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:
0.093 ft/min
Step-by-step explanation:
V = 4/3 π r³
Take derivative with respect to time:
dV/dt = 4π r² dr/dt
Plug in values:
141 = 4π (11)² dr/dt
dr/dt = 141 / (484π)
dr/dt ≈ 0.093
The radius is increasing at 0.093 ft/min.
Answer:
A, B and C
Step-by-step explanation:
Dilations are transformation in which a shape either gets bigger or smaller than the original image. Although it changes sizes it does not change shape.
Therefore, A, B and C are correct.
<h3>
Hope this Helps!</h3>
:)
Answer:
thirty three hundredths
Step-by-step explanation:
4/10 + ? = 73/100
4/10 is the same as 40/100
73-40=33
<u>33/100</u>
