Express each ratio as a fraction in simplest form. Hint: 1 yard = 3 feet.9 yards to 48 feet
Answers
To express a ratio we've to convert these figures into the simplest available ones, so, let's simplify using the smallest numbers, 9 yards to 16 yards.
9 is divisible by 3 only, and 16 can be divided by 2, 4, and 8. That means we cannot use a common denominator, so the simplest ratio will be the one we already have: 9/16.
Final answer:
To convert the ratio 9 yards to 48 feet into a fraction in simplest form, we need to first convert 9 yards into feet, which is 27 feet. Then, we express this ratio as a fraction, 27/48. To simplify this fraction, we divide both numerator and denominator by their GCD, which is 3, resulting in 9/16.
Explanation:
The student has asked to express the ratio 9 yards to 48 feet as a fraction in simplest form. Given that 1 yard equals 3 feet, we first need to convert 9 yards to feet. So, 9 yards * 3 feet/1 yard = 27 feet.
Now, let's express 27 feet to 48 feet as a fraction. The ratio is 27:48, and we can write this as the fraction 27/48. However, this is not the simplest form. We simplify a fraction by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD of 27 and 48 is 3. Therefore, we divide 27 and 48 by 3 to get 9/16. So, the fraction in simplest form is 9/16.
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(a) Describe the rule for translating center Q onto center P.
(b) Determine the scale factor for dilating circle Q so that it has the same radius as circle P.
(c) Are circles P and Q similar? Explain your answer.
Answers
center P(2, 0)
center Q(0, 4)
you would need to add 2 units in x axis, and subtract 4 units on y axis.
(b) Determine the scale factor for dilating circle Q so that it has the same radius as circle P.
P radius 20, Q radius 2, radiusQ*10 = radiusP, so the scale factor is 10
(c) Are circles P and Q similar? Explain your answer.
they are similar because a similarity transformation (translation, dilation) exists between them
Answers