Answer:
Step-by-step explanation:
The given postulate If two lines intersect, then they intersect in exactly one point is true because whenever the two lines intersect they intersect at one point only and we know that a postulate is a statement that we accept without proof.
The given theorem If two distinct planes intersect, then they intersect in exactly one line is true as theorem is a statement that has been proved and it has been proved that if two distinct planes intersect, then they intersect in exactly one line.
The figures are drawn to prove them.
Problem 1
<h3>Answer:
104 cubic inches</h3>
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Explanation:
The prisms are similar so they have the same shape, but different sizes.
The linear scale factor from small to large is:
large/small = 10/4 = 2.5
Meaning that we multiply each dimension of the smaller prism by 2.5 to get the corresponding side length of the larger prism
4*2.5 = 10
This linear scale factor is then cubed to get the volume scale factor
(2.5)^3 = 15.625
Which tells us:
larger volume = 15.625*(smaller volume)
smaller volume = (larger volume)/15.625
smaller volume = (1625)/15.625
smaller volume = 104 cubic inches
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Problem 2
<h3>Answer: 650 square inches</h3>
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Explanation:
We will go back to the linear scale factor of 2.5
This time, we square it to get (2.5)^2 = 6.25
This is the surface area scale factor.
larger surface area = 6.25*(smaller surface area)
larger surface area = 6.25*(104)
larger surface area = 650 square inches
The answer is 20000000000 1 plus 1 is two and 2 times 10000000000 is 20000000000
Answer:
(x-13)(x+3) = f(x) = x^2 -10x -39
Step-by-step explanation:
Answer:
Step-by-step explanation:
A geometric mean is just ![\sqrt[n]{term one * term two * term three * etc.}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bterm%20one%20%2A%20term%20two%20%2A%20term%20three%20%2A%20etc.%7D)
, where n is the number of terms.
i.e. Geometric mean of 5, 6, 7: there are three values, so the mean is ![\sqrt[3]{5*6*7}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B5%2A6%2A7%7D)
