Answer: n=9
Step-by-step explanation:
<u>Ans</u><u>wer</u>
a)
![{(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)](https://tex.z-dn.net/?f=%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%2036%20%3D%28%202b%20-%2011%29%282b%20%20%2B%20%201%29)
b)
![9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)](https://tex.z-dn.net/?f=9%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20%20%3D%20%20%283a%20-%204%29%283a%20%2B%2011%29)
c)
![( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )](https://tex.z-dn.net/?f=%28%20%7B4%20-%2011m%29%7D%5E%7B2%7D%20%20-%201%20%3D%28%203%20-%2011m%20%29%28%205%20-%2011m%20%29)
<u>Explanation</u>
a) The given expresion is
![{(2b - 5)}^{2} - 36](https://tex.z-dn.net/?f=%20%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%2036)
We rewrite as difference of two squares
![{(2b - 5)}^{2} - 36 = {(2b - 5)}^{2} - {6}^{2}](https://tex.z-dn.net/?f=%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%2036%20%3D%20%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%20%20%7B6%7D%5E%7B2%7D%20)
Recall that:
![{x}^{2} - {y}^{2} = (x + y)(x - y)](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%7By%7D%5E%7B2%7D%20%20%3D%20%28x%20%2B%20y%29%28x%20-%20y%29)
This implies that:
![{(2b - 5)}^{2} - 36 =( {(2b - 5)} -6)(2b - 5 )+ 6)](https://tex.z-dn.net/?f=%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%2036%20%3D%28%20%7B%282b%20-%205%29%7D%20-6%29%282b%20-%205%20%29%2B%206%29)
Or
![{(2b - 5)}^{2} - 36 =( 2b - 5-6)(2b - 5 + 6)](https://tex.z-dn.net/?f=%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%2036%20%3D%28%202b%20-%205-6%29%282b%20-%205%20%2B%206%29)
This simplifies to give:
![{(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)](https://tex.z-dn.net/?f=%7B%282b%20-%205%29%7D%5E%7B2%7D%20%20-%2036%20%3D%28%202b%20-%2011%29%282b%20%20%2B%20%201%29)
b) The second expression is
![9 - {(7 + 3a)}^{2}](https://tex.z-dn.net/?f=9%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20)
We rewrite as perfect squares yo get:
![9 - {(7 + 3a)}^{2} = {3}^{2} - {(7 + 3a)}^{2}](https://tex.z-dn.net/?f=9%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20%20%3D%20%20%7B3%7D%5E%7B2%7D%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20)
This gives:
![9 - {(7 + 3a)}^{2} = ({3} - {(7 + 3a)})({3} + {(7 + 3a)})](https://tex.z-dn.net/?f=9%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20%20%3D%20%20%28%7B3%7D%20-%20%20%7B%287%20%2B%203a%29%7D%29%28%7B3%7D%20%20%2B%20%20%7B%287%20%2B%203a%29%7D%29)
This implies that
![9 - {(7 + 3a)}^{2} = ({3} - 7 + 3a)({3} + 7 + 3a)](https://tex.z-dn.net/?f=9%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20%20%3D%20%20%28%7B3%7D%20-%20%207%20%2B%203a%29%28%7B3%7D%20%20%2B%207%20%2B%203a%29)
We simplify to get:
![9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)](https://tex.z-dn.net/?f=9%20-%20%20%7B%287%20%2B%203a%29%7D%5E%7B2%7D%20%20%3D%20%20%283a%20-%204%29%283a%20%2B%2011%29)
c) The third expression is:
![( {4 - 11m)}^{2} - 1](https://tex.z-dn.net/?f=%28%20%7B4%20-%2011m%29%7D%5E%7B2%7D%20%20-%201)
We obtain the difference of two squares as:
![( {4 - 11m)}^{2} - 1 =( ( {4 - 11m)} - 1 )( ( {4 - 11m)} + 1 )](https://tex.z-dn.net/?f=%28%20%7B4%20-%2011m%29%7D%5E%7B2%7D%20%20-%201%20%3D%28%20%28%20%7B4%20-%2011m%29%7D%20%20-%201%20%29%28%20%28%20%7B4%20-%2011m%29%7D%20%20%2B%201%20%29)
We simplify within the parenthesis to get:
![( {4 - 11m)}^{2} - 1 =( 4 - 11m - 1 )( 4 - 11m+ 1 )](https://tex.z-dn.net/?f=%28%20%7B4%20-%2011m%29%7D%5E%7B2%7D%20%20-%201%20%3D%28%204%20-%2011m%20%20-%201%20%29%28%204%20-%2011m%2B%201%20%29)
We simplify further to get;
![( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )](https://tex.z-dn.net/?f=%28%20%7B4%20-%2011m%29%7D%5E%7B2%7D%20%20-%201%20%3D%28%203%20-%2011m%20%29%28%205%20-%2011m%20%29)
Answer:
p>5
Step-by-step explanation:
Answer: Absolute value is always positive so the two negative answers can’t be it. The plotted dot is also clearly past 1 on the number line so .75 doesn’t make sense either. The only logical answer is 1.25
Answer:
B
Step-by-step explanation:
if you connect and extend to points it forms a line with a y-intercept of 2 when x is zero
y = mx + b m the slope equals 1
y = x +2