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MatroZZZ [7]
3 years ago
6

Need help with the blanks

Mathematics
1 answer:
Crazy boy [7]3 years ago
3 0
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
------------------------------------------------------
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
-----------------
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
-----------------
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
-----------------
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.
-----------------
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
-----------------
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
-----------------
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
-----------------
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
-----------------
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
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4. 8th degree

Step-by-step explanation:

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Ge A flower bed has the shape of a rectangle 24 feet long and 9 feet wide. What is its area in square yards? Be sure to include
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Answer:

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Step-by-step explanation:

convert the dimensions into yards using the conversion

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3 years ago
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daser333 [38]

y=(-2x)+5

Step-by-step explanation:

4 0
2 years ago
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3ft long with a diameter of 2.2 ft . S
Contact [7]

4 minutes 34 seconds will takes to empty the tank, if the starts completely full and oil drained at a rate of 2.5 ft^{3} per minute.

Step-by-step explanation:

              The given is,

                         Tank is shaped like a cylinder that is 3 ft long with a diameter of 2.2 ft.

                          Oil drained at a rate of 2.5 ft^{3} per minute.

Step:1

       Time taken to dry the oil tank is,

                           T   = \frac{Volume of oil}{Oil drain rate}  ....................................(1)

Step:2

      Volume of the oil is,

                           V = \pi  r^{2} h.................................................(2)

      Where, r - Radius of Cylinder

                             r = \frac{d}{2}

                             r = \frac{2.2}{2}

                             r = 1.1 ft

      From eqn (1),

                        V =  \pi × 1.1^{2} × 3

                           = 11.40398 ft^{3}

Step:3

     From equation (1)

                           = \frac{11.40398}{2.5}

                           = 4.56

                           = 4.56 minutes

                      T  = 4 minutes 34 seconds

Result:

      Time taken to dry the oil tank is 4 minutes 34 seconds, if a cylinder is 3 ft long with a diameter of 2.2 ft and oil is drained at a rate of 2.5ft^3 per minute.

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2 years ago
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Answer:

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Step-by-step explanation:

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