½ is the same as 0.5 and the ratio of _____.
1 answer:
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The solution of the equation is and
Explanation:
The equations are and
First we shall solve the equation graphically.
The image of the graph is attached below.
This contains the solution to the system of equations.
The equations and
are plotted on the graph.
The intersection of these two equations are the solutions of the system of equations.
Thus, the intersection of the two equations are and
Now, we shall solve the equation algebraically.
Let us solve the equation using substitution method.
Let us substitute in
, we get,
Adding both sides by 2x, we have,
Adding both sides by 2, we get,
Dividing both sides by 3,
Thus, the value of x is 3.
Substituting in
, we get,
Thus, the value of y is 1.
Hence, The solution of the equation is and
Answer:
A, B and C
Step-by-step explanation:
In the equation: 3y=27x
Making y the subject of the equation, we have:
The constant of proportionality between y and x is 9.
We want to determine which relationships have the same constant of proportionality 9.
<u>Option A</u>
y=9x
The constant of proportionality is 9.
<u>Option B</u>
2y=18x
Divide both sides by 2 to obtain: y=9x
The constant of proportionality is 9.
<u>Option C</u>
x=3, y=1/3
Substitution into y=kx gives:
1/3=3k
k=9
The constant of proportionality is 9.
<u>Option D</u>
x=6, y=2/3
Substitution into y=kx gives:
2/3=6k
k=2/3*6=4
The constant of proportionality is 4.
<u>Option E</u>
When x=2, y=18
Substitution into y=kx gives:
18=2k
k=9
However, when x=4, y=27
Substitution into y=kx gives:
27=4k
k=6.75
This is not a proportional relation since the constant of proportionality is not equal.
The correct options are A, B and C