graph the function f: f(x)=√x²-4 x+4 and determine its range and discuss its monotony​

Answer: 18.7

Step-by-step explanation:

Find the lengths of AB, BC, and CA

AB = [tex]\sqrt{(4-(-1))^{2} + (-1-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1

BC = [tex]\sqrt{(0-(-1))^{2} + (-3-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1

CA = [tex]\sqrt{(0-4)^{2} + (-3-(-1))^{2} }[/tex] = 2[tex]\sqrt{5}[/tex] ≈ 4.5

7.1 + 7.1 + 4.5 = 18.7

The value of a is -3 and the value of k is 10

A parabola is a U-shaped plane curve where any point is equidistant from a fixed point (known as the focus) and from a fixed line known as the directrix. The parabola is an integral part of the conic section topic

The section of a right circular cone by a plane parallel to the generator of the cone is a parabola. It is the location of a point that moves so that the distance from the fixed point (the focus) is equal to the distance from the fixed line (the directrix).

The fixed point is called the focus

A fixed line is called a directrix

Solving an algebraic equation is the process of finding a number or set of numbers that, when substituted for the variables in the equation, reduce them to an identity. Such a number is called the root of the equation

Here the equation y = a(x -2)^2 + k...........(1)

and two points A(1,7) and B(4, -2) is given

We need to find the value of a and k

Put A(1,7) in equation (1) , we get,

7 = a + k ,therefore k = 7 - a......(2)

Put B(4, -2) in equation (1), we get,

-2 = 4a + k........(3)

Put k= 7-a in (3)

-2 = 4a+7 -a

3a = -9

a= -3

From equation (2) , we get k = 7-(-3)= 10

Hence the value of k is 10 and the value of a is -3

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For the given points to lie on the parabola,

a = -3 and k = 10.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).

According to the question,

Equation of parabola : y = a[tex](x-2)^{2}[/tex] + k

Points A(1,7) and B(4,-2)

For the points to lie on the parabola,

7 = a[tex](1-2)^{2}[/tex]+k

7 = a + k

Similarly,

-2 = a[tex](4-2)^{2}[/tex] + k

-2 = 4a + k

On solving the two equations simultaneously, we get,

a = -3

k = 10

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Answer:

The longest side of room is 24m

The direction of the difference between the 2 measurements.

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The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.

Brief Description of Mean and Interquartile Range

While interquartile range only assesses the middle half of the data, mean and range deal with the entire set of data. The mean is significant in statistics because it helps us determine where a dataset's "center" is. The mean contains information from each observation in a dataset as a result of how it is calculated.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The second and third quartiles, or the center half of your data set, are contained in the interquartile range (IQR).

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Answer:

(3x − 1)(x 8)

Step-by-step explanation:

Considering the critical points of the function, we have that:

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = 3x^3 - 16x + 2[/tex]

The derivative is:

[tex]f^{\prime}{x} = 6x^2 - 16[/tex]

The critical points are given as follows:

[tex]6x^2 - 16 = 0[/tex]

[tex]x^2 = \frac{16}{6}[/tex]

[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]

[tex]x = \pm 1.63[/tex]

For x < -1.63, one example of the derivative is:

[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]

Positive, hence increasing.

For -1.63 < x < 1.63, one example of the derivative is:

[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]

Negative, hence decreasing.

For x > 1.63, one example of the derivative is:

[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]

Positive, hence increasing.

Hence:

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The initial amount of the element is 16

The function is given as:

f(t) = 16(1/2)^t

Set t = 0, to determine the initial amount

f(0) = 16(1/2)^0

This gives

f(0) = 16 * 1

Evaluate

f(0) = 16

Hence, the initial amount of the element is 16

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]

[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]

[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]

[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]

[tex]\qquad❖ \: \sf \:20x = - 9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

________________________________

→ 2(3x + 1) + 3(5x + 2) = x – 1

→ 6x + 2 + 15x + 6 = x – 1

→ 21x + 8 = x – 1

→ 21x – x = – 1 – 8

→ 20x = – 9

→ x = –9/20

________________________________

1) Difference of  the populations  of Germany and  Brazil = 1.16 X 10^8

2) Difference of  the populations  of Brazil and the  United States = 1.2 X 10^8

3) Sum of the  populations of  Brazil and  Germany = 2.76 X 10^8

4) Sum of the  populations of  the United States  and Brazil = 5.12 X 10^8

According to the statement

we have given that the populations of  three countries which are

United States is 3.16 × 10^8 and  Brazil is 1.96 × 10^8 and Germany is 8.0 × 10^7

And we have to arrange the sums and differences in increasing order of their values.

so, we have to find the

a) the difference of  the populations  of Germany and  Brazil

So,

Difference of  the populations  of Germany and  Brazil =  1.96 X 10^8 - 8 X 10^7 = 116000000 = 1.16 X 10^8

And then we have to find the

b) the sum of the  populations of  the United States  and Brazil

So,

Sum of the  populations of  the United States  and Brazil = 3.16 X 10^8 + 1.96 X 10^8 = 512000000 = 5.12 X 10^8

And then we have to find the

c) the difference of  the populations  of Brazil and the  United States

So,

Difference of  the populations  of Brazil and the  United States = 3.16 X 10^8 - 1.96 X 10^8 = 120000000 = 1.2 X 10^8

And then we have to find the

d) the sum of the  populations of  Brazil and  Germany

So,

Sum of the  populations of  Brazil and  Germany:  1.96 X 10^8 + 8 X 10^7 = 276000000 = 2.76 X 10^8

NOW, we arrange the sum and difference in increasing order of their values.

So,

1) Difference of  the populations  of Germany and  Brazil = 1.16 X 10^8

2) Difference of  the populations  of Brazil and the  United States = 1.2 X 10^8

3) Sum of the  populations of  Brazil and  Germany = 2.76 X 10^8

4) Sum of the  populations of  the United States  and Brazil = 5.12 X 10^8

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Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]

To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Subtract 2 from 5.

Subtract 3 from 4.

For any term t, t¹ =t.

Therefore, the correct option is "B".

The fraction based on the information given illustrated for each person.

Me: $14.89

Friend 1: $7.27

Friend 2: $25.67

Friend 3: $11.59

Total = $59.42

The fraction for each person will be:

Me: $14.89 = 14.89/59.42 = 0.25

Friend 1: $7.27 = 7.27/59.42 = 0.12

Friend 2: $25.67 = 25.67/59.42 = 0.32

Friend 3: $11.59 = 11.59/59.42 = 0.195

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Answer:

There are 24 frames of animation in 1 second of anime.    Step-by-step explanation:    There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.

The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

In this question,

A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.

A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.

The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.

The American Express Traveler's Check identification number is 783920*814.

In Airline tickets, there are several digits plus a check digit.

Divide the ID number by 7. The check digit is the remainder.

Sum of digits = 7+8+3+9+2+0+8+1+4

⇒ 42

Now divide the sum by 7, the remainder is

⇒ 42 mod 7 = 42 - (5×7)

⇒ 42 mod 7 = 6

Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

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Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

y = 3x + 3

Step-by-step explanation:

See attached image.

If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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Answer:

Step-by-step explanation:

For two side measures and one angle measure to form one distinct triangle, the given angle must be between the given sides, or opposite the longest side.

When the given measures are ...

The given angle is opposite the longest side, so one distinct triangle can be formed.

No triangle can be formed if the given angle is opposite the shorter given side, and either of ...

__

Additional comment

As we can see from the above, the only ambiguous cases arise when the given angle is opposite the shorter given side. When that happens, the ratio of the shorter to longer given side relative to the sine of the given angle determines the nature of the solution:

Answer:

1

0

Step-by-step explanation:

The distance from Jim's home to the gym is 12 km.

Speed is defined as the rate at which the position of object is changed.

Speed = Distance / Time

Here, there are two different speeds given for the same distance.

Average speed is the total distance travelled by the total time taken.

If distance is a constant,

Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.

Average speed = (2 × 15 × 10) / (15 + 10)

                          = 12 km/hr

So, Total distance travelled = Average speed × total time taken

                                              = 12 × 2

                                              = 24

Distance = 24 / 2 = 12

Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.

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The equation can be used to find other combinations of x and y is  y^2 = (1/16)x^3

The direct variation from the square of y to the cube of x is represented as:

y^2 = kx^3

Where k represents the variation constant.

When x = 4, y = 2.

So, we have:

2^2 = k * 4^3

This gives

4 = 64k

Divide both sides by 64

k = 1/16

Substitute k = 1/16 in y^2 = kx^3

y^2 = (1/16)x^3

Hence, the equation can be used to find other combinations of x and y is  y^2 = (1/16)x^3

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The experimental probability that the subsequent booth competitor will receive a reward is 3/8.

The possibility of an event occurring is determined by probability.

The probability of the occurrence ranges from 0 to 1.

If the event doesn't happen, it = 0;

otherwise, it = 1.

For instance, the likelihood that it will storm on Sunday ranges from 0 to 1. If it storms, the event is given a value of 1. If it doesn't, the event is given a value of zero.

Depending on the outcome of a study that has been run several times, the experimental probability is calculated.

The number of winners in the games divided by the total number of competitors in those games determines the probability that the following competitor will earn a reward.

So, here the probability = 6/16 = 3/8 (by dividing both the numerator and the denominator by 2).

Therefore, the final solution is P= 3/8 .

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Answer:

d. x =0 or x = -6

Step-by-step explanation:

x(x + 6) = 0

This is telling us that either x is 0 or x is -6, because:

1) when x = 0, 0*(0+6)=0, and

2) when x = -6, -6*(-6+6) = 0;  -6(0) = 0

Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.

The form of quadratic equations is given as

ax2 + bx + c = 0

So, for the quadratic equation, we have

x² - x = 12

Let's make it into quadratic form

x² - x - 12 = 0

Bill solved it as

x(x - 1) = 12

This is wrong, because quadratic equations must be written in the form before solving for the variables

Jenna solved it as

x 2 - x - 12 = 0

Jenna is correct because she converted the equation to a quadratic form before solving for the variables.

Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.

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i. The number of people who like banana only is 20.

ii. The number of people who like none of the fruits is zero.

iii. The number of people who like at most one fruit is 30.

The question has to do with sets.

A set a collection of well ordered items

Since we have 55 people, 3x + 5 people like banana and x + 5 people like apple. If all the people who like apple also like banana and if 2x + 15 people like at least one of fruit then, we have that

3x + 5 + x + 5 + 2x + 15 = 55

3x + 2x + x + 5 + 5 + 15 = 55

6x + 30 = 55

6x = 55 - 25

6x = 30

x = 30/6

x = 5

Since the number of people who like banana only is 3x + 5.

So, number of people who like banana only is n = 3x + 5

= 3(5) + 5

= 15 + 5

= 20

So, the number of people who like banana only is 20.

Since from the question, a person likes at least one fruit, either banana, apple or both. No one likes none of the fruits.

So, the number of people who like none of the fruits is zero.

To like at most one fruit, the person either likes apple or banana.

So, their sum is n = 3x + 5 + x + 5

= 4x + 10.

Since x = 5, we have n = 4x + 10.

= 4(5) + 10

= 20 + 10

= 30

So, the number of people who like at most one fruit is 30.

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Answer:

[tex]l = 5.63 \\ [/tex]

hope this helps

158/4 as a mixed number in the simplest term is  [tex]39\frac{3}{4}[/tex]

The given fraction is 158/4

The number of times that 158 can be divided by 4 = 39

4 x 39 = 156

The remainder = 159 - 156

The remainder = 3

The mixed number is of the form:

[tex]Quotient\frac{Remaider}{Divisor}[/tex]

Therefore, the mixed number is [tex]39\frac{3}{4}[/tex]

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Answer:

Step-by-step explanation:

Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.

5 - 3 × (a³-b²)²                           a=3 and b=5

5 - 3 × (3³ - 5²)² =

5 - 3 × (27  - 25)² =

5 - 3 × (2)² =

5 - 3 × 4 =

5 - 12 =

-7

The error in the steps is that In step 1, she should have also distributed -3/8  over –16d, to get 3 + 6 d + 2 d = 24

Given the following equation as shown below

-3/8(-8-16d)+2d = 24

Step 1 Distribute -3/8 over the expression in parentheses

3 + 6d + 2d = 24

Simply the like terms

3 + 8d = 24

Subtract 3 from both sides of the equation.

8d = 24 - 3

8d = 21

d = 21/8

Hence the error in the steps is that In step 1, she should have also distributed -3/8  over –16d, to get 3 + 6 d + 2 d = 24

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Answer:

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

Step-by-step explanation:

x² + y² - 2x - 8 = 0

x² - 2x + y² = 8

Complete the square in x.

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

Center: (1, 0); radius: 3

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

The diameter of circle O in the image given is: AB.

The diameter of a circle can be referred to as the largest chord in a circle which is the line segment that passes through the center of a circle with both ends on the circle.

In the image given, AB is the largest chord and also passes through the center of the circle, O.

Thus, the diameter is: AB.

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Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).

We know that for each bowl, she needs 1/2 cups of milk.

And we also know that she has a total of (3 + 3/5) cups of milk.

To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:

(3 + 3/5)/(1/2)

We can rewrite the total as:

3 + 3/5 = 15/5 + 3/5 = 18/5

Then the quotient becomes:

(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5

So she can make 7 bowls of cereal (and some leftover milk).

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