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: Second option.
Step-by-step explanation:
The slope of a line can be calculated with this formula:
Then, you need to choose two points of the line shown in the graph and substitute them into the formula for calculate the slope:
Let's pick the points (-4,4) and (4,-2).
Substituting:

Simplifiying, you get that the slope of the line in the graph is:

Answer:
120
Step-by-step explanation:
15/1.5=10
10 x 12=120
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

From this form,

you can determine the coordinates of the vertex to be (1, 3)
Step-by-step explanation:
a) 24.7×52.3=1291.81
On rounding off to 3 significant digits we get
1290
b)


=31.304951
On rounding off to 5 significant figures we get
=31.305
c)
![\sqrt[3]{78} = 4.27265](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B78%7D%20%20%3D%204.27265)
On rounding off to 2 significant figures we get
=4.3
Hence required answers
a)1290
b)31.305
c)4.3
I hope it helped you