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FromTheMoon [43]
3 years ago
11

Precalc.

Mathematics
1 answer:
viktelen [127]3 years ago
6 0
Domain: x>0.

(\log_2x)^2+7\log_2x+12=0

Substitute t=\log_2x\in\mathbb{R}. We have:

 t^2+7t+12=0\\\\a=1\qquad b=7\qquad c=12\\\\\\\Delta=b^2-4ac=7^2-4\cdot1\cdot12=49-48=1\\\\\sqrt{\Delta}=\sqrt{1}=1\\\\\\
t_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-7-1}{2}=\dfrac{-8}{2}=-4\\\\\\
t_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3

For t₁ there will be:

\log_2x=t_1\\\\\log_2x=-4\\\\2^{-4}=x\\\\x=\dfrac{1}{2^4}\\\\\\x=\dfrac{1}{16}=0,0625\\\\\\\boxed{x\approx0,063}

and for t₂:

\log_2x=t_2\\\\\log_2x=-3\\\\2^{-3}=x\\\\x=\dfrac{1}{2^3}\\\\\\x=\dfrac{1}{8}\\\\\\\boxed{x=0,125}

Answer d)


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Cube and cube roots 27000<br>​
boyakko [2]

Answer:

lcm for cuberoot

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2*5*3

30

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cube

multiply 27000 three times with itself

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6 0
3 years ago
Read 2 more answers
There is a vendor at a carnival selling bags of cotton candy. Each bag of cotton candy has the same cost. She starts each day wi
umka21 [38]

Answer:

The cost of each cotton candy bag is $4.

Step-by-step explanation:

Consider the provided information.

Let, the vendor has x dollar at the starting of each day.

Let, the cost of each cotton candy bag is y.

Now when she sells a total of 12 bags, she has $128.

x+12y=128  .....(1)

After she sells a total of 20 bags, she has $160.

x+20y=160  ....(2)

Subtract equation 1 from equation 2.

(x+20y)-(x+12y)=160-128

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6 0
3 years ago
1/5+1/4+2/5 this is adding fractions with unlike denominators what is the answer
attashe74 [19]
What you would do is change all the fractions to 20ths so they have a common denominator. For 1/5, you multiply 4x5 to get 20 in the denominator. Whatever you multiply on the bottom, you must do at the top. Do that for all fractions and you would get this:
4/20 + 5/20 + 8/20= 17/20 because denominator stays the same, add the values in the numerator.
ANSWER: 17/20
5 0
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Which relationship between x and y in the equation shows a proportional relationship?
Harlamova29_29 [7]

Answer:

the answer is c

Step-by-step explanation:

at least they got a relationship

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kipiarov [429]

Answer:

Step-by-step explanation:

We have to make 5 place serial number with first two as alphabets and last three as digits.

The alphabets are bonded to first 6 ( A, B, C, D, E, F) where as digits are 10 (say 1 to 10).

Let the serial number be S1 S2 S3 S4 S5.

For Alphabets

For S1 we have 6 alphabets.

Now for S2 we are left with 5 alphabets since there is no repetition one alphabet will be fix for S1.

So the possible combination for S1 S2= 6x5=30.

For Digits

We did the same as we did for alphabets, for S3 we have 10 possibilities, and for S4 and S5 9 and 8 respectively due to the no repetition condition.

So the possible combinations for S3 S4 S5 = 10x9x8=720

So the total number of serial numbers are 30+720=750.

7 0
3 years ago
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