Two angles are supplementary. If one angle is 45° less than twice of the other angle, find the two angles.

we will call the two angles a and b

a = 105

b = 75

Step-by-step explanation:

Supplementary means the two angles add up to 180 degrees.  Now this turns into a system of equations problem.  let's call the two angles a and b.

Lets say angle a is 45 degrees less than twice the other angle.  that means a = 2b - 45.  The first part told us a + b = 180

a + b = 180

a = 2b - 45

Now this is actually super easy to do.  Normally you would have to do algebra to one of the two equations so there is one variable by itself.  the second equation already has that.

now look at the other equation.  instead of a though make a = 2b - 45

a + b = 180

2b - 45 + b = 180

Now use algebra to solve for b

2b - 45 + b = 180

b = 75

Now, go back to the first two equations.  put 75 in for b for either one of them and you will get the answer to a.

a + 75 = 180

a = 105

or

a = 2*75 - 45

a = 105

Now we can check.  a=105 and b = 75

do both add up to 180?  yep.  is a 45 less than twice b?  or using numbers, is 105 45 less than twice 75?  well twice 75 is 150.  and 105 is 45 less than that, so yep!

Let me know if there was anything you didn't get.  Also you could totally have started with the other equation first and got a = 180 - b or b = 180 - a and gotten the same answer.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

4

step-by-step explanation: