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Molodets [167]
3 years ago
6

Subtract 2x/ x^2 -9 - 5/ x^2 - x - 12

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
5 0

Answer:

Let's do an example first and then summerize what are the techniques to complete the square for quadratic equation in order to solve for x. -2x^2 + 5x + 12 = 0 -2x^2 + 5x =  -12 -2 (x^2 - 5/2 x) = -12 so 2ab = 5/2 x  ("2ab" refers to the formula (a+b)^2 = a^2 + 2ab + b^2  or (a+b)^2 = a^2 - 2ab + b^2 ) Since a=1 (because x^2 is the a^2 in the formula), we get 2*1*b = 2b = 5/2 x, so b = 5/4 That means to complete the square we will add "b^2" (which is (5/4)^2 here) and then subtract (5/4)^2 in the parenthesis: -2 [ x^2 - 5/2 x + (5/4)^2 - (5/4)^2 ] =  -12 Now that is same as  -2 (x - 5/4 )^2 + (-2) * (-5/4)^2 = -12 To simplify it we follow these steps: -2 (x - 5/4 )^2 + 2 * 25/16  = -12 -2 (x - 5/4 )^2 + 25/8  = -12 Multiply both sides of the equation by 8 we get this: -16 (x-5/4)^2 +25 = -96 then -16 (x-5/4)^2  = -121   Techniques summerization: To complete the square for quadratic equation in order to solve for x, first we need to move the terms without x (which is "c" in the "ax^2+bx+c=0" form) to the right side of the equation. Then we divide both sides of the equation by "a" in the "ax^2+bx+c=0" equation. Through the formula (a+b)^2 = a^2 + 2ab + b^2  or (a+b)^2 = a^2 - 2ab + b^2 we will then figure out the value of "b", so then we know what is the b^2 we need to add then subtract. Finally just simplify the equation. Hope this helps.

Step-by-step explanation:

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Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.
Natalija [7]

Answer:

x=3 , x=-3

Step-by-step explanation:

e^{lnx^2} -9= 0

Add 9 on both sides

e^{lnx^2}=9

To remove base 'e' we take ln on both sides

ln e^{lnx^2}=ln9

lnx^2=ln(9)

Both sides have ln , so we make the terms equal

x^2=9

Take square root on both sides

x=+-3

x=3 , x=-3

5 0
3 years ago
Solve the following system of equations using the substitution method.
sergey [27]

Answer:

y=1; x=2

Step-by-step explanation:

Substitution:

x=2y

2x+5y=9

=> if x=2y, plug in the x value into other equation, so

----------------------------------------------------------------------------

2(2y)+5y=9

4y+5y=9

9y=9

y=1

You have the Y value, so now solve for X

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plug in y value to x=2y

so x=2(1)

x=2

5 0
3 years ago
Noelle ran 4 1/2 miles in the morning and 3 1/4 miles in the evening. How far did Noelle run that day?
KIM [24]
You just add all the numbers together:
3 1/8+ 4 1/2+ 4 1/4
=25/8+9/2+17/4
=25/8+36/8+34/8
=95/8
=11 7/8

Ugh.. did you type in the numbers correctly? My guess would be it was meant to be B tho :)

6 0
3 years ago
Shawna took a test that had a total of 20 items. She got 4/5 of the items correct. How many items did she get correct?
ehidna [41]

Shawna got 16 items correct

Step-by-step explanation:

To find the percentage of answers or part of total answers we multiply the fraction with the total number of items.

Given

Total items on test = 20

Correct items fraction = 4/5

Then,

Correct\ items=\total\ items * \fraction\ of\ correct\ answers\\= 20 * \frac{4}{5}\\=\frac{80}{5}\\=16

Shawna got 16 items correct

Keywords: Percentage, fractions

Learn more about fractions at:

  • brainly.com/question/7419893
  • brainly.com/question/730852

#LearnwithBrainly

4 0
3 years ago
If 7 is the mean of 10,3,4,a,6,9 and 10.find the value of a
nydimaria [60]

Answer:

a = 7

Step-by-step explanation:

I think, what you need to do, is first understand how to find the mean of anything: It's quite simple, actually, just add up all the numbers, then divide that number by the number of numbers. So, let's put it in perspective:

10, 3, 4, a, 6, 9, 10

7 is the mean. 7 is the number of numbers.

If, to find the mean is: 10 + 3 + 4 + a + 6 + 9 + 10= 7a ÷ 7, then: 10 +3 + 4+ 6 + 9 +10= 42

42 plus what divided by 7 is the question now.

42 + a ÷  7= 7

So, 7 times 7, that's 49 minus 42 and you've got your answer: 7

8 0
3 years ago
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