Answer:
Please check the explanation.
Step-by-step explanation:
Part a)
Given that the two parallel lines are crossed by a transversal line.
Given that
m∠2 = 2x + 54 and m∠6 = 6x - 11
Angle ∠2 and ∠6 are corresponding angles.
Corresponding angles are congruent.
Thus,
m∠2 = m∠6
2x + 54 = 6x - 11
flipe the equation
6x - 11 = 2x + 54
subtract 2x from both sides
6x - 2x - 11 = 2x - 2x + 54
4x - 11 = 54
adding 11 to both sides
4x - 11 + 11 = 54 + 11
4x = 65
dvide both sides by 4
4x/4 = 65/4
x = 16.2500 (round to 4 decimal places)
Part b)
We have already determined
x = 16.2500
Given
m∠2 = 2x + 54
substitute x = 16.2500 in the euation
= 2(16.2500) + 54
= 86.5°
As angle ∠2 and angle ∠1 lie on a straight line. Hence, the sum of their angles must be 180°.
i.e.
m∠1 + m∠2 = 180°
substituting m∠2 = 86.5° in the equation
m∠1 + 86.5° = 180°
subtracting 86.5° from both sides
m∠1 + 86.5° - 86.5° = 180° - 86.5°
m∠1 = 93.5°
Therefore, the measure of angle m∠1 is:
Here, you just want to solve it by finding a common denominator.
1/5+2/7, because she read 1/5 and 2/7 of the book on separate days. The common denominator is 35.
7/35+10/35
=17/35
So that's how much of the book she read before Saturday.
Now it says that on Sunday she read 5/9 of the remaining pages, meaning:
1-17/35 should give us our answer
35/35-17/35=18/35
But since it says she read 5/9 of the remaining pages, we need to multiply 18/35 by 5/9 to get what 5/9ths of 18/35 is.
(18/35)(5/9)=2/7
Therefore she read 2/7ths of the book on Sunday.
Answer:
I'm pretty sure it is (a)
V=(4/3)(pi)(r^3)
V=(4/3)(pi)(8^3)
V=(4/3)(pi)(512)
V=(2048/3)(pi), or around 2144.660585
