equal.
The sides have been labelled ABCD as stated in the question, and the point X is extended to point B to form angle XBC and also extended to point C to form angle XCB. Upon careful observation we shall notice that a triangle has been formed with sides BXC and angle X is a right angle, which measures 90 degrees.
The sum of angles in a triangle equals 180, therefore,
Angle XBC + Angle XCB + Angle X = 180
Substituting for the given values we now have the following;
4a + 12 + 6a - 2 + 90 = 180
10a + 10 + 90 = 180
10a + 100 = 180
Subtract 100 from both sides of the equation
10a = 80
Divide both sides of the equation 10
a = 8
If XCB = 6a - 2,
Substitute for the value of a
XCB = 6(8) - 2
XCB = 48 - 2
XCB = 46
Therefore angle XCB measures 46 degrees.
Jeremy is incorrect because a negative plus a negative will always be a negative.
The width would be 2.25 cm.
Answer:
In vertex form we have y = (x + 2)^2 - 10
Step-by-step explanation:
x^2+4x-6=0 is in standard form; we want it in the form y - k = a(x - h)^2.
Complete the square within x^2+4x-6=0
We get x^2 + 4x - 6 = 0 => x^2 + 4x + 4 - 4 - 6, or
y = (x + 2)^2 - 10
Comparing this to y = (x - h)^2 - 10, we see that the vertex is at
(h, k) : (-2, -10)
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>