Calculating an Original Dimension A triangle has a base of 7.2 centimeters and height of 10.24 centimeters. A large triangle has a base of question mark centimeters and a height of 25.6 centimeters.

The diagram represents the process of creating a scale drawing from an original using a scale factor of 0.4. The base of the original drawing must be:
17.6 cm
18 cm
33.5 cm
45 cm

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Ответ:

rouchedavisin4

15.09.2021

Mathematics

The correct options are

(B) the value of b is $\dfrac{1}{36}.$

Step-by-step explanation: We are given that Tori examined the pattern of exponents in the following table :

$\textup{power of 6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{value}\\\\6^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~216\\\\6^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~36\\\\6^1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6\\\\6^0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1\\\\6^{-1}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a\\\\6^{-2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b$

We are to select the true statements based on the above pattern.

We will be using the following property of exponents :

$x^{-y}=\dfrac{1}{x^y}.$

Therefore, we get

$a=6^{-1}=\dfrac{1}{6^1}=\dfrac{1}{6}.$

and

$b=6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}.$

Also, the value of the exponent is decreasing and we see that

$\dfrac{216}{36}=\dfrac{36}{6}=\dfrac{6}{1}=\dfrac{1}{\frac{1}{6}}=\dfrac{\frac{1}{6}}{\frac{1}{36}}=6.$

So, each previous value is divided by 6.

Thus, the correct options are

(B) the value of b is $\dfrac{1}{36}.$

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