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Rus_ich [418]
3 years ago
11

Evaluate one third of the sum of 15 and 6

Mathematics
2 answers:
IgorLugansk [536]3 years ago
7 0

Answer:

7

Step-by-step explanation:

15 plus 6 equals 21

21 divided by 3 is 7

Harman [31]3 years ago
7 0

Answer:7

Step-by-step explanation:

sum of 15 and 6

15+6=21

1/3 Of The sum

1/3 of 21

1/3 x 21

(1x21)/3

21/3=7

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If f(x)=x2-2x and g(x)=6x=4, for which value of x does (f+g)(x)=0
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X = -2
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Find 6/7 of £60 to the nearest penny.
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Step-by-step explanation:

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1+2-3+4+5-6+7+8-9...+97+98-99
zaharov [31]

Answer:

  1584

Step-by-step explanation:

The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.

__

<h3>series of partial sums</h3>

The partial sums, taken 3 terms at a time, are

  1+2-3 = 0

  4+5-6 = 3

  7+8-9 = 6

...

  97+98-99 = 96

So the original series is equivalent to ...

  0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)

That is, the sum is 3 times the sum of the consecutive integers 1..32.

__

<h3>consecutive integers</h3>

The sum of integers 1..n is given by the equation ...

  s(n) = n(n+1)/2

__

<h3>series sum</h3>

Using this to find the sum of our series, we find it to be ...

  series sum = 3 × (32)(33)/2 = 1584

_____

<em>Alternate solution</em>

The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...

  1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)

Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).

Computed that way, we find the sum to be ...

  (99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584

3 0
2 years ago
Algebra Word Problem, 9th Grade, Station 2, please help!
Minchanka [31]

ANSWER


ANSWER TO QUESTION 1.

If you give x surfing lessons, then you will earn $ 25x


If you are charged $200 for using the place, then your profit will reduce by $200.


The profit function is given by


P(x)=25x-200 dollars.


The y-intercept is  -200. It is negative because it is a cost which is a liability. So it does not add to your profit.


ANSWER TO QUESTION 2.

The slope is 25. It is positive because as the number of hours increases, the profit earned also increases. In other words there is a direct relation between the number of hours worked and the profit earned.



ANSWER TO QUESTION 3.

The slope intercept form is when an equation is written in the form;

y=mx+c,


where m is the slope and c is the y-intercept. The profit function in slope intercept form is

P(x)=25x-200


ANSWER TO QUESTION 4.

If you break even, then the difference between the revenue and cost is zero. So we equate the profit function to zero.


25x-200=0



25x=200


x=8


Therefore you need to give 8 different lessons to break even.


ANSWER TO QUESTION 5.

If you give 20 lessons, the x=20. We need to substitute


x=20 in to the profit function to calculate the profit made after 20 lessons.

P(20)=25(20)-200


P(20)=500-200


P(20)=300.


ANSWER TO QUESTION 6.

If the new price is $75, then the new profit function becomes


P(x)=75x-200


ANSWER TO QUESTION 7.

To find the number of lessons that lets you break even, we equate the new profit function to zero.

75x-200=0

We solve for x by adding 200 to both sides of the equation.



\Rightarrow 75x=200

We now divide through by 75

\Rightarrow x=\frac{200}{75}


\Rightarrow x=2\frac{2}{3}


Therefore you would have to 2\frac{2}{3} lessons to break even. That is approximately 3 lessons.


ANSWER TO QUESTION 8.

If you give 20 lessons and we want to find the profit you made with this new profit function, then we have to plug in x=20 in to P(x)=75x-200.


That is,


P(20)=75(20)-200


P(20)=1500-200


P(20)=1300 dollars

















3 0
3 years ago
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