B is the midpoint of AC. If Ab= x +5 and BC = 2x-11, find the measure of Ab.

1 answer:

4 0

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Measurement of "AC" :

(x + 5) + (2x − 11) ;
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Find the measurement of "AB" [which is: "(x+5)" ]:
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First, simplify to find the measurement of "AC" :
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(x + 5) + (2x − 11) ;

= (x + 5) + 1(2x − 11) ;

= x + 5 + 2x − 11 ;

→ Combine the "like terms" ;

x + 2x = 3x ;

5 − 11 = - 6 ;
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to get: 3x − 6 ;
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So, (x + 5) + (2x − 11) = 3x − 6 ;
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Solve for: "(x + 5)"
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We have:
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(x + 5) + (2x − 11) = 3x − 6 ;

Subtract: "(2x − 11)" ; from EACH SIDE of the equation ;
to isolate "(x + 5)" on one side of the equation;
and to solve for "(x + 5)" ;
________________________________________________________
→ (x + 5) + (2x − 11) − (2x − 11) = (3x − 6) − (2x − 11) ;

→ (x + 5) = (3x − 6) − (2x − 11) ;
_________________________________________________
Note: Simplify: "(3x − 6) − (2x − 11)" ;

→ (3x − 6) − (2x − 11) ;

= (3x − 6) − 1(2x − 11) ;

= 3x − 6 − 2x + 11 ;
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→ Combine the "like terms" :
_____________________________
+3x − 2x = 1x = x ;

-6 + 11 = 5 ;
_____________________________
To get: x + 5 ;

So we have:
______________________________
x + 5 = x + 5 ;
______________________________

So, x = all real numbers.

x = ℝ

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B. 1.2 x $10^{-4}$

Step-by-step explanation:

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Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

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There are 21 ways Tim choose 2 books from the 7 recommended book

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Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula for combinations is:

$n C_{r}=\frac{n !}{r !(n-r) !}$

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

Substituting values in above formula, we get

$\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}$

For a number n, the factorial of n can be written as,

$n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1$

Therefore, we get

$7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21$