Answer:
The answer is 2
Step-by-step explanation:
Use a calculator.
Answer:
(a) True
(b) False
(c) True
(d) False
(e) False
(f) True
(g) False
(h) True
(i) True
(k) True
Step-by-step explanation:
(a) Two lines parallel to a third line are parallel
True
(b) Two lines perpendicular to a third line are parallel
Only for lines on the same plane
Therefore, false
(c) Two planes parallel to a third plane are parallel
True
(d) Two planes perpendicular to a third plane are parallel
The two planes can be at an angle to each other and so intersect
Therefore, false
(e) Two lines parallel to a plane are parallel
Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect
Therefore, false
(f) Two lines perpendicular to a plane are parallel
True
(g) Two planes parallel to a line are parallel
Where the planes are not parallel to each other, they will intersect
Therefore, false
(h) Two planes perpendicular to a line are parallel
True
(i) Two planes either intersect or are parallel
True
(k) A plane and a line either intersect or are parallel
True.
B. 21 Bo; 23 Erica
C. 16 Bo; 28 Erica
D. 19 Bo; 25 Erica
Answer: D. 19 Bo; 25 Erica
Step-by-step explanation:
Let x represent the number of yoga classes that Bo teaches in a week.
Let y represent the number of yoga classes that Erica teaches in a week.
Between the two of them, they teach 44 yoga classes each week. This means that
x + y = 44 - - - - - - - - - - -1
If Erica teaches 13 fewer than twice as many as Bo, it means that
y = 2x - 13
Substituting y = 2x - 13 into equation 1, it becomes
x + 2x - 13 = 44
3x = 44 + 13 = 57
x = 57/3 = 19
y = 2x - 13 = 2 × 19 - 13
y = 25
Answer:
y = 64°
Step-by-step explanation:
From the picture attached,
m(∠E) = 90°
m(∠E) = m(∠D)
m(∠B) + 67° = 180° [pair of linear angles]
m(∠B) = 113°
m(∠C) + 75° = 180°
m(∠C) = 180° - 75°
= 105°
Since, sum of interior angles of a polygon = (n - 2) × 180°
Here, n = number of sides
For n = 5,
Sum of interior angles = (5 - 2) × 180°
= 540°
m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°
m(∠A) + 113° + 105° + m(∠D) + 90° = 540°
(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]
2(m∠D) = 232
m(∠D) = 116°
m(∠D) + y° = 180° [Linear pair of angles]
116 + y = 180
y = 64°
Answer:
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Step-by-step explanation: