Answer:
Δ JKL is similar to Δ ABC ⇒ D
Step-by-step explanation:
Similar triangles have equal angles in measures
In ΔABC
∵ m∠A = 15°
∵ m∠B = 120
∵ The sum of the measures of the interior angles of a Δ is 180°
∴ m∠A + m∠B + m∠C = 180°
→ Substitute the measures of ∠A and ∠B
∵ 15 + 120 + m∠C = 180
→ Add the like terms in the left side
∴ 135 + m∠C = 180
→ Subtract 135 from both sides
∴ 135 - 135 + m∠C = 180 - 135
∴ m∠C = 45°
The similar Δ to ΔABC must have the same measures of angles
If triangles ABC and JKL are similar, then
m∠A must equal m∠J
m∠B must equal m∠K
m∠C must equal m∠L
∵ m∠J = 15°
∴ m∠A = m∠J
∵ m∠L = 45°
∴ m∠C = m∠L
∵ m∠J + m∠K + m∠L = 180°
→ Substitute the measures of ∠J and ∠L
∵ 15 + m∠K + 45 = 180
→ Add the like terms in the left side
∴ 60 + m∠K = 180
→ Subtract 60 from both sides
∴ 60 - 60 + m∠K = 180 - 60
∴ m∠K = 120°
∴ m∠B = m∠K
∴ Δ JKL is similar to Δ ABC
6 foot makes 4.5 foot shadow
1 foot makes=4.5/6
so 50 foot =4.5/6*50 = tree makes 37.5 foot shadow
Answer: √90=3√5⋅2=3√10
Step-by-step explanation:
Well you see partition means to separate or divide. A line segment with end points a and b can be partioneded by another point by a given ratio, and a ratio is a comparison of two numbers. For other ratios besides 1:1 , it is necessary to determine the total number of parts that the line segment must be divided into. So in your case the point is 5:7 so you to determine the point that divides your line segment you just simply add the figure 5 a and the figure 7 together and you should end up with the sum of 12.
Answer:
B) The earthquake measuring 4.5 on the Richter scale is about 32 times more intense than an earthquake measuring 3.
Step-by-step explanation:
Let Ra = log(Ia/Io), and Rb = log(Ib/Io). Then for ...
Ra - Rb = 4.5 -3.0 = 1.5
log(Ia/Io) -log(Ib/Io) = 1.5 . . . . . . . . . . . substitute the given expressions
(log(Ia) -log(Io)) -(log(Ib) -log(Io)) = 1.5 . . . expand the logs
log(Ia) -log(Ib) = 1.5 . . . . simplify
log(Ia/Ib) = 1.5 . . . . . . . . write as a single log
Ia/Ib = 10^1.5 ≈ 32 . . . . take the antilog
The ratio of intensities is about 32, corresponding to choice B.
