1) Two angles of a triangle measure x + 9 and 2x - 7. What is the measure of the third angle as a
simplified expression in terms of x?

178 - 3x.

Step-by-step explanation:

The three angles in a triangle add up to 180 degrees so an expression for the third angle is:

180 - (x + 9) - (2x - 7)

Distributing the negative over the parentheses, we have

180 - x - 9 - 2x + 7

= 180 - 9 + 7 - x - 2x

=  180 - 2 - 3x

= 178 - 3x  (answer).

178-3x

Step-by-step explanation:

The three angles of a triangle add to 180 degrees

<1 +<2 +<3 = 180

Let angle 1 = x+9 and <2 =2x-7

x+9  + 2x-7 +<3 = 180

Combine like terms

3x+2 +<3 = 180

Subtract 3x from each side

3x-3x+2 +<3 = 180-3x

2+<3 = 180-3x

Subtract 2 from each side

2-2 +<3 = 180-2-3x

<3 = 178 -3x

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step-by-step explanation:

because i said it is

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: