Answer: 
Step-by-step explanation:
Using the same-side interior angles theorem, 
.
Using the alternate interior angles theorem, 
Take the sequence in 1a
The 10th term is 31
The 20th is 61
If you wanted to find these by continuing the series, you'd have to add 3 to the last number in the series, then 3 more, then 3 more, until you reach the 20th term. By this point, you will have added 3 to the first term 19 times. That's where the formula comes from. So here,
a = 4, the first term
n = 20, the number of the term we need
d = 3, how much we're adding each time between one term and the next
Then, to get the 20th term,
4 + (20 - 1) • 3 = 4 + (19 • 3) = 4 + 57 = 61
Answers
The 10th and 20th terms of each sequences are
a. 31; 61
b. 48; 98
c. 47; 97
(in <em>c</em>, you're adding the same <em>d</em> as in the sequence above, but your first term is one unit less)
d. -25; -75
(same thing as before, but now, <em>d</em> is negative)
e. 11.5; 16.5
(with <em>d</em>=1/2 or 0.5)
f. 6+1/2; 8+1/2
Use these to check your answers after applying the formula, but know that I calculated on the fly and didn't check these.
The range of the function y = -x² - 3x when the domain is {-5,0,2} is:
{-10, 0}.
<h3>What is the range of a function?</h3>
The range of a function is the set that contains the output values for the given domain of the function.
In this problem, the domain is:
{-5,0,2}.
Hence the output values are:
- -(-5)² - 3(-5) = -25 + 15 = -10.
- -(2)² - 3(2) = -4 + -6 = -10.
Hence the range is:
{-10, 0}.
-10 repeats, but goes only once on the range.
More can be learned about the range of a function at brainly.com/question/10891721
#SPJ1
Answer:
Therefore, the relation of the given ordered pairs does NOT represent a function as that x-coordinate values are repeated.
Step-by-step explanation:
We know that a relation is basically a set of input and output values, which are expressed in ordered pairs.
A relation may have any set of ordered pairs.
We also know that a function is a set of ordered pairs in which each x-element has only one y-element associated with it.
Consider the five ordered pairs
x y
-2 1
3 -4
-2 -7
4 6
5 7
The relation is: {(–2, 1), (3, –4), (–2, –6), (4, 6), (5, 7)}
From the table, it is clear that x-coordinate values are repeated.
In other words, x = -2 twice.
Therefore, the relation of the given ordered pairs does NOT represent a function.
