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2 years ago

10

To the nearest centimeter, what is the area of the shaded sector in the circle shown below? A. 12 cm2 B. 151 cm2 C. 23 cm2 D. 13

8 cm2

1 answer:

vovikov84 [41]2 years ago

6 0

Step-by-step explanation:

what are the sides given?

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Answer:

<em>The number of restaurant-purchased meals eaten in a restaurant is 75, the number eaten in a car is 33 and the number eaten at home is 55.</em>

Step-by-step explanation:

Suppose, the number of meals eaten in a restaurant is $x$ , in a car is $y$ and at home is $z$

The total number of meals eaten in a restaurant, in a car or at home is given as 163. So, the first equation will be......

$x+y+z=163 .............................(1)$

The total number meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. So, the second equation will be......

$y+z=x+13 ................................(2)$

Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. So, the third equation will be......

$x= z+20..................................(3)$

First, <u>substituting equation (2) into equation (1)</u>, we will get........

$x+(x+13)=163\\ \\ \Rightarrow 2x+13=163\\ \\ \Rightarrow 2x=163-13=150\\ \\ \Rightarrow x=\frac{150}{2}=75$

<em>Now plugging this $x=75$ into equation (3)</em>, we will get......

$75=z+20\\ \\ \Rightarrow z=75-20= 55$

<em>Plugging $x=75$ and $z=55$ into equation (1)</em> .........

$75+y+55=163\\ \\ \Rightarrow y+130=163\\ \\ \Rightarrow y=163-130=33$

So, the number of restaurant-purchased meals eaten in a restaurant is 75, the number eaten in a car is 33 and the number eaten at home is 55.

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