9)
Answer:
X=37/20
Explanation:
In a kite, one of the diagonals will bisect the other. So, 2(PT)=PR
By substitution, this becomes the equation
2(10x-1)=35
20x-2=35
20x=37
x=37/20
10)
Answer:
Angle TQR is 52 degrees
Explanation:
A kite only bisects one set of opposite angles, so angle TQR is congruent to angle TQP. To find angle TQP use this equation:
Angle TPQ+Angle TQP=90
This is possible because angle QTP is right(diagonals of kites are perpendicular) and because all triangles have interior angles that add up to 180 degrees. The remaining amount of degrees apart from the right angle should be 90 degrees(180-90=90).
Substitute:
38+ angle TQP= 90
Angle TQP= 52 degrees
Angle TQP is congruent to angle TQR, so
Angle TQR=52 degrees
Answer:
The volume of the regular tetrahedron is 283.5 m³
Step-by-step explanation:
The formula of the volume of the regular tetrahedron is V = 
A h, where
∵ The area of the base of a regular tetrahedron is 98.9 m²
∴ A = 98.9 m²
∵ The height of it is 8.6 m
∴ h = 8.6 m
→ Substitute them in the formula of the volume above
∵ V = (98.9)(8.6)
∴ V = 283.5133333 m³
→ Round it to the nearest tenth of a cubic meters
∴ V = 283.5 m³
∴ The volume of the regular tetrahedron is 283.5 m³
Answer: See explanation
Step-by-step explanation:
Population- Every student...
Sample- 10 students sitting together at a table in the cafeteria
Random Sample- 10 Students whose names...
Answer:
60, 75
150 165
240 255
330 345
Step-by-step explanation:
csc 4 theta = -2 sqrt(3)/3
Write in terms of sin
1/ sin (4 theta) = -2 sqrt(3)/3
Using cross products
-2 sqrt(3) = 3 sin (4 theta)
Divide each side by 3
-2 sqrt(3)/3 = sin (4 theta)
Take the inverse sin on each side
sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))
240 +360n = 4 theta
and 300 +360n = 4 theta where n is an integer
Dividing each side by 4
240/4 +360n/4 = 4/4 theta and 300/4 +360n/4 = 4/4 theta
60 + 90n = theta and 75 +90n = theta
We want all the values between 0 and 360
Let n=0
60, 75
n=1
60+90=150 and 75+90 =165
n=2
60+180= 240 75+180=255
n=3
60+270 = 330 75+ 270 =345
60£
Peter = 2 Angard
Angard = 3 Nick
Peter = 2 Angard = 6 Nick
Angard = 3 Nick
Nick = 1 Nick
6+3+1=10 Nick
60£/10 = 6£
Nick = 6£
Angvard = 3 Nick = 6£*(3) = 18£
Peter = 6 Nick = 6£*(6) = 36£
(prove: 6+18+36=60£)
