Analyzing Graphs of Functions
Which graph shows a function where f(2)= 4?
21
12
12y
12ty
8
8
8
8
4
4
4
х
4 8 12
-12-8 -4
4 8 12
-12-8-4
4 8 12
12-48-4
4 8 12
4
-12-84
8-44
-8
-12
8
-8
-12
-12 V
Intro
Done

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SOLUTION

From our question;

x = 13.9

Triangle BCD is similar to triangle EFG.

Answer:

-12

Step-by-step explanation:

y=-2x + 8

when x = 10

substitute the value of x in the equation

y = -2(10) + 8

y = -20 + 8

y = -12

Step-by-step explanation:

it is then simply scanned (multiplied).

the new point is

(-8 × 1/4, 0 × 1/4) = (-2, 0)

Given the following question:

(incomplete question)

To determine the degree of a polynomial we have to find the highest power IN the polynomial.

Example:

Since 6 is the highest power in the polynomial.

To find the leading coefficient of a polynomial is the first coefficient (number placed before a variable) in the polynomial.

Example one:

Since 4 is the first coefficient in the polynomial.

Example two:

Since 3 is the first coefficient in the polynomial.

ANSWER

EXPLANATION

We want to find the median of the data set.

First, we have to arrange the data values in the data set from least to greatest:

Since the number of data values in the data set is even (8), to find the median, find half of the sum of the two middle terms in the ordered dataset i.e. 5 and 9.

That is:

That is the median of the data set.

The commission of Jack on selling house is $7552.9.

Given that, Jack make on the sale of a $160,700 house if he receives 4.7% of the selling price.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let commission of Jack be x.

Now, x= 4.7% of 160,700

⇒ x = 0.047 × 160,700

⇒ x = 7552.9

Therefore, the commission of Jack on selling house is $7552.9.

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Applying the definition of the adjacent angles of a trapezoid, the value of x in quadrilateral TUVS is: x = 4.

The adjacent angles of a trapezoid are the angles that are found on the same leg of the trapezoid, and they are said to be supplementary to each other because they have a sum of 180 degrees.

Given that quadrilateral TUVS is a trapezoid, where angles SVU and TSV are adjacent angles, therefore:

m∠SVU + m∠TSV = 180°

m∠SVU = 139°

m∠TSV = (14x - 15)°

Substitute

139 + (14x - 15) = 180

139 + 14x - 15 = 180

Combine like terms

124 + 14x = 180

14x = 180 - 124

14x = 56

14x/14 = 56/14

x = 4

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Since the original triangle, which is triangle 1 has points A, B, and C.

The points in triangle 2 that corresponds to points A, B, and C are:

Points C, D, and A

Point C corresponds to point A

Point D corresponds to point B

POint A corresponds to point C

ANSWER:

Points C, D and A

Answer:

Step-by-step explanation:

The trigonometric functions are represented by the following function form:

Then, for the following function:

Since it is an arctan function reflected the y-axis:

Recall that when two angles add to give 90 degrees, they are called "complementary angles" This is the case here where you are adding an unknown angle to one that measures 51 degrees to obtain a right angle (90 degrees)

The unknown angle (?) is called the "complementary angle to the 51 degree one.

Please select the third option :

C. Complementary.

Do you remember how it looks an angle that measures 90 degrees? It looks like the angle formed by a square edge, or by two lines that are perpendicular to each other.

When you have two angles one in contact (adjacent) to the other and the two together complete a right angle , those two angles are called complementary angles. There is nothing profound to derive from that, but that it is simply a definition.

If the table is linear we can find an equation in the form

in which b is the y-intercept and

The red triangle is the original figure

The green triangle is the image

Scale factor is 4

Answer:

0.12

Step-by-step explanation:

15/25 as a decimal is 0.6

0.6(0.2)  Time 0.6 by the scale factor to get 0.12.

The behavior of the function is given as follows:

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. Said differently, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x-axis (as x approaches -∞).

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The curve of the function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.

Given that,
A graph has been shown the behavior of the graph is to be discussed.

When a function is graphed, the function must show something likewise increasing, decreasing, and contant relationship.

Here
As per the observation, the graph starts from A and seems to be decreasing up to B and further it is Constant up to C and then increases up to D, afterward it is decreasing up to E.

Thus, the curve of function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.

