Triangle DEF was dilated according to the rule DO,(x,y) to create similar triangle D'E'F'.
2 answers:
A dilation is a transformation, with center O and a scale factor of k
that is not zero, that maps O to itself and any other point P to P'.
The center O is a fixed point, P' is the image of P, points O, P and P'
are on the same line.
Thus, a dilation with centre O and a scale factor of
maps the original figure to the image in such a way that the
distances from O to the vertices of the image are times the distances
from O to the original figure. Also the size of the image are <span> times the
size of the original figure. Also the two resulting figures (i.e. the image and the pre-image are congruent)
Thus in the dilation of triangle DEF, the following are true.</span>
<span>∠F corresponds to ∠F'.
The measure of ∠E' is the measure of ∠E.
△DEF ≈ △D'E'F'</span>
Thus, a dilation with centre O and a scale factor of
Thus in the dilation of triangle DEF, the following are true.</span>
<span>∠F corresponds to ∠F'.
The measure of ∠E' is the measure of ∠E.
△DEF ≈ △D'E'F'</span>
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Answer:
a.
b.
Step-by-step explanation:
I attach the diagram of the new water tank.
a. In order to find the volume of the tank in cubic feet, we will need to calculate the volume of a cylinder. We know that its base measures and its height is
.
The volume ''V'' of a cylinder is :
Where '''' is the diameter of the base and ''
'' is the height of the cylinder.
If we replace all the data in the equation :
We found out that the volume of the tank in cubic feet is
b. We know that 1 cubic foot of water is equal to 7.5 gallons. To find the amount of gallons that the new tank can hold, we need to do an unit conversion.
This equivalence is given to us :
⇒ Using the equivalence ⇒
Finally, the new tank will hold of water.
The first digit of the password can be any of the ten digits - 10 possibilities.
A digit cannot be repeated, so the second digit can be any digit except the one you chose for the first digit - 9 possibilities.
The third digit can be any digit except the digits you chose for the first and second digit - 8 possibilities.
Using the rule of product:
There are 720 passwords.
A digit cannot be repeated, so the second digit can be any digit except the one you chose for the first digit - 9 possibilities.
The third digit can be any digit except the digits you chose for the first and second digit - 8 possibilities.
Using the rule of product:
There are 720 passwords.