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IrinaK [193]
3 years ago
12

3(3x+2)<8(x+2)<6(5x-12) =

Mathematics
2 answers:
iren [92.7K]3 years ago
8 0
3(3x+2) < 8(x+2) < 6(5x-12)\\\\9x+6 < 8x+16 < 30x-72\\\\\#1\\9x+6 < 8x+16\ \ \ \ \ |subtract\ 6\ from\ both\ sides\\9x < 8x+10\ \ \  \ \ \ \ |subtract\ 8x\ from\ both\ sides\\x < 10\\\\\#2\\8x+16< 30x-72\ \ \ \ \ \ \ \ |subtract\ 16\ from\ both\ sides\\8x < 30x-88\ \ \  \ \ \ \  \ \ |subtract\ 30x\ from\ both\ sides\\-22x < -88\\22x > 88\ \ \ \ \ \ \ \ \ |divide\ both\ sides\ by\ 22\\x > 4\\\\From\ \#1\ \cap\ \#2\ we\ have\ 4 < x < 10\Rightarrow x\in(4;\ 10)
kolezko [41]3 years ago
7 0
3(3x+2) < 8x + 16 => x < 10 
8x + 16 < 30x - 72  => 22x > 88 => x > 4
solution is  4  < x < 10
 
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Product in standard form (explain)<br> (3+6i)(4+9i)
ololo11 [35]
First you have to factor (aka, multiply) your binomial (which is what you have written) usually it helps to organize your thinking, and help tell what you need to multiply, to use the binomial chicken(or crab claw, what ever you want to call it) which basically you draw two arches, one arch connecting the 3 and 4, and then the other the 3 and 9i. on the opposite side (depending on wheater you connected then from the top or bottom) you connect (with an arch) the 6i and the four, and then the 6i to the 9i.

so now you multiply each piece you've connected:
3 x 4= 12
3 x 9i= 27i 
6i x 4= 24i
6i x 9i= 54i^2 

after  you've done this you can move on to  putting it into standard form, which just means you put things in descending order, depending on how many exponents the x (or in this case i) has.
your largest exponent is 54i^2, so that's first in out equation, next 27i, and 24i (you can combine these because they are like term) which equals 51i, after that you just add the 12 on the end, so the final equation looks like this:

54i^2+51i+12


4 0
3 years ago
Suppose a triangle has two sides of length 3and 4 and that the angle between these two sides is 60. What is the length of the th
tangare [24]

9514 1404 393

Answer:

  A.  √13

Step-by-step explanation:

You can make an educated guess and come to the right conclusion.

The triangle is nearly an equilateral triangle. A triangle with two sides 3 and an angle of 60° would have a third side of 3. A triangle with two sides of 4 and an angle of 60° would have a third side of 4.

So, the third side must be between 3 and 4. Here is an evaluation of the answer choices:

__

A -- between 3 and 4, the correct choice

B -- 3, too short

C -- 1.73, too short

D -- more than 4, too long

__

The question can be answered using your triangle solver app on your calculator, or using the Law of Cosines.

  c = √(a^2 +b^2 -2ab·cos(C))

  c = √(3^2 +4^2 -2·3·4·(1/2)) = √(9 +16 -12)

  c = √13 . . . . . length of the side opposite the 60° angle

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Answer:

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Step-by-step explanation:

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