By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.
This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.
Then:
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are <em><u>same-side interior angles</u></em>. Because AB and DC are <em><u>parallel</u></em>, the same-side interior angles must be <em><u>supplementary</u></em> by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
Answer:
-2<x<8
see below for graph
Step-by-step explanation:
First, we need to solve the inequality.
Inequality: |x-3|<5
Split into two equations:
x-3<5
x-3>-5 (notice how the sign is flipped when we make the number negative)
let's start with x-3<5
add 3 to both sides
x<8
now
x-3>-5
add 3 to both sides
x>-2
The graph is below
the intersection is the solution.
Notice how I made the maroon line go to the right- which shows that it's greater than (for x>-2) and the silver line go to the left, which shows that it's less than (for x<8)
the equation is -2<x<8
Hope this helps!
Answer:
y
−
7
=
−
6
/11
⋅
(
x
+
7
)
Step-by-step explanation:
Find the point-slope form.
Point-slope formula: y-y₁=m(x-x₁)
Lets say that the two unknown integers are
and
.
We know the following things about
and
:
And, we want to find
.
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for
:
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of
and
, which are 12 and 14, and directly compute their product; however, the approach described is more elegant.
Answer:
x = 4
Step-by-step explanation:
