Answer: 334
Step-by-step explanation:
6 consecutive numbers can be written as:
n, n+1, n+2, n + 3, n + 4, n + 5,
The addition of those 6 numbers is:
n + n+1 + n+2 + n + 3 + n + 4 + n + 5
6n + 1 + 2 + 3 + 4 + 5 = 6n + 15
Let's find the maximum n possible:
6n + 15 = 2020
6n = 2020 - 15 = 2005
n = 2005/6 = 334.16
The fact that n is a rational number means that 2020 is can not be constructed by adding six consecutive numbers, but we know that with n = 334 we can find a number that is smaller than 2020, and with n = 335 we can found a number bigger than 2020.
So with n = 334 we can find one smaller.
6*334 + 15 = 2019
and we can do this for all the values of n between 1 and 334, this means that we have 334 numbers less than 2020 that can be written as a sum of six consecutive positive numbers.
Answer:
The cost per duck is $5.00 and $8.00 for chickens
Step-by-step explanation:
The equation would be like this:
50c + 30d = 550 (divide this by 10)
5c + 3d = 55
3d = 55 - 5c (multiply by 3)
9d = 165 - 15c
Next,
44c + 36d = 532 (divide this by 4)
11c + 9d = 133
11c + 165 - 15c = 133
11c - 15c = 133 - 165
-4c = -32 (divide by -4)
c = 8
Therefore, the cost of each chicken is $8.00
9d = 165 - 15c
9d = 165 - 15(8)
9d = 165 - 120
9d = 45 (divide by 9)
d = 5
Answer:
64x^2+112x+49
Step-by-step explanation:
Answer:
x is 12
Step-by-step explanation:
7.5÷5=1.5
1.5×8=12
Answer: x = "-1 " ; <u>and</u>: "(1 ± √3) / 2" .
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Explanation:
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Given: 3x³ − 2x + 1 = 0 ; Find "x" ;
Factor: "3x³ − 2x + 1" ;
3x³ − 2x + 1 = (3x² <span>− 3x + 1)(x + 1) ;
Now, set the equation equal to "0" (zero);
</span> (3x² − 3x + 1)(x + 1) = 0 ;
x = 0 ; when:
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(x + 1) = 0 ; and/or: when:
(3x² − 3x + 1) = 0 ;
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Start with "x + 1 = 0" ;
Subtract "1" from each side of the equation ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
x + 1 − 1 = 0 − 1 ;
x = -1 ;
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Now, try:
3x² − 3x + 1 = 0 ;
Since: "3x² − 3x + 1 " cannot be factored; and since:
"3x² − 3x + 1 = 0" ; is written in the "quadratic equation format"; that is:
"ax² + bx + c = 0 ; a ≠ 0; We can use the "quadratic equation formula" to solve for "x" ;
in which "a = 3" ;
"b = -3" ;
"c = 1" ;
The quadratic equation formula is:
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x = [-b ± √(b²−4ac] / 2a ;
= ? (Let us plug in our known values for "a, b, & c"l
x = { [-(-3] ± [√[(-3²) − (4*3*1)] } / {2* 3} ;
x = [3 ± √(9 − 12)] / 6
x = [3 ± √(-3 )] / 6 ;
x = (1 ± √3) / 2 .
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So, the answers are: x = " -1 " ; and: "</span>(1 ± √3) / 2 " .
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