The height of the green pyramid constructed by Natalie while playing with magnetic building tiles is 26.25 cm.
<h3>
Volume of the orange pyramid</h3>
The volume of the orange pyramid is calculated as follows;
V = ¹/₃Ah
where;
- A is the base area of the pyramid
- h is the height of the pyramid
V = ¹/₃ x (7²) x 5
V = ¹/₃ x (245 cm³)
<h3>
Volume of the green pyramid</h3>
Voume = 21 x [¹/₃ x (245 cm³)]
Volume = 1,715 cm³
<h3>Height of the green pyramid</h3>
V = ¹/₃Ah
3V = Ah
h = 3V/A
h = (3 x 1715) / (14²)
h = 26.25 cm
Learn more about area of pyramid here: brainly.com/question/22744289
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Answer:
Step-by-step explanation:
-14 + 2x + 3 = 4x - 13 - 7x
We can first add the numbers and coefficients on either side:
2x - 11 = -3x - 13
Then, we can add 3x to both sides:
5x - 11 = -13
We can add 11 to both sides
5x = -13 + 11 = -2
Lastly, we can divide both sides by 5
x = -2 / 5
You would start by finding the area of the circle and then finding the area of the rectangle. After finding both, subtract the area of the rectangle from that of the circle. <span />
From the law of sines, we have:

,
where x and y are the sides opposite to angles X and Y, respectively.
Substituting the known values, we have:

, thus

.
Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.
We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.
Thus, there is only one triangle that can be formed under these conditions.