Help with this ASAP :) Solve the system of linear equations by graphing.
2 answers:
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Answer:
Step-by-step explanation:
Well, since there is no image I thought I would provide what a rectangle would probably look like in your case. The rectangle can be split into half parts 4 ways.
<h2><em><u>Ways it can be Split:</u></em></h2>1. We can split it the hotdog way, or staright down the rectangle (drawing provided down below)
2. We can split it the Hamburger way, again drawing is provided.
3. We can split it from the top-left corner to the bottom-right, and the opposite way around.
Answer:
35.
So that we have:
KLN = 54 JKN =36
LKN = 72 NMJ = 18
KNM = 126 JLM = 72
LJM = 90 KLM = 126
36.
CE = 6√13
37.
m∠Z = 88°
38.
m∠GFE = 85
Step-by-step explanation:
35.
As KLMN is a kite:
+) KL = KN
=> Triangle KLN is an isosceles triangle.
=> m∠KLN = m∠ KNL = m∠KNJ = 54°
In triangle KLN, total measure of three internal angles are 180 degree, so that: m∠KLN + m∠ KNL + m∠ LKN = 180°
=> 54 + 54 + m∠ LKN = 180°
=> m∠ LKN = 180 - 54 - 54 = 72°
+) KM is the bisector of both Angle LKN and Angle LMN
So that we have:
- m∠JKN = 1/2 m∠LKN = 1/2 * 72 = 36°
- m∠NMJ = 1/2 m∠LMN = 1/2 * 36 = 18°
+) KM and LN is perpendicular to each other at point J
=> m∠LJM = 90°
+) m∠KLM = m∠KNM; m∠KLM + m∠KNM + m∠LKN + m∠LMN = 360°
=> m∠KLM + m∠KLM + 72 + 36 = 360
=> 2 m∠KLM = 360 - 72 - 36 = 252
=> m∠KLM = 252/2 = 126 = m∠KNM
+) We have: m∠KLM = m∠KLN + m∠JLM
=> m∠JLM = m∠KLM - m∠KLN = 126 - 54 = 72
36.
As BCDE is a kite, we have:
+) BC = BE; CD = DE = 21
+) BD is perpendicular to CE and intersect each other point F
=> Angle CFD = 90
=> Triangle CFD is the right triangle
According to Pythagoras theorem: CF^2 + DF^2 = CD^2
=> CF^2 = CD^2 - DF^2 = 21^2 - 18^2 = 441 - 324 = 117
=> CF =
+) According to the feature of a kite shape, F is midpoint of CE
=> CF = FE = 1/2 x CE
=>CE = 2 x CF = 2 x
So that CE = 6√13
37.
As given, WXYZ is a kite shape.
According to the feature of a kite shape, angle ZWX and angle ZYX are equal to each other.
=> ∠ZWX = ∠ZYX
=> 8x -23 = 6x +11
=> 8x - 6x = 11 + 23
=> 2x = 34
=> x = 34/2 = 17
=> ∠ZWX = 8x - 23 = 8*17 - 23 = 113°
=> ∠ZWX = ∠ZYX = 113°
As WXYZ is a kite shape, so that total measure of 4 internal angles of it are 360 degree
So that we have:
∠Z + ∠ZWX + ∠ZYX + ∠WXY = 360
=> ∠Z + 113 + 113 + 46 = 360
=> ∠Z = 360 -113 -113-46 = 88°
So that the measure of ∠Z is 88°
38.
As GDEF is a kite shape. As we can see, GE is the longer diagonal, so that it is the bisector of both Angle DGF and Angle DEF.
H is on GE and GE is the bisector of Angle DEF, so we have:
m∠HEF = m∠GEF = 1/2. m∠DEF = 1/2 . (12x- 16)= 6x - 8
As GDEF is a kite shape so that the two diagonals DF and GE are perpendicular to each other, so that: m∠EHF = 90
In the triangle EHF, m∠EHF = 90
=> EHF is a right triangle
=> m∠HEF + m∠EFH = 90
=> 6x - 8 + 3x -1 = 90
=> 9x = 90 + 8 + 1 = 99
=> x = 99/9 =11
=> m∠HEF = 6x - 8 = 6*11 - 8 = 58 = m∠GEF
GE is the bisector of both Angle DGF
=> m∠EGF = 1/2. m∠DGF = 1/2 . 74 = 37
In the triangle GEF, total measure of three internal angles are 180
=> m∠GFE + m∠EGF + m∠GEF = 180
=> m∠GFE + 37 + 58 = 180
=> m∠GFE = 85