Answer:
Parallel postulate : ALTERNATE INTERIOR ANGLES THEOREM.
Step-by-step explanation:
ALTERNATE INTERIOR ANGLES THEOREM : if a transversal cuts 2 parallel lines, then the alternate interior angles are said to be congruent.
( alternate interior angles : in the given figure, DCB and ABC are alternate interior angles.
ACB and CBD are another pair of alternate interior angles.)
[ theorem is an accepted truth or a verified correct statement already i.e, take protractor and measure it will be same in EVERY case. though i have provided the proof below..]
PROOF: since we know that vertically opposite angles will be congruent, so the angle vertically opposite to DCB will be same as DCB. ( refer attachment for vertically opposite angles) now, as corresponding angles will be congruent (see attachment to know what are corresponding angles), the angle vertically opposite to DCB and ABC are corresponding angles. therefore DCB and ABC are also equal
hence, ABC=DCB.
Answer:
4.83 minutes
Step-by-step explanation:
The one who took the shortest time ro cover the same distance is regarded as the first runner to complete the race. Since 4.83<4.89 then it means the shortest time is 4.83 minutes. This means that Brandon finished the race first since he took less duration compared to Ricardo. The time for Brandon is given as 4.83 minutes hence this is the duration required in the question.
Solution: The dilation of gk by a scale factor of 2 centered at (-2,-4) is 
and 
.
Explanation:
It is given that the scale factor is 2 and center of dilation is (-2,-4).
If the center of dilation is (a,b) with scale factor k, then the dilation of a point P(x,y) is determined by the given formula.
.....(1)
To find the g' substitute x=0, y=0, a=-2, b=-4 and k=2 in equation (1).
To find the k' substitute x=4, y=4, a=-2, b=-4 and k=2 in equation (1).
Therefore, the dilation of gk by a scale factor of 2 centered at (-2,-4) is and .
Answer:
55years
Explanation:
According to the given expression
FV = P +Prt
P is the initial deposit = $1000
FV is the future value = 4(1000) = $4000
r is the rate = 5.5% = 0.055
Required
Time t
Substitute the given values into the expression as shown;
FV = P +Prt
4000 = 1000 + 1000(0.055)t
4000 - 1000 = 55t
3000 = 55t
Swap
55t = 3000
t = 3000/55
t = 54.5years
t = 55years
This means it will take the deposit of $1000 55years to quadruple
Answer:
450 is 10x's as much as 4500
Step-by-step explanation:
450 times 10 is 4500, my guy .
and once again I'M CORRECT!!!
