Solution:
<u>Given:</u>
- Length of rectangle = 4a + 3b
- Width of rectangle = 7a - 2b
- Perimeter of rectangle = 2W + 2L
Let's simplify the perimeter of the rectangle by using the expression for the perimeter.
- => 2W + 2L
- => 2(7a - 2b) + 2(4a + 3b)
- => 14a - 4b + 8a + 6b
- => 22a + 2b
Hence, the polynomial that represents the perimeter of the rectangle is 22a + 2b.
-84= -4b -4(-7 -8b)
⇒ -84= -4b -4* (-7) -4*(-8b) (distributive property)
⇒ -84= -4b+ 28+ 32b
⇒ -84 -28= 32b -4b
⇒ -112= 28b
⇒ -112/28= b (inverse operation)
⇒ -4= b
Final answer: b= -4
The slope would be -2/3x and the y intercept would be -7
The greater number is 21, this is correct since 21 + 3 is 24, and 21 - 3 is 18. Thus, it fulfills all necessary requirements