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Paul [167]
4 years ago
9

Solve the radical equation. m - 3 = √ 19 - 3m. Which is an extraneous solution to the radical equation?

Mathematics
2 answers:
Sphinxa [80]4 years ago
7 0
The answer is m=5 and m=-2. There is no extraneous solution for this equation.

kari74 [83]4 years ago
5 0

Answer:

  The extraneous solution is m = -2

Step-by-step explanation:

This is normally solved by squaring both sides and solving the resulting quadratic.

(3-m)^2=19-3m\\\\m^2-3m-10=0 \quad\text{subtract 19-3m}\\\\(m-5)(m+2)=0 \quad\text{factor}

The values of m that make the factors zero are 5 and -2. For m=5, the equation becomes ...

  5-3 = √(19-3·5)   ⇒   2 = √4 . . . . . true

For m = -2, the equation becomes ...

  -2-3 = √(19-3(-2))   ⇒   -5 = √25 . . . . . not true

The extraneous solution is m = -2.

_____

Solving the equation graphically, it becomes readily apparent that the only solution is m=5. Extra work is required to see the extraneous solution is m=-2.

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A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times?
GaryK [48]

The required probability of the coin landing tails up at least two times is 15/16.

Given that,
A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times is to be determined.

<h3>What is probability?</h3>

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
In the given question,
let's approach inverse operation,
The probability of all tails  = 1 / 2^7 because there is only one way to flip these coins and get no heads.
The probability of getting 1 head = 7 /2^7
Adding both the probability = 8 / 2^7
Probability of the coin landing tails up at least two times = 1 - 8/2^7
                                                                                     = 1 - 8 / 128
                                                                                     = 120 / 128
                                                                                     = 15 / 16

Thus, the required probability of the coin landing tails up at least two times is 15/16.

Learn more about probability here:

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7 0
1 year ago
Can someone please help me with this???
tino4ka555 [31]

Answer:

1 cm

Step-by-step explanation:

To solve this problem we can use the Pythagorean theorem. In fact the diagonal of a rectangle is an hypotenuse of a right triangle, while the length is a leg. The width is the other leg

width = √2^2 - (√3)^2 = √4 - 3 = √1 = 1 cm

8 0
3 years ago
Solve the system of equations by elimination.
n200080 [17]

Answer:

Step-by-step explanation:

1. 2x - 9y = 23

2 x = 9 y + 23

y = (2 x)/9 - 23/9

2 x - 9 y - 23 = 0

2. 5x - 3y = -1

5 x + 1 = 3 y

y = (5 x)/3 + 1/3

5 x - 3 y + 1 = 0

I belive that should help you out a bit :D

4 0
3 years ago
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Answer:

y = 8.13 x -16125.713


hope it helps

Step-by-step explanation:

Sum of X = 14004

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Mean X = 2000.5714

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Sum of squares (SSX) = 53.7143

Sum of products (SP) = 436.7143

Regression Equation = ŷ = bX + a

b = SP/SSX = 436.71/53.71 = 8.13032

a = MY - bMX = 139.57 - (8.13*2000.57) = -16125.71277

ŷ = 8.13032X - 16125.71277

8 0
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85x + 7x= 84x + 40

Simplified further

92x = 84x + 40
7 0
3 years ago
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