According to the details provided in the question, m∠2 = 41°, m∠5 = 94°, and m∠10 = 109°. Since ∠2 is congruent to ∠9 (alternate interior angles), we establish that m∠2 = m∠9 = 41°. Utilizing the angle sum property, we have m∠8 + m∠9 + m∠10 = 180°, leading to m∠8 + 41 + 109 = 180°. Thus, m∠8 equates to 30°. From the triangle's angle sum, m∠2 + m∠7 + m∠8 = 180°, resulting in 41 + m∠7 + 30 = 180°. Consequently, m∠7 calculates to 109°. Also, m∠6 + m∠7 = 180°, so m∠6 comes to 71°. Given that m∠5 + m∠4 = 180°, we have m∠4 = 86°. Lastly, using the triangle angle sum theorem again, m∠4 + m∠3 + m∠9 = 180°, so m∠3 calculates to 53°. Thus, through the angle relationship, m∠1 + m∠2 + m∠3 = 180°, leading to m∠1 = 86°.
Cost for 6 days of climbing = $10 * 6 = $60
Cost for a pair of shoes = $84
Total expenditure = $169
Thus, the cost for one harness = $169 - $(84+60)
harness = $169 - $144 = $25
Thus, the final answer is $25.
Response:
0.14 s
Detailed breakdown:
s = -2.7 t² + 40t + 6.5
Set s = 12
12 = -2.7t² + 40t + 6.5 Rearranging yields
-2.7t² + 40t + 6.5 - 12 = 0
-2.7t² + 40t - 5.5 = 0
Utilize the quadratic formula
a = -2.7; b = 40; c = -5.5
x = 7.41 ± 7.27
x₁ = 0.14; x₂ = 14.68
The graph indicates roots at x₁ = 0.134 and x₂ = 14.68.
The surface of the Moon stands at -12 ft. Thus, the ball will reach a height of 12 ft above the Moon’s surface (crossing the x-axis) at 0.14 s.
The second root indicates when the ball is again 12 ft above the lunar surface as it descends.
