John runs 15 miles in 3 hours how many miles can John run per hour
1 answer:
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Answer:
Part 1) The scale factor is 2
Part 2) The perimeter of the enlarged rectangle is 19 units
Part 3) The area of the enlarged rectangle is 19.5 square units (the area of the enlarged rectangle is 4 times the area of the original rectangle)
Step-by-step explanation:
we know that
A dilation is a non-rigid transformation that produce similar figures
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
The ratio of its perimeter is equal to the scale factor and the ratio of its areas is equal to the scale factor squared
<em>step 1</em>
<em>Find the scale factor</em>
Let
z ---> the scale factor
step 2
Find the perimeter of the enlarged rectangle
Multiply the perimeter of the original rectangle by the scale factor
The perimeter of the original rectangle is
so
The perimeter of the enlarged rectangle is
step 3
Find the area of the enlarged rectangle
Multiply the area of the original rectangle by the scale factor squared
The area of the original rectangle is
so
The area of the enlarged rectangle is
The area of the enlarged rectangle is 4 times the area of the original rectangle
step 4
Find the value of b
Multiply the corresponding side of the original rectangle by the scale factor
Verify the perimeter of the enlarged rectangle
----> is ok
Verify the area of the enlarged rectangle
---> is ok
The A option is correct.
<h2>Ratio and proportion</h2>A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given
The interest rate applied to the present value has on the monthly payment P in the formula
The effect an increase in i.
<h3>How to find it?</h3>on simplifying the equation, we get
Let n be the constant, then the equation will be
It is clear that V is proportional to i.
An increase in i, the interest rate, will not change P, the monthly payment.
Thus, the A option is correct.
More about the ratio and the proportion link is given below.