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Olin [163]
2 years ago
6

Write the absolute value function as a​ piecewise-defined function with linear parts.

Mathematics
1 answer:
KengaRu [80]2 years ago
6 0

The piecewise-defined function with linear parts ​f(x)= |2x + 9|

f(x) = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

<h3>How to write piecewise functions?</h3>

To write this function as a piecewise function, you have to use the definition of absolute value.

The absolute value equation is; ​f(x)= |2x + 9|

The definition says that;

|x| = {x   x ≥ 0)

     {-x   x < 0}

Applying this definition to the function you get:

|2x + 9| = {2x + 9   2x + 9 ≥ 0)

     {-2x - 9   2x + 9 < 0}

After simplifying the inequalities you get:

|2x + 9| = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

So finally you can write the piecewise  function as:

f(x) = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

Read more about piecewise function at; brainly.com/question/18499561

#SPJ1

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Answer:

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Step-by-step explanation:

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A function of random variables used to estimate a parameter of a distribution is an unbiased estimator.

An unbiased estimator is one in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, an unbiased estimator captures the true population value of the parameter on average, this is because the mean of its sampling distribution is the truth.

Also, we know that the bias of an estimator (b) that estimates a parameter (p) is given by; E(b) - p

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

<em>Generally, in statistical analysis, sample mean is an unbiased estimator of the population mean while the sample variance is an unbiased estimator of the population variance.</em>

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4 years ago
Solve the following system of equations by using the inverse of a matrix.
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Answer:

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Step-by-step explanation:

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4 years ago
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3 0
3 years ago
Charles is reading about computers. He learns that a computer processor can perform one command in approximately 0.000000016
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<em><u>The number 0.000000016 is expressed in scientific notation is:</u></em>

1.6 \times 10^{-8}

<em><u>Solution:</u></em>

Given that,

Charlie learns that a computer processor can perform one command in approximately 0.000000016  nanoseconds

We have to express in scientific notation

<em><u>Step 1:</u></em>

Given number is:

0.000000016

Move the decimal point in 0.000000016 until there is only one non-zero digit to the left of the decimal point

Here,

Move the decimal 8 places to the right to get 1.6

We have moved the decimal to left, therefore, exponent is negative

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8 0
3 years ago
Use rectangle ABCD and the given information to solve each problem.
solong [7]

Problem 1

<h3>Answers:</h3><h3>angle 6 = 50</h3><h3>angle 7 = 50</h3><h3>angle 8 = 40</h3>

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

Work Shown:

point E = intersection point of diagonals.

x = measure of angle 6

y = measure of angle 8

angle 7 is also x because triangle AED is isosceles (AE = ED)

Focus on triangle AED, the three angles A, E, D add to 180

A+E+D = 180

x+80+x = 180

2x+80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

So both angles 6 and 7 are 50 degrees.

Turn to angle 8. This is adjacent to angle 7. The two angles form a 90 degree angle at point A. This is because a rectangle has 4 right angles.

(angle7)+(angle8) = 90

50+y = 90

y = 90-50

y = 40

angle 8 = 40 degrees

=================================================

Problem 2

<h3>Answers:</h3><h3>angle 2 = 61</h3><h3>angle 3 = 61</h3>

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

Work Shown:

Angle 5 is 29 degrees (given). So is angle 4 because these are the base angles of isosceles triangle DEC (segment DE = segment EC)

angle 3 and angle 4 form a 90 degree angle

x = measure of angle 3

(angle 3)+(angle 4) = 90

x+29 = 90

x = 90-29

x = 61

Angle 2 is congruent to angle 3 since triangle BEC is isosceles (BE = EC), so both angle 2 and angle 3 are 61 degrees each.

4 0
4 years ago
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