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Daniel [21]
3 years ago
14

Write the number as an improper fraction, 10 3/4

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
3 0
To write a mixed fraction as an improper fraction, simply multiply the denominator by the whole number and add on the result to the numerator. The denominator part will remain the same throughout. 

10\frac{3}{4}

In this case:
- 10 is the whole number component
- 3 is the numerator
- 4 is the denominator

Multiple the denominator (4) by the whole number component (10). 
4×10=40

Add the numerator (3) to the answer you had in the previous step (40).  
3+40=43

Since the denominator remains same throughout, in this case, 10\frac{3}{4} as an improper fraction would be \frac{43}{4}


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We see AC^2=AB^2+BC^2 so B is the right angle.


That was preliminary and probably indicated in an associated figure.


Now we want the line through the midpoint of the legs, AB and BC, in standard form.


The midpoint of AB is the average of the coordinates of A and B:


\left( \dfrac{-5 +1}{2}, \dfrac{5+1}{2} \right) = (-2,3)


The midpoint of BC is


\left( \dfrac{1 + 3}{2}, \dfrac{1 + 4}{2} \right) = ( 2, \frac 5 2)


The line through those points is


(y - 3)(2 - -2)=(x - -2)(\frac 5 2 - 3)


4y - 12 =  (x+2)(- \frac 1 2)


8y - 24 = -x -2


x + 8y = 22


That's the answer. Let's check it.


Midpoint of AB is (-2,3), -2 + 8(3)=22 good.


Midpoint of BC is (2,5/2), 2+8(5/2)=22 good.


\textrm{Answer: } x + 8y = 22


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