The greatest common factor of those numbers is 8.
Answer:
x² + y² = 100
6² + 8² = 100
36 + 64 = 100
100 = 100
Because this is a true statement, the answer is yes, it does lie on the circle.
Answer:
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Step-by-step explanation:
4x + 5y = -13
2(4x + 5y) = 2(-13)
8x + 10y = -26 (equation 1)
5x - 2y = -8
5(5x - 2y) = 5(-8)
25x - 10y = -40 (equation 2)
equation 1 + equation 2,
(8x + 10y) + (25x - 10y) = (-26) + (-40)
8x + 10y + 25x - 10y = -26 + -40
33x = -66
x = -2
substitute x = -2 into equation 1,
8x + 10y = -26
8(-2) + 10y = -26
-16 + 10y = -26
10y = -10
y = -1
The values of x and y are -2 and -1 respectively.
Answer:
The expression that shows how long the two machines will operate simultaneously is:

Step-by-step explanation:
We know that:
x: hours to manufacture a deck of cards for machine A
y: hours to manufacture a deck of cards for machine B
z: hours that machine A operates alone
The number of decks manufactured only by machine A is:

So, the remaining decks are given by:

Then, the combined rate of machines A and B would be:

The work-rate formula is:

Hence, the time that the two machines work simultaneously is:

