Answer: The system of equations have many solutions and the correct options are A,B and D.
Explanation:
The given equations are,
..... (1)
.... (2)
Simplify the second equation.
Divide both sides by 3.
It is same as equation (1). Since equation (1) and (2) are same, therefore all the points lies on the line or which satisfies the equation are the solution of the given system of equations.
Test the points whether the point lies on the line or not.
Check for point A(6,-7).
LHS and RHS are equal, therefore the point A is the solution of the system of equations.
Check for point B(2,1).
LHS and RHS are equal, therefore the point B is the solution of the system of equations.
Check for point C(-2,-9).
LHS and RHS are not equal, therefore the point C is not the solution of the system of equations.
Check for point D(-4,13).
LHS and RHS are equal, therefore the point D is the solution of the system of equations.
Therefore the options A,B and D are correct.
Answer:
degree of length = 1
degree of width = 1
degree of height = 3
degree of volume = 4
Step-by-step explanation:
V = (4x - 1)( x)(x³) = (4x² - x)x³ = 4x∧5 - x∧4
dV/dx = 20x∧4 - 4x³
d²V/dx² = 80x³ - 12x²
80x³ - 12x² = 0
4x²(20x - 3) = 0
20x - 3 = 0
20x = 3
∴ x = 3/20
Length, 4x - 1 = 4 (3/20) - 1 = 3/5 - 1 = -2/5
∴ degree of length = 1
Width, x = 3/20
∴ degree of width = 1
Height, x³ = (3/20)³ = 27/8000
∴ degree of height = 3
Volume, 4x∧5 - x∧4 = 4(3/20)∧5 - (3/20)∧4 = 4(243/3200000) - (81/160000) = 243/800000 - 81/160000 = (243 - 405)/800000 = - 162/800000 = - 81/400000
∴ degree of volume = 4
It is given that Mr Martin takes 12 minutes to drive his bus route without stopping on any of the stops.
On Tuesday, it took him 14 minutes when he stooped to take the passengers. He estimated that it takes 30 sec for each stop.
60 second = 1 minute.
30 second = 0.5 minutes.
Let us assume, there were x stops.
Since it takes him 12 minutes without stopping, 12 minutes here acts as a fixed time.
Total time is given by the equation
.... (1)
where t is the total time and x is the number of passengers.
To find the number of passengers, solve equation (1) for x ,
.... (2)
Plug y= 14 into equation number (2) gives 4 stops.
<span>In the question "Ray UW is the angle bisector of VUT.
If mVUW = (4x + 6)° and mWUT = (6x – 10)°, what is the measure of WUT?"
It was given that UW is the angle bisector of VUT, which means that mVUW = mWUT.
i.e. 4x + 6 = 6x - 10
6x - 4x = 6 + 10
2x = 16
x = 8
Therefore, the measure of WUT = 6x - 10 = 6(8) - 10 = 48 - 10 = 38
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