Answers:
33. Angle R is 68 degrees
35. The fraction 21/2 or the decimal 10.5
36. Triangle ACG
37. Segment AB
38. The values are x = 6; y = 2
40. The value of x is x = 29
41. C) 108 degrees
42. The value of x is x = 70
43. The segment WY is 24 units long
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Work Shown:
Problem 33)
RS = ST, means that the vertex angle is at angle S
Angle S = 44
Angle R = x, angle T = x are the base angles
R+S+T = 180
x+44+x = 180
2x+44 = 180
2x+44-44 = 180-44
2x = 136
2x/2 = 136/2
x = 68
So angle R is 68 degrees
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Problem 35)
Angle A = angle H
Angle B = angle I
Angle C = angle J
A = 97
B = 4x+4
C = J = 37
A+B+C = 180
97+4x+4+37 = 180
4x+138 = 180
4x+138-138 = 180-138
4x = 42
4x/4 = 42/4
x = 21/2
x = 10.5
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Problem 36)
GD is the median of triangle ACG. It stretches from the vertex G to point D. Point D is the midpoint of segment AC
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Problem 37)
Segment AB is an altitude of triangle ACG. It is perpendicular to line CG (extend out segment CG) and it goes through vertex A.
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Problem 38)
triangle LMN = triangle PQR
LM = PQ
MN = QR
LN = PR
Since LM = PQ, we can say 2x+3 = 5x-15. Let's solve for x
2x+3 = 5x-15
2x-5x = -15-3
-3x = -18
x = -18/(-3)
x = 6
Similarly, MN = QR, so 9 = 3y+3
Solve for y
9 = 3y+3
3y+3 = 9
3y+3-3 = 9-3
3y = 6
3y/3 = 6/3
y = 2
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Problem 40)
The remote interior angles (2x and 21) add up to the exterior angle (3x-8)
2x+21 = 3x-8
2x-3x = -8-21
-x = -29
x = 29
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Problem 41)
For any quadrilateral, the four angles always add to 360 degrees
J+K+L+M = 360
3x+45+2x+45 = 360
5x+90 = 360
5x+90-90 = 360-90
5x = 270
5x/5 = 270/5
x = 54
Use this to find L
L = 2x
L = 2*54
L = 108
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Problem 42)
The adjacent or consecutive angles are supplementary. They add to 180 degrees
K+N = 180
2x+40 = 180
2x+40-40 = 180-40
2x = 140
2x/2 = 140/2
x = 70
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Problem 43)
All sides of the rhombus are congruent, so WX = WZ.
Triangle WPZ is a right triangle (right angle at point P).
Use the pythagorean theorem to find PW
a^2+b^2 = c^2
(PW)^2+(PZ)^2 = (WZ)^2
(PW)^2+256 = 400
(PW)^2+256-256 = 400-256
(PW)^2 = 144
PW = sqrt(144)
PW = 12
WY = 2*PW
WY = 2*12
WY = 24
The volume of sphere in terms of 
is 288 cubic inches, if the sphere has a radius of 6 inches.
Step-by-step explanation:
The given is,
A sphere has a radius of 6 inches
Step:1
Formula for volume of sphere is,
...........................(1)
where, r - radius of sphere
From given,
r - 6 inches
Equation (1) becomes,
= 
( ∵ 
= 6×6×6 =216 )
= 
( The volume of the sphere in terms of π, So keep the value of )
= 288
= 288 Cubic inches
Volume of sphere, V = 288 Cubic inches
Result:
The volume of sphere in terms of is 288 cubic inches, if the sphere has a radius of 6 inches.
Answer:
M = 8 N = 10
Step-by-step explanation:
Multiplying exponents adds the exponent, meaning that inside of the brackets, it is a^4 * b^5. Multiply the exponents by two because you are squaring the entire equation. Therefore, m=8 and n=10
Let N be the number to find
firstly: 66 2/3 = 200/3 = 66.6666 & in % it's = 0.66666
secondly N x 0.6666= 90 then N = 90/0.6666 =135
Answer:
See explanation
Step-by-step explanation:
To find the percentage of a number, multiply the number by the decimal form of the percentage.
To find the decimal point of a percentage, remove the percent sign, then move the decimal point two spaces to the left. For example, 25% becomes 0.25.
Now, let's move on to solving the problems.
1. 0.22 * 198 = 43.56 (option #4)
2. 0.07 * 980 = 68.6 (option #2)
3. 0.15 * 75 = 11.25 (option #3)
4. 0.45 * 62 = 27.9 (option #1)
