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2 years ago

Explain why a + b = d. B A C swer

Mathematics

1 answer:

bixtya [17]2 years ago

4 0

Answer:

Explanation below

Step-by-step explanation:

Angles in a Triangle

There are two basic relations of angles we need to recall:

Supplementary angles add up to 180°
Internal angles of a triangle add up to 180°

Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:

c = 180 - ( a + b )

Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus

c = 180 - d

From the two relations above, it follows that:

a + b = d

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Answer:

135 minutes

Step-by-step explanation:

Let

y -----> the number of pages to finish reading the book

x ----> the number of hours

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the unit rate or slope of the linear equation

b is the y-intercept or initial value

In this problem we have

Xanthia

$m=100\ pages/hour$

$b=225\ pages$

$y=-100x+225$ ----> the slope is negative because is a decreasing function

For y=0

substitute and solve for x

$0=-100x+225$

$100x=225$

$x=2.25\ hours$ ---> Xanthia's time to finish reading the book

Molly

$m=50\ pages/hour$

$b=225\ pages$

$y=-50x+225$ ----> the slope is negative because is a decreasing function

For y=0

$0=-50x+225$

$50x=225$

$x=4.5\ hours$ --- Molly's time to finish reading the book

To find out how many more minutes than Xanthia would it take for Molly to finish reading the book, subtract Xanthia's time from Molly's time

$4.5\ h-2.25\ h=2.25\ h$

Convert to minutes

Multiply by 60

$2.25\ h=2.25(60)=135\ minutes$

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