20 pts look at the quadrilateral shown below:

terra writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

terra's proof

1. ao = oc because it is given that diagonals bisect each other.
2. bo = od because it is given that diagonals bisect each other.
3. for triangles aob and cod, angle 1 is equal to angle 2 as they are
4. therefore, the triangles aob and cod are congruent by sas postulate.
5. similarly, triangles aod and cob are congruent.
6. by cpctc, angle abd is equal to angle bdc and angle adb is equal to angle dbc.
7. as the alternate interior angles are congruent the opposite sides of quadrilateral abcd are parallel.
8. therefore, abcd is a parallelogram.

which is the missing phrase in terra's proof?
a. alternate interior angles
b. corresponding angles
c. same-side interior angles
d. vertical angles

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

it has to have an angle of 90 degrees