MATHEMATICS HIGH SCHOOL

Prove that, if:y=\frac { { x }^( n+1 ) }{ n+1 } +C

Then:

\n \n \frac { dy }{ dx } ={ x }^( n )

By differentiating...

Answers

Answer 1
Answer: y=(x^(n+1))/(n+1)+C\n\ny'=\left((x^(n+1))/(n+1)+C\right)'\ny'=\left((x^(n+1))/(n+1)\right)'+C'\ny'=(1)/(n+1)\cdot (x^(n+1))'+0\ny'=(1)/(n+1)\cdot (n+1)x^n\ny'=x^n

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Determine the vertex form of g(x) = x2 + 2x – 1. Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3). On a coordinate plane, a parabola opens up. It goes through (negative 1, 2), has a vertex at (1, negative 2), and goes through (3, 2). On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3). On a coordinate plane, a parabola opens up. It goes through (negative 3, 2), has a vertex at (negative 1, negative 2), and goes through (1, 2).

Answers

The vertex form of the quadratic equation is:

g(x) = (x + 1)^2 - 2

And the graph can be seen at the end

How to get the vertex form of the quadratic equation?

For a quadratic equation with leading coefficient a, and with vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we have:

g(x) = x^2 + 2x - 1

First, we need to find the vertex. by using the known formula we get:

h = -2/(2*1) = -1

To get the value of k, we need to evaluate g(x) in x = -1.

g(-1) = (-1)^2 + 2*-1 - 1 = 1 - 2 - 1 = -2

So the vertex is (-1, -2), which means that the vertex form is:

g(x) = (x + 1)^2 - 2

And its graph can be seen below.

If you want to learn more about quadratic equations:

brainly.com/question/1214333

#SPJ2

Answer:

the last one I think

Step-by-step explanation:

janet's gross pay is $750, from which $31 is deducted for oasdi, $10 for medicare, and $14 for income tax. what is her net pay?

Answers

Answer:

The net pay of  is janet's $695 .

Step-by-step explanation:

As given

janet's gross pay is $750.

From gross pay $31 is deducted for oasdi, $10 for medicare, and $14 for income tax.

Thus

Net pay =  gross pay  -  deducted for oasdi - deducted for medicare - deducted for income tax .

Put the value in the above

Net pay =  750 -  31 - 10 - 14

Net pay =  750 -  55

Net pay = $695

Therefore the net pay is  $695  .
$750 - $31-$10-$14=695

Which is the graph of f(x)=100(0.7)

Answers

You don't have any variables... you're graphing a constant.
It's literally a straight line at 70.
It would just be a straight line sideways at 70

a ship is 45 miles east and 30 miles south of port. if the captain wants to sail directly to south port, what beating sold be taken

Answers

probaly you meant  'what bearing should be taken'

so use pythagorean theorem
c=distance from position to south port
b=45
a=30

a^2=B^2=c^2
30^2+45^2=c^2
900+2025=c^2
2925=c^2
square root of both sides
15 times √13
aprox
54.08
54.1
opposite of east=west
opposite of south=north

bearing=
54.1 miles north-west
Well
          East
45 miles > > > >
   <                   v
         <             v 30 miles South
 North      <      v
       West       <  Δ= ship

A right angle is formed, so we use Pythagoras.

45 ^(2) +30 ^(2)=2925
√(2925)=54.08

Therefore,  the route should be 54 miles North West

A bag contains 12 slips of paper of the same size. Each slip has one number on it, 1-12. Describe an impossible event.

Answers

There are many impossible events. Here are a few. 
I'm sure you can think of at least 15 more:

-- Pull 5 multiples of 3 from the bag.

-- Pull 3 multiples of 5 from the bag.

-- Pull 7 odd numbers from the bag.

-- Pull 7 even numbers from the bag.

-- Pull two slips from the bag whose sum is more than 21 .

-- Pull three slips from the bag whose sum is more than 33 .

-- Pull two slips from the bag whose sum is less than 3 .

-- Pull three slips from the bag whose sum is less than 6 .

-- Pull two slips from the bag whose product is more than 132 .

-- Pull two slips from the bag whose product is less than 2 .

etc.

darcy likes to eat peanut butter and raisins on apple slices. on each apple slice she puts 1/16 cup of peanut butter and 8 raisine.Darcy has 2/5 cup of peanut butter and 80 raisins . She eats a whole number of apple slice until the peanut butter is all gone . what fraction of the 80 raisins did she eat ?

Answers

The answer is 7/10.

For one apple slice, Darcy needs 1/16 cup of peanut butter and 8 raisins. She has 2/5 cup of peanut butter. To compare how many butter she has and she needs we will divide 2/5 with 1/1

This means that Darcy needs 5/80 cup of peanut butter and 8 raisins.
If she has 32/80 cup of peanut butter, she will have it only fo 6 or 7 apple slices (32/80 ÷ 5/80 = 6.4) depending how it is rounded. If she prepares 6 apple slices, she will still have a little of peanut butter left (0.4 = 2/5 of cup). So, she will prepare 7 apple slices so the butter will be all gone.

For 7 apple slices, she needs 56 raisins (7 × 8 raisins).
That is 56 raisins out of 80 raisins, so fraction of the 80 raisins did she eat is:
(56)/(80) = (7)/(10)
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