Answer:
104
155
180
Step-by-step explanation:
an easy way is to solve what is in the parenthesis then multiply by the outside number
but if you need to use the distributive property:
1. 4 x (20 - -6)
(4 x 20) - (4 x -6) = 80 - -24 = 80 + 24 = 104
2. -5 x (24 - -7)
(-5 x 24) - (-5 x -7) = -120 - 35 = 155
3. 12 x (-30 + 45)
(12 x -30) + (12 x 45) = -360 + 540 = 180
we have

the vertex of the function g(x) is the point 
the vertex of the function f(x) is the point 
so
the rule of the translation of g(x) to f(x) is
(x,y)------> (x,y-4)
that means
the translation is
units down
therefore
the equation of the function f(x) is

therefore
<u>the answer is</u>

Answer:
The answer is 360 ways
Step-by-step explanation:
Answer:
Yes; Opposite sides are congruent, and diagonals are congruent.
Step-by-step explanation:
we have

we know that
the formula to calculate the distance between two points is equal to
step 1
Find the length of the sides
<u><em>Find the distance AB</em></u>
substitute the values
<u><em>Find the distance BC</em></u>
substitute the values
<u><em>Find the distance CD</em></u>
substitute the values
<u><em>Find the distance AD</em></u>
substitute the values
Compare the length sides
AB=CD
BC=AD
therefore
Opposite sides are congruent
step 2
Find the length of the diagonals
<u><em>Find the distance AC</em></u>
substitute the values

<u><em>Find the distance BD</em></u>
substitute the values

Compare the length of the diagonals
AC=BD
therefore
Diagonals are congruent
The figure is a rectangle, because Opposite sides are congruent, and diagonals are congruent