Answer:

Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have that
The line pass through the points
<em>Find the value of the constant of proportionality k</em>
For x=2/5, y=1/2
substitute


Answer:
g=
Step-by-step explanation:
To begin you want to isolate the g. So you add
to both sides. On the left is cancels out so it looks like this:

Next, you find the Least Common Denominator (LCD) which is 16. And since one fraction already has a denominator of 16 you leave it as it is. The other fraction, however, needs to be multiplied (both top and bottom) by 4 to get the denominator (bottom) to 16. So:

Multiplying it out you get:

Lastly, just add across:

You're done!

Jason runs the same distance each day. In one 7-day period he ran 40 1/4 miles. He knows that there is a proportional relationship between n, the number of days, and t, the total distance he runs. Tell whether each statement is True or False.
A. The relationship can be expressed as n=5.25t. True or False
B. The graph of the equation is a straight line through (0,0). True or False
C. The unit rate is 5.75. True or False
The answer is A
Answer:
Conjecture : 2xy / ( x + y ) ≤ √xy
Step-by-step explanation:
Harmonic mean of x and y = 2xy/( x + y )
<u>Formulate a conjecture about their relative sizes </u>
we will achieve this by computing harmonic and geometric means
Geometric mean = √xy
harmonic mean = 2xy/( x + y )
Conjecture : 2xy / ( x + y ) ≤ √xy
attached below is the proof