For this case we have the following equation:
y = x2-4x + 3
Deriving we have the following equation:
y '= 2x-4
We equal zero and clear x:
2x-4 = 0
x = 4/2
x = 2
Substituting in the given equation we have:
y = (2) ^ 2-4 (2) +3
y = 4-8 + 3
y = -1
The vertex will be the ordered pair:
(x, y) = (2, -1)
Answer:
(x, y) = (2, -1)
option B
<h3>
Answer: x = 45</h3>
Work Shown:
x+x+90 = 180 .... all three angles of a triangle add to 180
2x+90 = 180
2x = 180-90
2x = 90
x = 90/2
x = 45
This is a 45-45-90 right triangle. We also consider it an isosceles right triangle because the base angles (45) are equal.
Answer: x = 50
Concept:
Here, we need to know the idea of alternative interior angles and the angle sum theorem.
<u>Alternative interior angles</u> are angles that are formed inside the two parallel lines, and the values are equal.
The <u>angle sum theorem</u> implies that the sum of interior angles of a triangle is 180°
If you are still confused, please refer to the attachment below or let me know.
Step-by-step explanation:
<u>Given information:</u>
AC ║ DE
∠ABC = 85°
∠A = 135°
<u>Find the value of ∠BAC</u>
∠A + ∠BAC = 180° (Supplementary angle)
(135°) + ∠BAC = 180°
∠BAC = 45°
<u>Find the value of ∠BCA</u>
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)
(85°) + (45°) + ∠BCA = 180°
∠BCA = 50°
<u>Find the value of x (∠EBC)</u>
∠EBC ≅ ∠BCA (Alternative interior angles)
Since, ∠BCA = 50°
Therefore, ∠EBC = 50°
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Non-collinear points: These points, like points X, Y, and Z in the above figure, don't all lie on the same line. Coplanar points: A group of points that lie in the same plane are coplanar. Any two or three points are always coplanar. Four or more points might or might not be coplanar.
Step-by-step explanation: