What makes a zero? Using zero to simplify algebraic expressions

The range and domain for the exponential function and logistics function are Expotentioal function : Domain= (2,  infinity )

Exponential function:

An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria. Some bacteria double every hour.

In exponential notation, a number usually is expressed as a coefficient between one and ten times an integral power of ten, the exponent. To express a number in exponential notation, write it in the form: c × 10n, where c is a number between 1 and 10 (e.g. 1, 2.5, 6.3, 9.8) and n is an integer (e.g. 1, -3, 6, -2

Definition of logarithmic function: a function (such as y = log x or y = ln x) that is the inverse of an exponential function (such as y = ax or y = ex) so that the independent variable appears in a logarithm.

Expotentioal funtion :

Domain= (2,  infinity )

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The exponential function's and the logistical function's range and domain are Exponential purpose: Domain= (2, infinite ) (2, infinity )

Explicit function

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

The exponential function's and logistics's domain and range

When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

A number is typically written in exponential notation as a coefficient between one and ten times an integral power of ten, the exponent. When writing a number in exponential notation, use the format: c 10n, where c is an integer and n is a number between 1 and 10 (for example, 1, 2.5, 6.3, 9.8).

A logarithmic function is one that is the inverse of an exponential function, such as y = ax or y = ex, and causes the independent variable to appear in a logarithm. Examples of such functions include y = log x and y = ln x.

Expotentioal funtion :

Domain= (2,  infinity )

The fifth angle measure of the polygon is 112°

Since a pentagon is made up of three triangles, its total angles are 3 * 180 * 540. The following formula may be used to get the pentagon's total interior angles: We are aware that the interior angle sum of a polygon with n sides is equal to (n - 2) 180°.

Let the missing angle be x.

The sum of the angles of pentagon is 540°

540 = 100 + 103 + 111 + 114 + x

540 = 428 + x

x = 540 - 428

x = 112

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Доброе утро, отве    $3,500

Answer:  $405 each:)

Step-by-step explanation:

You would subtract 24 from 9721 and then it will give you 405.041666666 so you will round and it will be 405 each

Answer:

$405

Step-by-step explanation:

24x405=9721$

The APR of the given transaction to the nearest tent of a percent is; 4.8%

We find how much you will pay for the car using the down and monthly payments:

3290 + 333.97(48) = $19608.56

Thus, the interest is:

I = (19608.56 - 16450) = $3158.56

Use the simple interest formula:

I = Prt

where;

I is the interest.

P is the principal.

r is the interest rate is the time in years.

Substitute I = $3158.56, P = $16450, and t = 4 years (48 months):

Thus;

3158.56 = (16450)r(4)

Expanding gives;

​3158.56 = 65800r

r = 3158.56/65800

r ≈ 0.048 = 4.8%

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Answer:

85°

Step-by-step explanation:

→ Find the sum of the angles in the triangle

53 + 42 = 95

→ Find what the sum of angles in a triangle should be

180

→ Subtract 95 from it

180 - 95 = 85°

1. The equation is: y = 35x + 50

2. The significance of the slope is: A. The ant travels at an average of 35 meters per minute.

3. Distance would be 490 meters.

4. Number of minutes will be: 16.

Given that x = minutes, and y = distance, then we would have the following coordinates:

(2, 120)

(6, 260)

1. The slope (m) = change in y / change in x = 260 - 120 / 6 - 2

Slope (m) = 35

Substitute m = 35, and (x, y) = (2, 120) into y = mx + b to find b

120 = 35(2) + b

120 = 70 + b

120 - 70 = b

b = 50

Substitute m = 35 and b = 50 into y = mx + b to write the equation

y = 35x + 50

2. The slope of the graph 35.

The significance of the slope is: A. The ant travels at an average of 35 meters per minute.

3. When x = 14, we have:

y = 35(14) + 50

y = 490

Distance would be 490 meters.

4. Substitute y = 610 into y = 35x + 50

610 = 35x + 50

610 - 50 = 35x

560 = 35x

560/35 = 35x/35

16 = x

x = 16

Number of minutes will be: 16.

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The maximum number of performers in each row so that all the rows are equal in length is C. 16.

It should be noted that there are 48 instruments and 32 flag bearers and only one type of performer can be in each row.

The maximum number of performers in each row so that all the rows are equal in length will be the highest common factor between both numbers.

It should be noted that the highest common factor between 32 and 48 is 16

Therefore the correct option is C.

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break down the equations into parts and use simultaneous equation method to solve it

Answer:

  (x, y) = (2, 3)

Step-by-step explanation:

You want the solution to the system of equations.y=-2x+7, y=5x-7.

Equating the expressions for y gives ...

  -2x +7 = 5x -7

  14 = 7x . . . . . . . add 7+2x

  2 = x . . . . . . . . . divide by 7

  y = 5(2) -7 = 3 . . find y from the second equation

The solution is (x, y) = (2, 3).

Perimeter = 16.4 units

Using the heron's formula, Area ≈ 10.4 units².

The heron's formula is used to find the area of a triangle with known side lengths of all its three sides, a, b, and c. The heron's formula is given as: Area = √[s(s - a)(s - b)(s - c)], where s = half the perimeter of the triangle

s = (a + b + c)/2.

Given the following:

K (-4,-1) ,

L(-2, 2),

M (3,-1)

Use the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find KL, LM, and KM.

KL = √[(−2−(−4))² + (2−(−1))²]

KL = √13 ≈ 3.6 units

LM = √[(−2−3)² + (2−(−1))²]

LM = √34 = 5.8 units

KM = √[(−4−3)² + (−1−(−1))²]

KM = √49 = 7 units

Perimeter = 3.6 + 5.8 + 7 = 16.4 units

Semi-perimeter (s) = 1/2(16.4) = 8.2 units

KL = a ≈ 3.6 units

LM = b = 5.8 units

KM = c = 7 units

s = 8.2

Plug in the values into √[s(s - a)(s - b)(s - c)]

Area = √[8.2(8.2 - 3.6)(8.2 - 5.8)(8.2 - 7)]

Area = √[8.2(4.6)(2.4)(1.2)]

Area = √108.6336

Area ≈ 10.4 units²

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The number of short-sleeve shirts ordered is 150.

The number of long-sleeve shirts ordered is 225.

23s + 28.50l = $9,862.50 equation 1

s + l = 375 equation 2

Where:

s = number of short-sleeve shirts ordered

l =  number of long-sleeve shirts ordered

The first step is to multiply equation 2 by 23

23s + 23l = 8,625 equation 3

Subtract equation 3 from equation 2

1237.50 = 5.5l

Divide both sides by 5.5

l = 225

s = 375 - 225 = 150

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Answer:

  (41, 43, 45)

Step-by-step explanation:

You want three consecutive odd integers such that the sum of the first and third is 43 more than the second.

Let n represent the middle (second) of the integers. Then the first is (n-2) and the third is (n+2). The given relation can be written as the equation ...

  (n -2) +(n +2) = n +43

Simplifying gives ...

  2n = n +43

  n = 43

  n-2 = 41

  n+2 = 45

The three integers are (41, 43, 45).

__

Additional comment

When working consecutive integer problems, it often works well to let a variable represent the middle one, or their average value.

Answer:

x=48, y=12

Step-by-step explanation:

Angles in a triangle add to 180°.

In triangle AOD,

[tex]90+x-6+x=180 \\ \\ 2x-6=90 \\ \\ 2x=96 \\ \\ x=48[/tex]

Similarly, in triangle COB, y=12.

Answer:

Domain: {3, 6, 11}

Range: {-5, -3, 4, 6}

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

Answer:

Step-by-step explanation:

ihe

Answer:

1st answer indeed

Step-by-step explanation:

ok so the steps are included in the given answer. hope you can figure it out. if not let me know. (:

For measuring the vegetable garden, Matsu should use the unit of feet.

Finding a number that represents the amount of anything is what measurement is all about.

For the given question;

The dimensions of the garden are the length. This could be calculated by using the two values in the option; That is inches and feet.

But as inches is a used for measuring the small length ad feet is the larger unit.

Thus, dimensions of the vegetable garden of Matsu are calculated by using feet.

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Answer:

For measuring the vegetable garden, Matsu should use the unit of feet.

What is defined as the measurement units?

Finding a number that represents the amount of anything is what measurement is all about.

A measurement unit is a unit of measurement that is used to represent a physical quantity.

For example, the unit of measurement is the defined magnitude of quantity that is being used as the norm for measuring the same type of quantity, as adopted and specified by law or convention.

The imperial unit, also known as the British imperial system, is the standard or default weights and measures system.

Metric System: The metric system is by far the most recent and widely used international system of measurement.

Natural System: Natural units are physical units of measurement that are entirely based on common physical constants.

For the given question;

The dimensions of the garden are the length. This could be calculated by using the two values in the option; That is inches and feet.

But as inches is a used for measuring the small length ad feet is the larger unit.

Thus, dimensions of the vegetable garden of Matsu are calculated by using feet.

