Answer:
x=3
z=65
Step-by-step explanation:
6x+97 and 14x+73 are vertical angles which means they are equal
6x+97= 14x+73
Subtract 6x from each side
6x-6x+97= 14x-6x+73
97 = 8x +73
Subtract 73 from each side
97-73 = 8x+73-73
24 = 8x
Divide each side by 8
24/8 = 8x/8
3 = x
Now we need to find z
6x+97 and z are supplementary angles which means they add to 180
6x+97 +z = 180
6(3) +97 +z = 180
18+97+z=180
Combine like terms
115+z = 180
Subtract 115 from each side
115-115 +z=180-115
z = 65
The common point between y = 2x + 5 and y = (1/2)x + 6 will have the same values for x and y.
Therefore, set the two y expressions equal to obtain
2x + 5 = (1/2)x + 6
Subtract (1/2)x from each side.
(3/2)x + 5 = 6
Subtract 5 from each side.
(3/2)x = 1
Multiply each side by 2/3.
x = 2/3.
From the first equation, obtain
y = 2*(2/3) + 5 = 19/3.
The common point is (2/3, 19/3). It is not equal to (3, 1/2).
Answer: False
Answer:
b = 9.1units
Step-by-step explanation:
Find the diagram attached
Using the similarity theorem of triangle
WX/XZ = WY/WX
Substitute;
b/a+5 = 6/b
b² = 6(a+5) ... 1
Also according to pythagoras theorem on triangle WYX;
b² = 6²+a²...2
Equate 1 and 2
6(a+5) = 6²+a²
6a+30 = 36 + a²
a²-6a+36-30 = 0
a²-6a+6 = 0
a = 6±√36+4(6)/2
a = 6±√60/2
a = 6±7.745/2
a = 13.745/2
a = 6.8725
Recall that
b² = 6²+a²
b² = 36+6.8725²
b² = 83.2313
b = 9.12units
b = 9.1units
Answer:
angle1=70
angle2=65
angle4=115
angle7=45
angel6=45
angle5=45
Step-by-step explanation:
110+angle1 = 180
angle1 =180-70
angle1 = 70
115+angle2=180
angle2=180-115
angle2=65
angle4=115 because lines are parallel
angle1+angle2+angle7=180 because triangle
70+65+angle7=180
135+angle7=180
angle7=180-135
angle7=45
angel6=45
angle5=45