Nathan took his car in for service and repairs. He had a coupon for 10% off. Original Prices • Labor $218.97 • Parts $303.47 • O
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Answer:
diagonal = = 12.8 inches (to the nearest tenth of an inch)
Step-by-step explanation:
As shown in the diagram attached to this solution:
Let the Length of the rectangular board = a
Let the width = b
Let the diagonal = d
where:
a = 10 inches
b = 8 inches
d = ?
Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:
(hypotenuse)² = (Adjacent)² + (Opposite)²
d² = 10² + 8²
d² = 100 + 64
d² = 164
∴ d = √(164)
d = 12.806 inches
d = 12.8 inches (to the nearest tenth of an inch)
<em>N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.</em>
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form or
in this problem we have
the point is on the line of direct variation
so
Find the constant of proportionality k
-------> substitute ------>
the equation is
Remember that
If a point is on the line of direct variation
then
the point must satisfy the equation of direct variation
we're proceeding to verify each point
<u>case A)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
the point is on the line of direct variation
<u>case B)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
the point is on the line of direct variation
<u>case C)</u> point
Substitute the value of x and y in the direct variation equation
-------> is not true
therefore
the point is not on the line of direct variation
<u>case D)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
the point is on the line of direct variation
<u>case E)</u> point
Substitute the value of x and y in the direct variation equation
-------> is not true
therefore
the point is not on the line of direct variation
<u>case F)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
the point is on the line of direct variation
therefore
<u>the answer is</u>