Answer:
18 minutes
Step-by-step explanation:
Given that the time (T) varies directly as the number of spectators (S) and varies inversely as number of open exits (E).
Hence:
T ∝ S; T ∝ 1 / E
Let k be the constant of proportionality. This gives:
T = kS / E
when T = 12 minutes, S = 20000, E = 20. Hence:
12 = k(20000) / 20
20000k = 240
k = 12 / 1000
This gives:
T =
When S = 36000, E = 24, we are to calculate the time (T):
T = 18 minutes
Answer:
Niki's time for one lap is 1 min 10 sec
Step-by-step explanation:
Let
x ----> niki's time for one lap
Remember that
so
we know that
Niki's time for one lap multiplied by 0.90 (percentage in decimal form) must be equal to Toya's time for one lap
so
The linear equation that represent this problem is
solve for x
Convert to min
Answer:
x = 5±2√7
Step-by-step explanation:
This quadratic cannot be factorised via the factorisation method, so we use the quadratic formula :
x = or x =
(The reason I did 2 equations is because brainliest does not allow me to do the ± in the equation insert thing )
x = or x =
x = or x=
x = or x =
x = or x =
Hope this helped and brainliest please
8x = 12
<h3>Explanation:</h3>Subtracting the first equation from the second, you get ...
... (5x +2y) -(3x +2y) = (7) -(5)
... 2x = 2 . . . . . the first answer choice is true
___
Multiplying this expression for x by 4, we get
... 8x = 8 . . . . . the second answer choice (8x=12) is false
___
Adding thee first equation to the second, you get ...
... (3x +2y) +(5x +2y) = (5) +(7)
... 8x +4y = 12
... 8 + 4y = 12 . . . . . . use the value of 8x just computed
... 4y = 4 . . . . . . . . . . subtract 8; the third answer choice is true
_____
<em>Alternate approaches</em>
In short, if you solve the system by any of the methods available, you find x=1 and y=1, so the second answer choice is clearly the correct one:
... 8x ≠ 12
By Cramer's method:
... x = (2·7-2·5)/(2·5-2·3) = 4/4 = 1
... y = (5·5-7·3)/4 = 4/4 = 1
By graphing, see attached.
By substitution (for 2y):
... 5x +(5-3x) =7 . . . . . using 2y=5-3x
... 2x = 2 . . . . . . subtract 5
... x = 1 . . . . . . . .divide by 2
... 5 -3·1 = 2y = 2 . . . . substitute x into the expression for 2y
... y = 1 . . . . . . . divide by 2
By matrix methods, see the second attachment. (x, y) = (1, 1), found in the rightmost column of the result.
