We have the base measurement for the triangles composing the sides. We need their altitude.
Imagine a right triangle with these sides:
(1) from the apex of the pyramid to the point on the base directly underneath it (471 ft);
(2) from the middle of base edge to the point underneath the apex (half of 708 ft = 354 ft);
(3) the hypotenuse, the altitude of a triangular side.
Using the Pythagorean Theorem, we find the hypotenuse to be
√(471^2 + 354^2) = about 589.2 feet
Now we add up the four triangles' areas. Each is base * altitude / 2, so:
4 x 708 x 589.2 / 2
= 2 x 708 x 589.2
= 834,307.2 square feet, the lateral area.
Answer:
1.Triangle is heavier than a square.
2.Circle is lighter than the triangle and square.
3.3 squares won't be balanced between one triangle.
Step-by-step explanation:
Imagine Triangle is 10 and Square is 3
Triangle is heavier.
Imagine Circle is 1
3+3+3=9 also 3 squares
3 squares + 1 circle = 10
as one circle equals 1.
Here is the solution...
1) ![\sqrt[3]{135} \\](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%5C%5C)
Solution
We can rewrite ![\sqrt[3]{135} = \sqrt[3]{27} *\sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D%20%5Csqrt%5B3%5D%7B27%7D%20%2A%5Csqrt%5B3%5D%7B5%7D)
Here, ![\sqrt[3]{27} = 3](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%20%3D%203)
Now substitute the value, we get
![\sqrt[3]{135} = 3 \sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D%203%20%5Csqrt%5B3%5D%7B5%7D)
The answer is ![3\sqrt[3]{5}](https://tex.z-dn.net/?f=3%5Csqrt%5B3%5D%7B5%7D)
2) ![-5\sqrt[3]{40} Solution[tex]-5\sqrt[3]{40} = -5\sqrt[3]{8} *\sqrt[3]{5}](https://tex.z-dn.net/?f=-5%5Csqrt%5B3%5D%7B40%7D%20%3C%2Fp%3E%3Cp%3E%3Cstrong%3ESolution%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%5Btex%5D-5%5Csqrt%5B3%5D%7B40%7D%20%3D%20-5%5Csqrt%5B3%5D%7B8%7D%20%2A%5Csqrt%5B3%5D%7B5%7D)
Here ![\sqrt[3]{8} = \sqrt[3]{2^{3} } = 2\\](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%20%5Csqrt%5B3%5D%7B2%5E%7B3%7D%20%7D%20%3D%202%5C%5C)
Therefore, we get ![-5*2\sqrt[3]{5} = -10 \sqrt[3]{5}](https://tex.z-dn.net/?f=-5%2A2%5Csqrt%5B3%5D%7B5%7D%20%3D%20-10%20%5Csqrt%5B3%5D%7B5%7D)
The answer is-10 \sqrt[3]{5}[/tex]
2) ![2\sqrt[3]{5} * 4\sqrt[3]{8}](https://tex.z-dn.net/?f=2%5Csqrt%5B3%5D%7B5%7D%20%2A%204%5Csqrt%5B3%5D%7B8%7D)
Solution
![\sqrt[3]{8} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%202)
Now plug in the above in the given expression, we get
{2*4*2 = 16]
The answer is ![16\sqrt[3]{5}](https://tex.z-dn.net/?f=16%5Csqrt%5B3%5D%7B5%7D)
Answer: B.20
Step 1: Understand the graph
In the graph provided, each line goes up by 10 on the y-axis, with the graph marking each 50. On the x-axis, every 5 lines is equal to 1, as indicated on the graph.
Step 2: Find the unit rate
To find the unit rate, we need to find where the line hits 1 on the x-axis. To do so, go to one on the x-axis, and go up until you find where the line hits. Then we see the value on the y-axis to know the unit rate. In this case, it is on the second line above. Since we established in step 1 that each line is equal to 10 on the y-axis, we know that the two lines will be equal to 20.
This is your answer! The unit rate is 20. Hope this helps! Comment below for more questions.