The formula to convert a temperature from degrees Fahrenheit (F˚) to degrees Celsius (C˚) is C˚=59F˚−1609. 1) Write a formula to convert from degrees Celsius to degrees Fahrenheit by solving for F˚ in the equation above. 2) Are the equations from the problem statement and from part 1 inverses? EXPLAIN

Step-by-step explanation:

Given the formula to convert a temperature from degrees Fahrenheit (F˚) to degrees Celsius (C˚) as C˚=5/9F˚−1609.

To write the formula to convert °C to °F , we will make °F the subject of the formula

Add 1609 to both sides of the equation

C˚+1609=5/9F˚−1609.+1609

C+1609 = 5/9F

Cross multiply

9(C+1609) = 5F

Divide both sides by 5

9/5 (C+1609) = F

Hence the formula to convert from degrees Celsius to degrees Fahrenheit is 9/5 (C+1609) = F.

B) To check whether they are inverses we need to check if F(C) = C(F)

To get F(C) we will substitute F into C as shown;

F = 9/5 (C+1609)

C˚=5/9F˚−1609.

F(C) = 9/5 ((5/9F˚−1609.)+1609)

F(C) =  9/5 * 5F/9 -1609 + 1609

F(C)  = 9/5 * 5F/9

F(C) = 45F/45

F(C) = F

Similarly for C(F)

C(F) = (5/9(9/5 (C+1609))˚−1609.

C(F) = (C+1609) -  1609

C(F) = C

This shows that both equations are inverses of each other

the two may have that, even a breakdown is probably offered

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