<h2>
Answer/Step-by-step explanation:</h2>
Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.
The ratio of between y-variable and x-variable would be constant.
Direct variation can be represented by the equation,
, where k is a constant. Thus,

From the table given, it seems, as x increases, y also increases. Let's find out if there is a constant of proportionality (k).
Thus, ratio of y to x, 
k = 0.5.
If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into
, should give us the same constant if proportionality.
Let's check:
When x = 2, and y = 1:
,
,
When x = 3, y = 1.5:
,
When x = 5, y = 2.50:
,
The constant of proportionality is the same. Therefore, the relationship forms a direct variation.
Complete Question:
On a number line, the coordinates of X, Y, Z, and W are −8, −5, 4, and 6, respectively. Find the lengths of the two segments below. Then tell whether they are congruent.
and 
Answer:


They are not congruent
Step-by-step explanation:
Length of segment XY:
Coordinate of X = -8
Coordinate of Y = -5
= |-8 -(-5)| = |-8 + 5| = 3
Length of ZW:
Coordinate of Z = 4
Coordinate of W = 6
= |4 - 6| = 2
≠
, therefore, they are not congruent.
case 1,
Let the CP be ₹x,
SP = ₹2400
Profit = SP – CP
= 2400 – x
Profit % = {(2400–x)/ x} × 100%
According to the question,
{(2400–x)/ x} × 100 = 25
=> (2400–x)/ x= 25 /100
=> 100(2400–x) = 25x [ cross multiplication]
=> 240000 – 100x = 25x
=> 240000 = 25x + 100x
=> 240000 = 125x
=> 240000/125 = x
=> x = 1920
So, CP = ₹1920
case 2,
SP = ₹2040
Profit = SP – CP
= 2040 – 1920
= ₹120
profit % = 120/1920 × 100%
= 16%
<h3>Thus, his profit would be 16% if he had sold his goods for ₹2040.</h3>
Answer:
ranges from 2890 miles to 5780 miles.
Step-by-step explanation:
Let us call
the number of miles the car travels, and
the number of gallons of gas that are used, then we have the relationship
<em>(this says the car travels 17 miles for each gallon of gas).</em>
Now, when
, we have


and when
, we have


So, when
goes from 170 to 340,
goes from
to
.
Therefore, when
ranges from 170 to 340 gallons, the distance traveled ranges from 2890 to 5780 miles.
So we know $8.50 per hour
One-time fee of $15 for uniform
x hours per week
y=8.5x-15