Find the measures of two supplementary angles if three times the measure of one angle is 12 degrees less than the measure of the other

42 and 138

Step-by-step explanation:

Supplementary angle mean that the sum of both angle will be 180 degrees. If the angle is X and Y the equation will be:

x + y = 180

x= 180-y

If three times the measure of one angle(X) is 12 degrees less than the measure of the other(Y), the equation will be

3x= y-12

If you insert first equation to second equation, you can find out:

3x= y-12

3(180-y)= y-12

540-3y= y-12

540+12= y+3y

552= 4y

y= 138

x=180- y

x= 180-138

x= 42

42° and 138°

Step-by-step explanation: If two angles are supplementary, then the sum of their measures is 180°.

In this problem, since we don't know the measures of our supplementary angles, let's call the first angle X. If an angle measures X°, then the measure of its supplement is 180 - X degrees.

So let's call X an angle and 180 - X its supplement.

Now to find the value of X, we can use the second part of the problem to set up an equation. "Three times the measure of one angle" that's 3x, "is" means equals, "12 degrees less than the measure of the other" would be 180 - X - 12.

3x = 180 - x - 12

Now we can solve for X by first simplifying on the right side by subtracting 12 from 180 and we have 3x = 168 - x. Now we add X to both sides of the equation and we get 4x = 168. Now we divide both sides of the equation by 4 in order to get X by itself. Diving both sides by 4, we find that X = 42.

So the measure of one angle which is X is 42°. The measure of its supplement which is 180 - 42 is 138°.

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.

b. is true. hope this . happy