Answer:
The volume of the dilated prism is 
.
Step-by-step explanation:
The original prism has base area 
and a height of 
.
The volume of the original prism is 
.
The prism is dilated by a scale factor of 
.
To find the volume of the dilated prism, we multiply the volume of the original prism by 
.
Answer:
(a) 25
(b) 9.27
Step-by-step explanation:
Step 1
We have to rearrange the given days set from least to highest
35, 40, 45, 55, 60
(a) the range
Range = The highest number - The least number
= 60 - 35
= 25
(b) the standard deviation of the data set
35, 40, 45, 55, 60.
We find the Mean
Mean = Sum of values/Number of values
= 35+40+45+55+60/5
= 235/5
= 47
We can find the standard deviation now.
The formula =
√(x - Mean)²/n
= √(35 - 47)²+ (40 + 47)² + (45 - 47)² + (55 - 47)² + (60 - 47)²/5
= √144 + 49 + 4 + 64 +169/5
= √430/5
= √86
= 9.273618495
Approximately = 9.27
Answer:
1. Interior angles:- B and F
C and G
2. Corresponding angles:- E and G
F and H
A and C
B and D
3. Equal
4. Angle A = 105
Angle C = 105
Angle D = 75
Angle E = 75
Angle F = 105
Angle G = 75
Angle H = 105
5. Angle D
6. Angle B = 65
Step-by-step explanation:
1. The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles.
∴ Pair of interior angles are:- 1) B and F
2) C and G
2. Corresponding angles:- the angles which occupy the same relative position at each intersection where a straight line crosses two others.
∴ Pair of corresponding angles:- 1) A and C
2) B and D
3) E and G
4) F and H
3. Angle D and E are equal as they form alternate exterior angles.
4. Angle B = 75 degrees
Angle A = (180-B) = 105 degrees
Angle C = (180-B) = 105 degrees(interior angles)
Angle D = B = 75 degrees(corresponding angles)
Angle E = B = 75 degrees(congruent angles)
Angle F = (180-B) = 105 degrees
Angle G = B = 75 degrees(alternate interior angles)
Angle A = (180-B) = 105 degrees
5. Angle D
6. Angle F = 115 degrees
Angle B = (180-115) = 65 degrees
Answer:
0.1 8 17
Step-by-step explanation:
Answer:
input = 5
Step-by-step explanation:
y = -2x - 6
When y = -16
-16 = -2x - 6
divide by -2 on both sides,
8 = x + 3
x = 8 - 3 = 5
