<span>time for airplane = 11 am to 1 pm = 2 hr
distance travelled by plane = 2a ------- (speed of plane is a mph)
time for auto = 3 am to 1 pm = 10 hr
distance travelled by plane = 10(a – 200)
2a = 10(a – 200)
8a = 2000
a = 250 mph ----- plane
and 250 – 200 = 50 mph ----- auto </span>
Since, this is parallelogram
so, opposite sides are equal
We will find value of sides
Calculation of AB:
we are given point A=(-2,3)
point B=(4,0)
we can use distance formula

now, we can plug values


Since, this is parallelogram
so, opposite sides are equal
so,

Calculation of AD:
point A =(-2,3)
point D=(-5,2)
we can use distance formula

now, we can plug values


Since, this is parallelogram
so, opposite sides are equal
so,

Calculation of AE:
point A=(-2,3)
point E=(-3,1)
we can use distance formula

now, we can plug values


(a)
we know that
perimeter of a parallelogram is sum of all sides
so,
perimeter is

now, we can plug values

...........Answer
(b)
we can use area of parallelogram formula

we can plug values

............Answer
The side length 51 is the hypotenuse.
24*24+45*45=2601
The square root of 2601 is 51.
Please note that the hypotenuse is most likely the longest side.
Answer:
- n = 5q; 25q+5n = 200
- (n, q) = (20, 4)
- Margie has 20 nickels and 4 quarters
Step-by-step explanation:
a) Using the defined variables, we can translate the problem statements to equations:
- n = 5q . . . . Margie has 5 times as many nickels as quarters
- 25q + 5n = 200 . . . . the total value of Margie's coins is 200 cents
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b) Substituting for n, we have ...
25q +5(5q) = 200
50q = 200 . . . . . . . collect terms
q = 200/50 = 4 . . . divide by the coefficient of q
n = 5·4 = 20
The solution is (n, q) = (20, 4).
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c) Since n represents the number of nickels Margie has, n=20 means Margie has 20 nickels. Similarly, q=4 means Margie has 4 quarters.