Which of the following could be the lengths of the three sides of a triangle?

To obtain an average (arithmetic mean) of exactly 2/3, what fraction must be added to 1/6, 1/2, and 1/3?

ollegr [7]

Answer:

D. 5/3

Step-by-step explanation:

$\frac{1/6+1/2+1/3+x}{4} =2/3$

$1/6+1/2+1/3+x=8/3$

$x=8/3-1/6-1/2-1/3$

$x=8/3-1/6-3/6-2/6$

$x=8/3-6/6$

$x=16/6-6/6=10/6$

simplified

$x=5/3$

Hope this helps

3 0

1 year ago

If you can drive 32 miles on one gallon of gas how many miles can you drive on 20 gallons?

Veseljchak [2.6K]

Answer:

640

Step-by-step explanation:

32 *20

4 0

2 years ago

Please help with the following

Neporo4naja [7]

Answer:

a: start at n=1 end at infinity equation = 4^n

b: start at n=3 end at 5 equation = n/(n+1)

c: start at n=1 end at 100 equation = (-1)^n*(1/n)

d: start at n=1 end at n=9 equation = -2

e: starts at n = 0, ends at infinity equation = 5 + 2n

f: starts at n = 0 ends at 4 equation = (7+n)*m^(6+n)

Let me know if you don't see how this works.

Step-by-step explanation:

So sigma notation has three parts, the start, the end and the equation, the start is below the sigma, the end is above and the equation of course is to the side. i will tell you the parts, but let me know if you need further explanation

4 + 16 + 64 + 256

I always start with checking if it is arithmetic which would mean something is added Well, you add 12 to 4 to get 16 and way more than 12 to get to 64, so that's not right.

Next I check geometric. 4*4 = 16 then 16*64, so we're good there. Geometric sequences have the form ab^x where a is the starting number and b is the number that is multiplied by. well both are 4 so we can just use 4^x, though with sigma notation n s usually used instead of x.

so, the equation is 4^n, the starting point is n=1 becaus the starting number is 4 and for 4^n to be 4 n has to be 1. Now, where does it end? Well it doesn't have one, which is shown by the ... at the end. so you should put infinity.

b. 3/4 + 4/5 + 5/6

Not arithmetic or geometric, you can't add anything to each or multiply anything 3/4 gets .05 added to it but 4/5 doesn't and 3/4 is mltiplied by 16/15 but 4/5 is not. So now we look for more special sequences..

Well for 3/4 4 is one more than 3, and the same in 4/5 and 5/6. Also, 4 is the denominator in the first then the numerator in the second, so we have a pattern. the equation is n/(n+1) then it starts at 3 and ends at 5 since there is no ...

c. -1 + 1/2 - 1/3 + 1/4 - ... + 1/100

Again, not arithmetic of geometric. First thing to notice is that it alternates from - to +, now how can a number do that? well what is a negative number to different exponents? let's take (-1)^1, (-1)^2, (-1)^3 and so on. ou'll notice this alternates between -1 and 1, so let's use that. also note the first number is negative, so we want to make sure that's the case for us.

Now for the numbers themselves. I think the pattern is pretty obvious 1/1, 1/2, 1/3 and so on, so the equation is 1/n up to 100. So this one does have an end, even though there's that ..., there is also a number after that though. So let's set this up with a start at 1 and end at 100

(-1)^n*(1/n) and it keeps the negative as the first number too

d. -2 - 2 - 2 - 2 - 2 - 2 - 2 - 2

This one's pretty easy, there are eight 2s. since the 2s have nothng to do with any variable the equation is just 2, and we can start at any n as long as we end at an n 8 away. let's do it normally and start at n=1 so we end at n=9

e. 5 + 10 + 17 + 26 + ...

... means no end again. No obvious pattern so let's check arithmetic and geometric. Well we add 5 to 5, 7 to 10 then 9. Now, those aren't the same numbers, but they are increasing 5 has 2 added to it to get to 7, then 7 gets 2 added to get to 9. so the equation is 5 + (2n) as long as it starts at n=0. So all together that's starts at n = 0, ends at infinity equation = 5 + 2n

f. 49m^6 + 64m^7 + 81m^8 + 100m^9 + 121m^10

Little bit tricky, hope you know your square numbers. more obviously though the exponents are increasing y 1, so we have that. m^(6+n) where n starts at 0 and then ends at 4 to get to m^(6+4) at the end. The numbers of the terms meanwhile are increasing as well. Hopefully you can tell they are square numbers. 49 = 7^2 64 = 8^2 and so on. so it starts at 7^2so now we know the equation is (7+n)m^(6+n). You could also play with the start and ending points to make it look simpler, but I would just go with that.

5 0

2 years ago

Rodrick and Valentina drove to the coast. Rodrick drove 38 9−− 10miles. Then Valentina drove the last 51 3− 5miles. How far did

ivolga24 [154]

I believe the answer would be 69 1/2 and/or 69.5

3 0

2 years ago

Read 2 more answers

Which statements about these two functions are true? Select the TWO that apply. Function A is a linear function and Function B i

KengaRu [80]

Answer:

Function A is a linear function and Function B is a nonlinear function

Function A has a positive rate of change

Step-by-step explanation:

<u><em>Verify each statement</em></u>

Option 1) Function A is a linear function and Function B is a nonlinear function

The statement is True

Because

Function A

The function A represent a proportional relationship that can be expressed in the form

Find the value of k

For x=1, y=5 ----> $k=\frac{5}{1}=5$

For x=2, y=10 ----> $k=\frac{10}{2}=5$

For x=3, y=15 ----> $k=\frac{15}{3}=5$

so

$y=5x$

The graph is a straight line

therefore

Function A represent a linear function

Function B

we have

$y=4x^2+2$

This is a quadratic equation (vertical parabola open upwards)

The graph is a curved line

therefore

Function B represent a nonlinear function, because the graph is not a straight line

Option 2) Function B has two y-intercepts at (0, 2) and (0, –2)

The statement is False

Because

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

$y=4(0)^2+2=2$

Therefore

The function B has only one y-intercept at (0,2)

Option 3) Function A has a positive rate of change.

The statement is True

Because

The rate of change of the function A is equal to the slope

The slope of the function A is m=5

Is a increasing function

As x increases the value of y increases

As x decreases the value of y decreases

Option 4) Function B has a negative rate of change

The statement is False

Because

To find the average rate of change, we divide the change in the output value by the change in the input value

we have

$y=4x^2+2$

Is a vertical parabola open upward

The vertex of the function B is the point (0,2)

For the domain ----> (-∞,0)

The function is decreasing ( the rate of change is negative)

For the domain ----> (0,∞)

The function is increasing ( the rate of change is positive)

4 0

3 years ago