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A rectangular garden has one side with a length of x + 7 another with a length 2x + 3

We are asked to find the perimeter of the garden

Let me draw this rectangular garden to better understand the problem

Recall that the perimeter of a rectangular shape is given by

Where W is the width and L is the length of the rectangular garden

Let us substitute the given values into the above formula

Now simplify the equation

Therefore, the perimeter of the rectangular garden is equal to 6x + 20.

Solution:

The cuboid is a solid-shaped figure formed by six faces. A cuboid is a simple figure. It has three dimensions - width, length, and height. Thus, the cuboid is a parallelepiped. Now, the surface area of the parallelepiped is the sum of the areas of all sides, that is:

where

l is the lenght

w is the width

and

h is the height

According to the figure given in the problem, we have that:

l = 30

w = 10

h = 10

thus, the surface area of the given cuboid would be:

So that, we can conclude that the correct answer is:

Answer:

Step-by-step explanation:

Let the acute angles be B and C.

If we add a parallel line through the point A, we'll see that:

And we know that:

Plug in the known parameters to get:

We are looking for the value of C:

The maximum displacement is 5, the angular frequency is 2π and the period of the motion is 1.

Kinematically speaking, an object under simple harmonic motion is described by the following equation:

y = A · cos (2π · t / T)

Where:

Please notice that the angular frequency ω, radians per second, is equal to 2π / T. Then, we find that the maximum displacement is 5, the angular frequency is 2π and the period of the motion is 1.

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The value of the angle x will be equal to 113.5°.

An angle may be defined as the figure which can be formed from two rays joining at a point. The lines will be called as the sides of the angle and the point at which the rays join is called vertex of the angle. There are generally 5 types of angles namely Acute angle, Obtuse angle, Reflex angle, Right angle and Complete angle. The value of a complete angle will be given as 360°. Since, in the question all the angles are measured to the nearest. So, the value of 59° could actually be something between 58.5° and 59.5°. Analogously, 108° is between 107.5° and 108.5°, and 81° is between 80.5° and 81.5°. Now, the summation of all four angles will be equal to 360°.

x + 58.5° + 107.5° + 80.5° = 360°

=> x = 360° - (58.5° + 107.5° + 80.5°)

=> x = 360° - 246.5°

=> x = 113.5° which is the required value.

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Using the normal distribution and the central limit theorem, it is found that the probabilities are given as follows:

24. Single person has an IQ score above 105: 0.3694.

25. Sample mean (55 people) above 105: 0.0067.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of IQ scores are given as follows:

[tex]\mu = 100, \sigma = 15[/tex]

The probability that a single person has an IQ score higher than 105 is one subtracted by the p-value of Z when X = 105, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (105 - 100)/15

Z = 0.33

Z = 0.33 has a p-value of 0.6306

1 - 0.6303 = 0.3694.

For the sample of 55, the standard error is:

[tex]s = \frac{15}{\sqrt{55}} = 2.02[/tex]

Hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (105 - 100)/2.02

Z = 2.48

Z = 2.48 has a p-value of 0.9933.

1 - 0.9933 = 0.0067.

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Answer:

177.12

Step-by-step explanation:

multiply 144 by 0.23 = 33.12

add 33.12 to 144

awnser is 177.12

The presented data for x and y show a significant, positive correlation with 0.78 serving as the coefficient of correlation.

The intensity and direction of a relationship between two variables are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a dataset. The other variables shift in the same direction when one changes.

The intensity and direction of a relationship between two variables are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a dataset.

Given x and y values in this case

x     1     2    3     4     5     6

y     3    4    9     7     2     18

xy   3    8   27  28   10   108

x²    1    4    9    16   25    36

y²    9  16  81    49     4   324

∑x = 21,  

∑y = 43,  

∑xy = 194,

∑x² = 91,

∑y² = 483,

n = 6

the relationship between x and y now:

r = (n∑xy - ∑x.∑y)/ √[{n∑x²- (∑x)²}{n∑y² - (∑y)²}]

r = ( 6 X 194 - 21 X 43 ) / √[ {6 X 91 - (21)²}{ 6 X 483 - (43)²}]

r = ( 1164 - 903) / √( 546 - 441)(2898 - 1849)

r = 261 / √ 105 X 1049

r = 261 / √110145

r = 261 / 331.88

r = 0.78

As a result, the x and y data's correlation coefficient is 0.78.

The strong, positive association between x and y

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Answer:

this is your answer hope this helps you

The roots of an equation is "solutions" of the equation. Solutions are the numerical values equal to the variable after solving it.

To determine the sum and product of the roots of a quadratic equation, the equation has to be written in the form ax²+bx+c = 0

From that form, the sum of the roots is given by -b/c and the product is c/a

For example, we want to find the sum and product of the roots of the quadratic equation 3x²-x = 2

Notice that the equation is not written in the form described above. So, it has to be written as 3x²-x - 2 = 0

From this form, we see that  and a = 3, b = -1 and c = -2

Therefore, the sum is -b/a = 1/3  while the product is c/a = -2/3 = -2/3

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The x–intercept of g(h(x)) is the option;

[tex] \displaystyle {-\frac{2}{3}}[/tex]

The x–intercept of a function is given by the point where the function intersects the x–axis.

From the given table, the slope of the graph of g(x), [tex] m_1 [/tex] is given by the equation;

[tex] \displaystyle{ m_1 = \frac{ - 4 - ( - 8)}{ - 4 - ( - 6))} = \frac{4}{2} = 2}[/tex]

The equation of g(x) in point slope form is therefore;

g(x) - (-4) = 2×(x - (-4)) = 2•x + 8

g(x) = 2•x + 8 - 4 = 2•x + 4

g(x) = 2•x + 4

The slope of the function h(x), [tex] m_2 [/tex] is found using the equation;

[tex] \displaystyle{ m_2 = \frac{ 8 - 14}{ - 4 - ( - 6))} = \frac{ - 6}{2} = - 3}[/tex]

h(x) presented in point and slope form is therefore;

h(x) - 8 = (-3)×(x - (-4)) = -3•x - 12

h(x) = -3•x - 12 + 8 = -3•x - 4

h(x) = -3•x - 4

g(h(x)) = 2•h(x) + 4

Plugging in the value of h(x) gives,;

g(h(x)) = 2×(-3•x - 4) + 4 = -6•x - 8 + 4

g(h(x)) = -6•x - 4

The x–intercept of g(h(x)) is given by the point where g(h(x)) = 0, which gives;

At the x–intercept, g(h(x)) = 0 = -6•x - 4

[tex] \displaystyle{ x = \frac{4}{-6} = -\frac{ 2}{3} }[/tex]

The x–intercept is [tex] \displaystyle{ -\frac{ 2}{3} }[/tex]

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We are given the percentages for males on the left side and the percentages for females on the right side.

We are trying to find four groups that make up nearly 1/2 of the male population, so we want the percentages for these groups to add up to nearly 50%.

Let's take a look at the lowest age groups of the male population, which in turn make up the highest proportion of the male population.

We have the age group 0-4, which makes up roughly 12%.

We have the age group 5-9, which makes up roughly 11%.

We have the age group 10-14, which makes up roughly 11%.

We have the age group 15-19, which makes up roughly 12.5%.

If we add all of these percentages together, we get:

12% + 11% + 11% + 12.5% = 46.5%

Since we cannot go any smaller than 46.5% because this is the closest percentage to 50%, the four groups that make up nearly one half of the male population must be:

Ages 0-4, 5-9, 10-14, and 15-19

The table and graph given show the information about two national parks.

It is required to find the rate of change of the population of the two parks between 2009 and 2014, and then determine the park that shows faster population growth during those years.

Notice that the variable x represents the number of years after 2005.

Hence, the years 2009 and 2014 represent, x=4 and x=9, respectively.

The formula for the rate of change of a function f(x) between x=a and x=b is given by the formula:

Calculate the rate of change for park A:

Substitute a=4 and b=9 into the formula:

Substitute f(9)=2870 and f(4)=2370 from the table for park A into the expression for the rate of change:

Calculate the rate of change for park B:

Substitute f(9)=2800 and f(4)=2200 from the graph of park B:

Notice that the rate of change in population for park B is higher than that of park A.

Hence, park B showed faster population growth during those years.

Answers:

Rate of change for park A= 100 swallows per year.

Rate of change for park B= 120 swallows per year.

Park B showed faster population growth during those years.

Answer:

182

Step-by-step explanation:

It’s literally 546 divided by 3