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fgiga [73]
3 years ago
10

Find the remainder when 2^1990 is divided by 1990.

Mathematics
1 answer:
german3 years ago
5 0
I am only in middle school, this question is for college. sorry
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The equation of the line of best fit of a scatter plot is y = −5x − 2. What is the slope of the equation?
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-5

Step-by-step explanation:

Because y=Mx=b and m is the slope

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A 26' long painting is how many yards long
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Three feet is 1 yard. 26 feet would be 26/3=8 2/3 yards long.
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Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.
Tasya [4]

Proof by contadiction.

Let assume there exist such positive integers a and b whose sum is a prime number p, that their greatest common divisor is greater than 1.

a,b\in\mathbb{Z^+}\\d=\text{gcd}(a,b)>1\\\\a=de\\b=df\\e,f\in\mathbb{Z^+}\\\\a+b=p\\de+df=p\\d(e+f)=p\\

Since p is a prime number and d>1, then d=p \wedge e+f=1, but we assumed earlier that e,f\in\mathbb{Z^+}, and there are no two positive integers that sum up to 1.

q.e.d.

7 0
3 years ago
What is the positive solution to this equation 4x^2+12x=135
Stels [109]

Answer:

answer for the equation is 6.75

5 0
3 years ago
Three numbers are in an arithmetic progression with a common difference of 6. if 4 is subtracted from the first number, 1 is sub
UkoKoshka [18]

Answer:

  either of {-9.5, -3.5, 2.5} or {7, 13, 19}

Step-by-step explanation:

Let x represent the first number of the arithmetic sequence. Then the second number is x+6, and the third number is x+12. The geometric sequence is then ...

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The common ratio is then ...

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Cross-multiplying gives ...

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  x² +10x +25 = 3x² +15x -108 . . . . eliminate parentheses

  0 = 2x² +5x -133 . . . . . . . . . . . . . . subtract the left side

  0 = (2x +19)(x -7) . . . . . . . . . . . . . . factor

  x = -9.5 . . or . . 7

The possible original three numbers are ...

  {-9.5, -3.5, 2.5} . .  or . . {7, 13, 19}

8 0
2 years ago
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