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lapo4ka [179]
3 years ago
13

Exercise 4.x2 Make a reasonable conjecture about the nth term in the sequence. 1 3 16 125 1296...

Mathematics
1 answer:
Ulleksa [173]3 years ago
4 0

Answer:

The nth term in the sequence is given by the equation:

n_{th} =(n+1)^{n-1}

Step-by-step explanation:

Arranging a table for n and nth:

\left[\begin{array}{ccc}n&nth\\1&1\\2&3\\2&16\\4&125\\5&1296\end{array}\right]

It is easier to notice that 16 and 125 result from the second power of 4 and the third of 5, respectively, which are one number below their respective position. That is why we can deduce that the base of the power is n+1.

For n=2, the base n+1 results in 3, which matches the nth term for n=2. Since 3 is the result of 3 to the power of 1, 16 is 4 to the power of 2, and 125 is 5 to the power of 3, all the powers are one number behind n, so the power is given by n-1, giving the equation:

n_{th} =(n+1)^{n-1}

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Does this set of ordered pairs represent a function? (-1,5)(0,-3)(2,7)(4,0)(7,5)
ruslelena [56]

Answer:

No

Step-by-step explanation:

You cant have 2 y values

6 0
3 years ago
Read 2 more answers
What is the solution to this equation? 4x+x-15+3-8=13
deff fn [24]

Answer:

x = 33/5

Step-by-step explanation:

4x+x-15+3-8=13

Combine like terms

5x -20 = 13

Add 20 to each side

5x-20+20 = 13+20

5x =33

Divide by 5

5x/5 = 33/5

x = 33/5

3 0
3 years ago
The equation of a line is y=-2x+1. What is the equation of the line that is parallel to the first line and passes through (2,2)?
Murrr4er [49]

Answer:

The equation in slope-intercept form is y=-2x+6.

The equation in standard form is 2x+y=6.

The equation in point-slope form is y-2=-2(x-2).

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

Parallel lines will have the same slope and different y-intercept.

Anyways the slope of y=-2x+1 is -2.

So the equation of our line we are looking for is -2.

So we know our equation is in the form y=-2x+b.

We must inf b using y=-2x+b with (x,y)=(2,2).

y=-2x  +b  with (x,y)=(2,2)

2=-2(2)+b

2=-4+b

Add 4 on both sides:

2+4=b

Simplify:

6=b

The equation is y=-2x+6.

Now it didn't say what form it wanted.

There are some forms I can give you like standard and point-slope form.

There is also general form but it is not too much different from standard form.

Standard form is ax+by=c where a,b, and c are integers if possible.

Point-slope form is y-y1=m(x-x1) where (x1,y1) is a point on the line and m is the slope.

So let's go for standard form (ax+by=c) first:

y=-2x+6

add 2x on both sides:

2x+y=6

This is standard form because it is in the form

ax+by=c.

Ok we know point (2,2) is on our line and we also know we have slope,m, is -2.

Point-slope form is

y-y1=m(x-x1)

y-2=-2(x-2)

8 0
3 years ago
What is the volume of the figure???
lianna [129]

Answer:

1530cm

Step-by-step explanation:

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6 0
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14×12 distributive property​
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186 if that’s the answer you where looking for if not comment here it will give me a notification and I will see
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