Answer:
Step-by-step explanation:
Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.
2p - 3q = 4 ...................... 1 * 3
3p + 2q = 9 ..................... 2 * 2
Multiplying equation 1 by 3 and 3 by 2:
6p - 9q = 12
6p + 4q = 18
Subtracting both equation
-9q-4q = 12-18
-13q = -6
q = -6/-13
q = 6/13
Substituting q = 6/13 into equation 2
2p - 3(6/13) = 4
2p - 18/13 = 4
2p = 4+18/13
2p = (52+18)/13
2p = 70/13
p = 70/26
p = 35/13
<em>Hence p = 35/13 and q = 6/13</em>
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<em>b) </em>If if 223ₓ = 87 find x
Using the number base system and converting 223ₓ to base 2 will give us;
223ₓ = 2*x² + 2*x¹ + 3*x⁰
223ₓ = 2x²+2x+3
Substituting back into the equation, 2x²+2x+3 = 87
2x²+2x+3-87 = 0
2x²+2x-84 = 0
x²+x-42 = 0
On factorizing:
(x²+6x)-(7x-42) = 0
x(x+6)-7(x+6) = 0
(x+6)(x-7) = 0
x+6 = 0 and x-7 = 0
x = -6 and 7
<em>Hence the value of x is 7 (neglecting the negative value)</em>
Answer:
90 customers
Step-by-step explanation:
Total shift time = 2 hours
1 hours = 60 minutes
Total shift time minutes = 2*60 minutes = 120 minutes
Average Time taken to serve 1 customer = 1 minute 20 seconds
lets convert 1 minute 20 seconds in fraction
60 seconds = 1 minute
20 seconds = 20/60 minutes = 1/3 minutes
Thus,
Average Time taken to serve 1 customer = 1 minute + 1/3 minutes = 4/3 minutes
Lets assume she served x customer in her 2 hour shift
total time taken to serve x customer =x*Average Time taken to serve 1 customer = 4x/3 minutes
Given that she the customers for her shift time which is 120 minutes
4x/3 minutes = 120 minutes
x = 120*3/4 = 90
Thus,
Kimiko served 90 customers and this is the number of customer which came through the drive thru during those 2 hours.
Answer:
24 ft²
Step-by-step explanation:
The formula to solve for area of a triangle is: 
. First multiply the base x height: 12 x 4 = 48. Now multiply by 1/2: 48 x 1/2 = 24. Your answer is 24 ft².
Hope it helps and is correct!
