One positive number is 5 less than twice a second number, and their product is 140. find the two numbers.

x, y - two positive numbers

one positive number is 5 less than twice a second number

(1)        x = 2y - 5

their product is 140

(2)    xy = 140

substitute from (1) to (2)

(2y - 5)y = 140      use distributive property

(2y)(y) - (5)(y) = 140

2y² - 5y = 140       subtract 140 from both sides

2y² - 5y - 140 = 0

use quadratic formula

a = 2, b = -5, c = -140

b² - 4ac = (-5)² - 4(2)(-140) = 25 + 1120 = 1145

substitute the value of y₁ to (1)

$12. that is my answer.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be