Step-by-step explanation:

Based on the events that occurred on January 5, and February 10, journal entries for Parks Construction Inc. are:

Date                 Account title                                          Debit            Credit

Jan. 5               Cash                                                 $4,400,000

                         Common stock                                                  $3,200,000

                          Paid-in capital in excess of par- Common      $1,200,000

Feb 10               Cash                                                 $450,000

                         Common stock                                                     $375,000

                          Paid-in capital in excess of par - preferred       $75,000

The cash would be:

= 400,000 x 11

= $4,400,000

The common stock value would be:

= 400,000 x 8

= $3,200,000

The cash from preferred stock:

= 5,000 x 90

= $450,000

Preferred stock:
= 50,000 x 75

= $375,000

The question is:
Journalize the entries to record the transactions on January 5 and February 10. . Refer to the Chart of Accounts for exact wording of account titles.

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The data set which would be best represented by a line graph is; Choice j: The change in population of a particular city over the last 100 years.

It follows from the task content that the data set which is best represented by a line graph is.to.he identified.

On this note, since choice J measures the change in a dependent quantity, population according to a change in the independent variable, time.

Consequently, choice J is best represented by a line graph.

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The abstract class Number is the superclass of classes BigDecimal , BigInteger , Byte , Double , Float , Integer , Long , and Short .

Step-by-step explanation:

She should report the Mean because it will be greater than the Median.

Let's start with the example from before. Imagine you teach a class with 20 students, and they take a test with 20 multiple choice questions about the Revolutionary War. Imagine that the grades you get back from scoring their tests look like this:

So you can see we have student #1 through student #20, and you can see that the scores range quite a bit. Looking at these scores you can see that one student, student #1, got a perfect score of 20 out of 20. Many students got scores somewhere in the middle, with five students getting half of the questions right - that would be a score of 10 out of 20. A few of the students did pretty well, only missing a few questions, While a few students did pretty badly but at least got a few of the questions right.

Let's say the principal of your school wants a quick summary of how your students did on their test. How would you summarize the results? The most common type of statistic, in either the context of the classroom assessment or in laboratory research projects, is statistics of summary. There are various types of Statistics of summary, but in general their purpose is to quickly give an general impression of the overall trend in results. So, just like you'd guess, based on the term Statistics of summary, these statistics just give you a ballpark idea of what happened on the test.

The most well-known statistic of summary is called the mean, which is the term we use for the arithmetic average score. When most people use the term 'average score,' what they're really referring to, technically, is what we call the mean. How do we calculate the mean? We simply add up all of the individual results, get the total, and then divide by the number of students in the class. In our example, you can see how this would look on the screen. If you add up the scores of 20 + 17 + 16 and so on through all 20 students, you get a total score of 210. You divide 210 by 20 (the number of students), and you get a mean of 10.5. You can see that this score, 10.5, is a pretty representative score of the middle score for this class, so it works nicely as a summary.

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The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that[tex]\overline x $\color \ - a\cdot\sigma \le 19.95}[/tex] and   [tex]\overline x $\color \ +a\cdot\sigma \geq 29.95}[/tex]

Use the given values of mean  [tex]\overline x[/tex] and normal deviation (σ) to notice the worth of "a".

         [tex]\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a[/tex]

On rounding off we get a = 2

Checking another inequality

         [tex]\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95[/tex]

Thus , 2 standard deviation include the all values from the given set of data .

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Using the probability concept, it is found that:

a) The probability is 0.682.

b) The probability is 0.578.

c) A student given a $1 bill is more likely to have spent the money than a student given four quarters.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, we have that out of the 44 students that were given four quarters, 30 students spent money purchasing gum, hence:

p = 30/44 = 0.682.

The probability is 0.682.

For item b, we have that out of 45 students that were given a $1 bill, 26 kept the money, hence:

p = 26/45 = 0.578.

The probability is 0.578.

Hence the correct option for item c is:

A student given a $1 bill is more likely to have spent the money than a student given four quarters.

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The mean age of the residents of a small town will be 27.74.

Midpoints of classes are:

4.5, 14.5, 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5

Hence,

Mean = (4.5*283 + 14.5*202 + 24.5*215 + 34.5*256 + 44.5*175 + 54.5*90 + 64.5*23 + 74.5*21 + 84.5*15 + 94.5*3)/(283 + 202 + 215 + 256 + 175 + 90 + 23 + 21 + 15 + 3)

Mean = (1273.5 + 2929 + 5267.5 + 8832 + 7787.5 + 4905 + 1483.5 + 1564.5 + 1267.5 + 283.5) / 1283

= 35593.5/1283

= 27.74

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