State a true conclusion. 1) If two planes intersect, their intersection is a line. 2) Plane R and plane S intersect. Conclusion:
2 answers:
Answer: The answer is "the intersection is a line".
Step-by-step explanation: The concept of lines and planes that we studied in geometry are familiar to us. For example-
(i) The intersection of two lines is a point.
(ii) A plane consists of a line and a point not on the line, etc.
Like these, we have another fact that suppose there are two planes. Then we have two options
(a) They do not intersect with each other.
(b) If they do so, then their intersection is a line.
See the attached figure, there are two planes P and Q, which intersect at the line AB.
Since the given two planes intersect, the using the above fact we can say that their intersection is a line.
Thus, the conclusion is "the intersection of two intersecting planes is a line."
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Answer:
Step-by-step explanation:
Width of the sign made by Darius initially = 2 feet
Length of the sign = 2 feet 6 inches
Dimension of the flyer are 10 inches by 8 inches. Since, in original sign the measure of length is greater, therefore, the length of flyer is 10 inches and its width is 8 inches.
In order to find the scale factor we must convert the lengths and widths to same units. Lets convert the length and width of sign into inches.
Since, 1 feet = 12 inches
Length of the sign = 2 feet 6 inches = 2(12) + 6 inches = 30 inches
Width of the sign = 2 feet = 2(12) inches = 24 inches
Now we can find the scale factor by either comparing the lengths or widths of both the designs. Scale factor will be equal to the ratio of corresponding lengths/widths.
So, the scale factor would be:
Length of Flyer : Length of Sign
= 10 inches : 30 inches
= 1 : 3
=
This shows, the length of flyer is times as that of the sign. So, the scale factor that Darius must use is
. The length and width of the flyer are
as that of the sign.
The same scale factor would result if we would have used the ratio of widths instead of the lengths.
Scale Factor = Width of Flyer : Width of sign
= 8 : 24
= 1 : 3
Therefore, Darius must type the scale factor of in his computer to get the size of the flyer.