Answer:
length = 12 miles
width = 6 miles
Step-by-step explanation:
<h3>Framing algebraic expression and solving:</h3>length = x miles
width = (x - 6) miles
Area of rectangle = 72 square miles
length * width = 72
x * (x - 6) = 72
x*x - 6*x = 72
x² - 6x - 72 = 0
Sum = -6
Product = -72
Factors = 6 , (-12) { 6 + (-12) = -6 and 6*(-12) =-72 }
Rewrite the middle term using the factors.
x² + 6x - 12x - 72 = 0
x(x + 6) -12(x + 6) =0
(x + 6)(x - 12) = 0
{x + 6 = 0 is rejected as length will not have negative value}
x - 12 = 0
length = 12 miles
Width = 12 - 6 = 6 miles
9514 1404 393
Answer:
see attached
Step-by-step explanation:
It is helpful to understand that the product of the binomial factors is ...
(ax +b)(cx +d) = ac·x² +(ad+bc)x +bd
For these problems you only need to look at the constant and the leading coefficient to find the missing values.
__
1. d = 8/-4 = -2
2. b = -24/(3·2·d) = -4; c = 3/(3·a) = 1
3. a = 2/c = 1; d = -24/b = 6
Based on the image, FJH is perpendicular to JI as these two lines form a right angle.
<h3>What is a perpendicular line?</h3>This name is given to a line that creates a right angle when it intersects or meets with another line.
This concept opposes the concept of parallel line, which is used to describe lines that never intersect and are always the same distance apart.
<h3>How do you identify a perpendicular line?</h3>Based on the above, in the image given two lines that can be classified as perpendicular are the lines FJH (horizontal lines) and JI (vertical line) as their intersection creates a right angle.
Learn more about coordinate planes in: brainly.com/question/14462788
#SPJ1
