Answer:
Step-by-step explanation:
Answer:
x = 7
Step-by-step explanation:
Notice that in the triangle, the angle is either known or in terms of x. This means we can make an equation: 82 + (9x - 6) + (6x - 1) = 180. Now, add up tthe terms to get 15x + 75 = 180, or 15x = 105 or x = 7.
Question 9
Given the segment XY with the endpoints X and Y
Given that the ray NM is the segment bisector XY
so
NM divides the segment XY into two equal parts
XM = MY
given
XM = 3x+1
MY = 8x-24
so substituting XM = 3x+1 and MY = 8x-24 in the equation
XM = MY
3x+1 = 8x-24
8x-3x = 1+24
5x = 25
divide both sides by 5
5x/5 = 25/5
x = 5
so the value of x = 5
As the length of the segment XY is:
Length of segment XY = XM + MY
= 3x+1 + 8x-24
= 11x - 23
substituting x = 5
= 11(5) - 23
= 55 - 23
= 32
Therefore,
The length of the segment = 32 units
Question 10)
Given the segment XY with the endpoints X and Y
Given that the line n is the segment bisector XY
so
The line divides the segment XY into two equal parts at M
XM = MY
given
XM = 5x+8
MY = 9x+12
so substituting XM = 5x+8 and MY = 9x+12 in the equation
XM = MY
5x+8 = 9x+12
9x-5x = 8-12
4x = -4
divide both sides by 4
4x/4 = -4/4
x = -1
so the value of x = -1
As the length of the segment XY is:
Length of segment XY = XM + MY
= 5x+8 + 9x+12
= 14x + 20
substituting x = 1
= 14(-1) + 20
= -14+20
= 6
Therefore,
The length of the segment XY = 6 units
Answer : d. 438.5 ft
The diagram for the given statement is attached below.
Two sides AB and AC are equal so the angle B = angle C
WE know sum of three sides of a triangle = 180
angle A + angle B + angle C = 180
55 + B + C = 180
B + C = 180 -55 = 125
B and C are equal so we divide 125 by 2
angle B = 62.5 and angle C = 62.5
Now we apply sin law
150 * sin(55) = sin(62.5) * a
122.8728066 = sin(62.5) * a
a = 
a= 138.52 feet
To find perimeter we add all the sides
150 + 150 + 138.52 = 438.52 feet
