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Vaselesa [24]
3 years ago
9

Solve using completing the square method 12 x square + 7 x square - 12 is equals to zero​

Mathematics
1 answer:
Nastasia [14]3 years ago
8 0

Answer:

  x = -4/3  or  3/4

Step-by-step explanation:

To solve the equation by completing the square, it is convenient to have the leading coefficient be 1. Accordingly, we divide the equation by 12:

  x^2 +7/12x -1 = 0

Add the constant.

  x^2 +7/12x = 1

Add the square of half the x-coefficient.

  x^2 +7/12x +49/576 = 1 +49/576

Write the left side as a square; simplify the right side.

  (x +7/24)^2 = 625/576

Take the square root.

  x +7/24 = ±25/24

  x = (-7 ±25)/24

  x = -4/3  or  3/4

_____

These solutions suggest the equation could be factored as ...

  (3x +4)(4x -3) = -0

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A pilot can travel for 140 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the w
quester [9]

Answer:

  -88 mph

Step-by-step explanation:

We can use the relation ...

  time = distance/speed

to compare the times in the two directions.

  \dfrac{140}{200+w}=\dfrac{360}{200-w}\\\\140(200-w)=360(200+w)\\\\200(140-360)=w(360+140)\\\\w=\dfrac{200(-220)}{500}=-88 \quad\text{miles per hour}

The wind speed is -88 miles per hour.

_____

The problem statement tells us the travel is slower <em>with</em> the wind than <em>against</em> the wind. Hence "with the wind" must be subtracting from the net speed. That is, the wind speed is negative.

4 0
3 years ago
.hoi I need a lil help
mihalych1998 [28]

Answer:

10

Step-by-step explanation:

4+5=9 and 1/2+1/2 =1  so 9+1=10

6 0
3 years ago
Read 2 more answers
P divided by 8????? asap nowwww
zlopas [31]

Answer:

I am not sure but if p/8=0 then it is correct

hope it helps! :D

3 0
2 years ago
Read 2 more answers
Keith won a cash prize in an art competition. He gave his mother 2/5 of the money he won. Of the remainder, 1/4 was given to his
USPshnik [31]

Answer:

300 dollars

Step-by-step explanation:

Let the original amount = x

x - 2/5x  was what his mother's share looked.

5/5 x - 2/5 x

3/5x is what is left.

3/5 x - 1/4 * 3/5 x - 2/3x * 3/5 = his sister's share and his brothers

3/5x - 1/4*3/5 x - 2/3 * 3/5 = 15

3/5x * (1 - 1/4 - 2/3) = 15

3/5 x 5/60 = 15

15 / 300 * x = 15

1/20  x = 15

x = 15 * 20

x = 300

7 0
2 years ago
Consider a sample with data values of 27, 24, 21, 16, 30, 33, 28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles. 20
densk [106]

Answer:

P_{20} = 20 --- 20th percentile

P_{25} = 21.75  --- 25th percentile

P_{65} = 27.85   --- 65th percentile

P_{75} = 29.5   --- 75th percentile

Step-by-step explanation:

Given

27, 24, 21, 16, 30, 33, 28, and 24.

N = 8

First, arrange the data in ascending order:

Arranged data: 16, 21, 24, 24, 27, 28, 30, 33

Solving (a): The 20th percentile

This is calculated as:

P_{20} = 20 * \frac{N +1}{100}

P_{20} = 20 * \frac{8 +1}{100}

P_{20} = 20 * \frac{9}{100}

P_{20} = \frac{20 * 9}{100}

P_{20} = \frac{180}{100}

P_{20} = 1.8th\ item

This is then calculated as:

P_{20} = 1st\ Item +0.8(2nd\ Item - 1st\ Item)

P_{20} = 16 + 0.8*(21 - 16)

P_{20} = 16 + 0.8*5

P_{20} = 16 + 4

P_{20} = 20

Solving (b): The 25th percentile

This is calculated as:

P_{25} = 25 * \frac{N +1}{100}

P_{25} = 25 * \frac{8 +1}{100}

P_{25} = 25 * \frac{9}{100}

P_{25} = \frac{25 * 9}{100}

P_{25} = \frac{225}{100}

P_{25} = 2.25\ th

This is then calculated as:

P_{25} = 2nd\ item + 0.25(3rd\ item-2nd\ item)

P_{25} = 21 + 0.25(24-21)

P_{25} = 21 + 0.25(3)

P_{25} = 21 + 0.75

P_{25} = 21.75

Solving (c): The 65th percentile

This is calculated as:

P_{65} = 65 * \frac{N +1}{100}

P_{65} = 65 * \frac{8 +1}{100}

P_{65} = 65 * \frac{9}{100}

P_{65} = \frac{65 * 9}{100}

P_{65} = \frac{585}{100}

P_{65} = 5.85\th

This is then calculated as:

P_{65} = 5th + 0.85(6th - 5th)

P_{65} = 27 + 0.85(28 - 27)

P_{65} = 27 + 0.85(1)

P_{65} = 27 + 0.85

P_{65} = 27.85

Solving (d): The 75th percentile

This is calculated as:

P_{75} = 75 * \frac{N +1}{100}

P_{75} = 75 * \frac{8 +1}{100}

P_{75} = 75 * \frac{9}{100}

P_{75} = \frac{75 * 9}{100}

P_{75} = \frac{675}{100}

P_{75} = 6.75th

This is then calculated as:

P_{75} = 6th + 0.75(7th - 6th)

P_{75} = 28 + 0.75(30- 28)

P_{75} = 28 + 0.75(2)

P_{75} = 28 + 1.5

P_{75} = 29.5

7 0
3 years ago
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