The line l with equation x - 2y + 2 = 0 crosses the y-axis at the point P. The line m with equation 3x + y - 15 = 0 crosses the y-axis at the point Q and intersects
l at the point R. Find the area of triangle PQR.​

Area of ΔPQR is 28 units²

Step-by-step explanation:

-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)

-rearrange the equation in the point-slope form y=mx+b  to find the y coordinate of the point P( 0, b)

x-2y+2 = 0, subtract x and 2 from both sides

-2y = -x-2, divide by -2 both sides

y= (1/2)x +1 so b=1 and P (0, 1)

-Q  is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)

-rearrange the equation in the point-slope form y=mx+b  to find the y coordinate of the point Q( 0, b)

3x +y -15 =0, subtract 3x and add 15 to both sides

y= -3x +15 so b=15 and Q(0,15)

-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15

(1/2)x +1 =  -3x +15, add 3x and subtract1

(1/2) x+3x = 15-1, combine like terms

(7/2)x = 14 , multiply both sides by 2

7x = 28, divide both sides by 7

x= 4

y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)

- the area of ΔPQR is (base *height)/2

base= 15-1= 14

height = 4

A= (14*4)/2 = 14*2 = 28

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

i would love   to but there is no graph shown

step-by-step explanation:

i am so sorry