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jeka57 [31]
3 years ago
7

Solve for x: −1 < x + 3 < 5

Mathematics
1 answer:
Inessa05 [86]3 years ago
3 0

Answer:

-4<x<2

Step-by-step explanation:

the picture is the steps

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Expand the following using the Binomial Theorem and Pascal’s triangle. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion o
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\bf (2x+3)^5\implies &#10;\begin{array}{llll}&#10;term&coefficient&value\\&#10;-----&-----&-----\\&#10;1&&(2x)^5(+3)^0\\&#10;2&+5&(2x)^4(+3)^1\\&#10;3&+10&(2x)^3(+3)^2\\&#10;4&+10&(2x)^2(+3)^3\\&#10;5&+5&(2x)^1(+3)^4\\&#10;6&+1&(2x)^0(+3)^5&#10;\end{array}

as you can see, the terms exponents, for the first term, starts at highest, 5 in this case, then every element it goes down by 1, till it gets to 0

for the second term, starts at 0, and every element it goes up by 1, till it gets to the highest

now, to get the coefficient, they way I get it, is "the product of the current coefficient and the exponent of the first term, divided by the exponent of the second term plus 1"

notice the first coefficient is always 1

so...how did we get 10 for the 3rd element?  well, 5*4/2
how did we get 10 for the fourth element?  well, 10*2/4


\bf (2x-3y)^4\implies &#10;\begin{array}{llll}&#10;term&coefficient&value\\&#10;-----&-----&-----\\&#10;1&&(2x)^4(-3y)^0\\&#10;2&+4&(2x)^3(-3y)^1\\&#10;3&+6&(2x)^2(-3y)^2\\&#10;4&+4&(2x)^1(-3y)^3\\&#10;5&+1&(2x)^0(-3y)^4&#10;\end{array}


\bf (3a+4b)^8\implies &#10;\begin{array}{llll}&#10;term&coefficient&value\\&#10;-----&-----&-----\\&#10;1&&(3a)^8(+4b)^0\\&#10;2&+8&(3a)^7(+4b)^1\\&#10;3&+28&(3a)^6(+4b)^2\\&#10;4&+56&(3a)^5(+4b)^3\\&#10;5&+70&(3a)^4(+4b)^4\\&#10;6&+56&(3a)^3(+4b)^5\\&#10;7&+28&(3a)^2(+4b)^6\\&#10;8&+8&(3a)^1(+4b)^7\\&#10;9&+1&(3a)^0(+4b)^8&#10;\end{array}

and from there, you can simplify the elements of the expansion by combining the coefficients

like for example, the 7th element of (3a+4b)⁸ will then be 1032192a²b⁶
7 0
3 years ago
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Vadim26 [7]
The <span> answer  is 6.75. Since if you divide the number by 8 you get 6.75.</span>
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The answer would be A Im Sure If not I apologize

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jeka94

Answer:

a. Current: 5 units/hour. Previous: 4.4 units/hour

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b. As this week's productivity = 5 units/hours which is larger than last week's productivity = 4.4 units/hour. The worker's productivity for this week has increased.

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