<u>Included sides AE and BE</u> need to be given as congruent to prove that triangle AEC is congruent to triangle BED by the Angle-Side-Angle (ASA) Congruence Theorem.
According to the Angle-Side-Angle (ASA) Congruence Theorem, if two angles and an included side of a triangle is congruent to corresponding two angles and an included side of another triangle, both triangles can be proven to be equal or congruent to each other.
We are know the following from the given image:
<AEC = <BED (vertical angles are congruent)
<EAC = <EBD (congruent angle)
This implies that two angles (<AEC and <EAC) in triangle AEC are congruent to two corresponding angles (<BED and <EBD) in triangle BED.
Therefore, to prove that both triangles are congruent by ASA, we need to be given that the included sides AE and BE are congruent.
Learn more about Angle-Side-Angle (ASA) Congruence Theorem here:
brainly.com/question/23968808
Answer:
- minimum value: 2
- axis of symmetry: x = -1
Step-by-step explanation:
A graphing calculator can answer this very quickly. The graph shows the minimum is 2, at x=-1. The axis of symmetry is the vertical line through that point so is x = -1.
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The extreme value of the quadratic ax^2 +bx +c is found at x = -b/(2a). Your quadratic has a=6 and b=12, so the extreme value is located on the line of symmetry at ...
x = -12/(2·6)
x = -1 . . . . . . . . . . line of symmetry; x-coordinate of vertex
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The leading coefficient of this even-degree polynomial is <em>positive</em>, so we know it opens <em>upward</em>. That means the vertex is a minimum.
The value of the function at the vertex is ...
f(-1) = 6(-1)^2 +12(-1) +8 = 6 -12 +8 = 2
The minimum value is 2.
Subsitute -4y for x
-4y+6y=18
2y=18
divide both sides by 2
y=9
sub back
x=-4y
x=-4(9)
x=-36
(x,y)
(9,-36)
Complete question :
The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.
Answer:
17
Step-by-step explanation:
From Pythagoras :
Hypotenus = sqrt(opposite² + adjacent²)
From the diagram
l = sqrt((l-9)² + 15²)
l² = (l² - 18x + 81 + 225)
Square both sides
l² = l² - 18x + 306
l² - l² = 306 - 18x
18l = 306
l = 306/18
l = 17
