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kipiarov [429]
3 years ago
9

Use the distributive property to write 35 + 15 as a sum with no common factors

Mathematics
1 answer:
kolezko [41]3 years ago
7 0
Here's one:

5(3+4)+3(20-5)

Think of different ways that add or multiply up to 35 or 15.
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Hewo Pls Answer the questions below TY!
Musya8 [376]

Answer:

dont worry if people report you for a answer that is not right lol trust me i know

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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
Use the intersect method to solve the equation. 14x^3-53x^2+41x-4=-4x^3-x^2+1x+4
UNO [17]

Answer:

x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

Step-by-step explanation:

Solve for x over the real numbers:

14 x^3 - 53 x^2 + 41 x - 4 = -4 x^3 - x^2 + x + 4

Subtract -4 x^3 - x^2 + x + 4 from both sides:

18 x^3 - 52 x^2 + 40 x - 8 = 0

Factor constant terms from the left hand side:

2 (9 x^3 - 26 x^2 + 20 x - 4) = 0

Divide both sides by 2:

9 x^3 - 26 x^2 + 20 x - 4 = 0

Eliminate the quadratic term by substituting y = x - 26/27:

-4 + 20 (y + 26/27) - 26 (y + 26/27)^2 + 9 (y + 26/27)^3 = 0

Expand out terms of the left hand side:

9 y^3 - (136 y)/27 - 1780/2187 = 0

Divide both sides by 9:

y^3 - (136 y)/243 - 1780/19683 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-1780/19683 - 136/243 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 136/243) - (1780 z^3)/19683 + z^2 (3 λ^2 - (136 λ)/243) + λ^3 = 0

Substitute λ = 136/729 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - (1780 u)/19683 + 2515456/387420489 = 0

Find the positive solution to the quadratic equation:

u = (2 (445 + 27 i sqrt(591)))/19683

Substitute back for u = z^3:

z^3 = (2 (445 + 27 i sqrt(591)))/19683

Taking cube roots gives 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) times the third roots of unity:

z = 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = -1/27 (-2)^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = 1/27 (-1)^(2/3) 2^(1/3) (445 + 27 i sqrt(591))^(1/3)

Substitute each value of z into y = z + 136/(729 z):

y = (68 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 1/27 (2 (27 i sqrt(591) + 445))^(1/3) or y = (68 (-2)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) - 1/27 (-2)^(1/3) (27 i sqrt(591) + 445)^(1/3) or y = 1/27 (-1)^(2/3) (2 (27 i sqrt(591) + 445))^(1/3) - (68 (-1)^(1/3) 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3))

Bring each solution to a common denominator and simplify:

y = (2^(1/3) ((27 i sqrt(591) + 445)^(2/3) + 68 2^(1/3)))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = 1/27 2^(1/3) (-1/(445 + 27 i sqrt(591)))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3))

Substitute back for x = y + 26/27:

Answer:  x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

5 0
3 years ago
HELP ASAP!! QUADRATIC FUNCTIONS!! <br><br> what is the equation in standard form of these points?
Mamont248 [21]
Y=-x²+5x


Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out
4 0
2 years ago
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Find all sets of three consecutive positive even integers with a sum no greater than 36
Deffense [45]

Answer:

hdejdd

f

f

f

f

4hrh

heh

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