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2 years ago

What are the domain and range of the function on the graph?

Mathematics

1 answer:

Vadim26 [7]2 years ago

6 0

Answer:

The domain: All real numbers.

The range: y>0

Step-by-step explanation:

Domain means all possible x values, and by looking at the graph it covers all real numbers.

Range means all possible y values, and since the x axis is a horizontal asyntope, the graph will never touch the x axis, which is why the range is y>0.

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The nth term of a sequence is 3n²-1

Anarel [89]

Answer: The number is 26.

Step-by-step explanation:

We know that:

The nth term of a sequence is 3n²-1

The nth term of a different sequence is 30–n²

We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.

we get:

3n²- 1 = 30–m²

Notice that as n increases, the terms of the first sequence also increase.

And as n increases, the terms of the second sequence decrease.

One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.

if m = 1, then:

3n²- 1 = 30–1²

3n²- 1 = 29

3n² = 30

n² = 30/3 = 10

n² = 10

There is no integer n such that n² = 10

now let's try with m = 2, then:

3n²- 1 = 30–2² = 30 - 4

3n²- 1 = 26

3n² = 26 + 1 = 27

n² = 27/3 = 9

n² = 9

n = √9 = 3

So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.

the number is:

3*(3)² - 1 = 26

30 - 2² = 26

The number that belongs to both sequences is 26.

6 0

2 years ago

Simplify 2x - 4) + 7(x + 2).<br> 9x + 6<br> 9x - 4<br> 09x - 6

d1i1m1o1n [39]

Answer:
Simplify 2x - 4) + 7(x + 2).
9x + 6
9x - 4
09x - 6
= 9x+10

6 0

2 years ago

A, B and C are the vertices of a triangle.

DiKsa [7]

Answer:

see below

Step-by-step explanation:

To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.

The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.

D (2,2)

You could also see this on a graph, see image.

E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.

E is (-1,1)

Then we are able to calculate the slope of DE and BC.

To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.

Slope of DE:

(2-1)/(2--1)

= 1/3

Slope of BC:

(0--2)/(3--3)

=2/6

=1/3

The slopes of BC and DE are equal, so the segments are parallel.

(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)