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Marianna [84]
3 years ago
8

The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possibl

e values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Mathematics
1 answer:
True [87]3 years ago
5 0

Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

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strojnjashka [21]

Answer:

P ( 5 < X < 10 ) = 1

Step-by-step explanation:

Given:-

- Sample size n = 49

- The sample mean u = 8.0 mins

- The sample standard deviation s = 1.3 mins

Find:-

Find the probability that the average time waiting in line for these customers is between 5 and 10 minutes.

Solution:-

- We will assume that the random variable follows a normal distribution with, then its given that the sample also exhibits normality. The population distribution can be expressed as:

                                   X ~ N ( u , s /√n )

Where

                            s /√n = 1.3 / √49 = 0.2143

- The required probability is P ( 5 < X < 10 ) minutes. The standardized values are:

                        P ( 5 < X < 10 ) = P (    (5 - 8) / 0.2143 <  Z  <  (10-8) / 0.2143   )

                                                 = P ( -14.93 < Z < 8.4 )

- Using standard Z-table we have:

                        P ( 5 < X < 10 ) = P ( -14.93 < Z < 8.4 ) = 1        

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3 years ago
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Step-by-step explanation:

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4 0
2 years ago
Determine the value of x which satisfies the following equation. <br> ln(4x+1)=6
Anika [276]

Answer:

Not Determinable

Step-by-step explanation:

Simplifying

Ln(4x + 1) = 6

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Solving

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Move all terms containing n to the left, all other terms to the right.

Reorder the terms:

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Combine like terms: 6 + -6 = 0

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The solution to this equation could not be determined.

6 0
3 years ago
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