Which transformations could be performed to show that

Mathematics

1 answer:

andre [41]3 years ago

3 0

Answer: a 180 degree rotation about the origin, then a dilation by a scale factor of 1/3

Step-by-step explanation:

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A recipe that makes 8 jumbo blueberry muffins calls for 1 3/4 teaspoons of baking powder. How much baking powder is needed to ma

Nitella [24]

Answer:

It takes $13\frac{1}{8}$ teaspoons of baking powder to make 5 dozen jumbo muffins.

Step-by-step explanation:

Two quantities a and b are directly proportional if when multiplying or dividing one of them by a number, the other is multiplied or divided by that number. That is, if one magnitude grows, the other will grow in the same proportion; while if one magnitude decreases, the other will decrease in the same proportion.

The simple rule of three allows us to establish the relationship of proportionality between two known values and, based on the knowledge of a third quantity, to calculate the value of the fourth.

In other words, it is necessary to know two magnitudes that will be proportional to each other, and a third magnitude, from which you want to find out, will be a fourth term through the relationship:

a ⇒ b

c ⇒ x

Then: $x=\frac{c*b}{a}$

where a, b, and c are the known data, and x is the fourth unknown.

In this case, the rule of three can be applied as follows: if 1 dozen contains 12 muffins, 5 dozen jumbo muffins, how many muffins does it contain?

$amount of jumbo muffins=\frac{5 dozen*12 jumbo muffins}{1 dozen}$

amount of jumbo muffins= 60

Now you apply the following rule of three: if 8 jumbo blueberry muffins requires 1 3/4 ( or, which is the same, 7/4)teaspoons of baking powder, 60 jumbo muffins how many teaspoons of baking powder does it require?

$teaspoons of baking powder=\frac{60*\frac{7}{4} }{8}$