Question 1:Look at the first attached image.
We want to solve for the height of the smaller building. Let's start by making a right triangle with angle of 15 degrees and adjacent side of 51 m.
Let's solve for the other leg. Multiply the tangent with 51 m to get the length of the other leg.


Now, subtract that from 207 to get the height of the smaller building.

That's your answer.
Question 2:
The angle of elevation is congruent to the angle of depression because they are alternate interior angles.
Thus, you can choose the 1st and 4th choices as your answer.
Question 3:Look at the second attached image.
Angle E is congruent to angle D for the same reasons mentioned in the last question.
We can create an equation.

Distributive property

Subtract both sides by 1 and 2x

Since E and D are congruent, just plug this value into one of the equations for E or D. You get 46.
The third choice is your answer. Hope this helps! :)
Answer:
Breadth = 8 cm
Length = 17 cm
Step-by-step explanation:
Given rectangle:
Breadth = x cm
Length = x + 9 cm
Area = length * breadth
= x * (x + 9)
= x² + 9x
Rectangle with length and breadth increased:
Breadth = x + 3 cm
Length = x + 9 + 3 = x + 12 cm
Area = 84 + (x² + 9x) cm²
(x +3) * (x +12) = 84 + x² + 9x
Use FOIL method
x*x + x*12 + 3*x + 3*12 = 84 + x² + 9x
x² + 12x + 3x + 36 = 84 + x² + 9x {add the like terms}
x² + 15x + 36 = 84 + x² + 9x
x² + 15x + 36 - 84 - x² - 9x = 0
6x - 48 = 0
6x = 48
x = 48/6
x = 8
Breadth = x = 8 cm
Length = x + 9 = 8 +9 = 17 cm
Answer:
x < -5
Step-by-step explanation:
- 2x - 7 > x+ 8
Add 2x to each side
- 2x+2x - 7 > x+2x+ 8
-7 > 3x+8
Subtract 8 from each side
-7-8 > 3x+8-8
-15 > 3x
Divide by 3
-15/3 > 3x/3
-5 >x
x < -5
Answer:
The per hour rate is 0.5 inches per hour
Step-by-step explanation:
Here, we want to calculate the rate at which the level of the water increased
Mathematically, we can get this by dividing the amount of increment by the time it took
That would be 3 inches divided by 6 hours
= 3/6 = 0.5 inches per hour
Answer:
7 x 7 x 7= 49 x 7= 343
3 x 3 x 3 x 3= 9 x 3 x 3= 27 x 3= 81