Answers
Question 16
[tex](f(x), g(x))=x^2, (x-9)[/tex]
Note it wants the pair, so you just include the definitions of the functions, not f(x)= and g(x)=Question 17
[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]
The values for first question are f(x) = x², g(x) = (x - 9) and for second question f(x) = √x, g(x) = 9 + √x.
A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called independent variable and output variable is called dependent variable. A composite function is the one which is written as a combination of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the parent functions will be f(x) = x² and g(x) = (x - 9).
in the second question the composite function is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.
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Related Questions
Three cubes of side 10 cm are joined end to end to form a cuboid as given in the figure. Find is total surface area.
Answers
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:
[tex]S\text{ =2(}lw+lh+wh\text{)}[/tex]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:
[tex]\begin{gathered} S\text{ =2(}lw+lh+wh\text{)} \\ \text{ = 2((}30\cdot10\text{)+(30}\cdot10\text{)+(10}\cdot10\text{))=}1400 \end{gathered}[/tex]So that, we can conclude that the correct answer is:
[tex]1400[/tex]
Graph the image of ∆KLM after a dilation with a scale factor of 4, centered at the origin.
Answers
The red triangle is the original figure
The green triangle is the image
Scale factor is 4
Which four groups make up nearly one half of the male population?
Answers
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
HELP! Use the graph to determine the behavior of the function between the indicated points.
Answers
The behavior of the function is given as follows:
A and B - DecreasingB and C - ConstantC and D - IncreasingD and E - Decreasing.What is a function?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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Points B and C are on parallel lines with s and T, respectively. The size of the angle BAC is 96 degrees. Find the acute angle between straight AC and straight t if it is known that it is three times the size of the acute angle between straight AB and straight S.
Answers
Answer:
72°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:
m∠BAC = B + CAnd we know that:
m∠BAC = 96C = 3BPlug in the known parameters to get:
B + 3B = 964B = 96B = 24We are looking for the value of C:
C = 3*24 = 72I need help with this practice Please read below ‼️‼️Use pencil and paper to graph the function, if you can’t, please use a drawing/writing tool that is *NOT* a graphing tool. If you cannot do this let me know
Answers
Answer:
Step-by-step explanation:
The trigonometric functions are represented by the following function form:
[tex]\begin{gathered} f(x)=\text{Atrig(Bx-C)}+D \\ \text{where,} \\ A=\text{ amplitud} \\ B,C=\text{ phase shift} \\ D=\text{ vertical shift} \end{gathered}[/tex]Then, for the following function:
[tex]f(x)=-\cot (x+\frac{\pi}{6})[/tex]Since it is an arctan function reflected the y-axis:
Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).
Answers
The x–intercept of g(h(x)) is the option;
[tex] \displaystyle {-\frac{2}{3}}[/tex]
What is a The x–intercept of a function?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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Please Help:What is the median of the data set?9, 3, 10, 12, 4, 5, 12, 2Enter your answer in the box. __
Answers
ANSWER
[tex]7[/tex]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:
[tex]2,3,4,5,9,10,12,12[/tex]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:
[tex]\begin{gathered} \frac{5+9}{2}=\frac{14}{2} \\ \Rightarrow7 \end{gathered}[/tex]That is the median of the data set.
What is the value for y in the following expression
when x = 10
y=-2x + 8
Answers
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
What is the image of ( − 8 , 0 ) after a dilation by a scale factor of 1/4 centered at the origin?
Answers
Step-by-step explanation:
it is then simply scanned (multiplied).
the new point is
(-8 × 1/4, 0 × 1/4) = (-2, 0)
Find a degree 3 polynomial having zeros -8, 2 and 8 and the coefficient of x3 equal 1.
Answers
The degree 3 polynomial is "x³-2x²-64x+128".
We have to find a polynomial of degree 3.We are given that the polynomial has -8, 2, and 8 as its roots.We are also given that the coefficient of x³ equals 1.If x = -8 is a root, then:(x+8) is a factor of the polynomial.If x = 2 is a root, then:(x-2) is a factor of the polynomial.If x = 8 is a root, then:(x-8) is a factor of the polynomial.All the three roots are of the same polynomial.So, the polynomial is the product of these factors.(x+8)(x-8)(x-2)(x²-64)(x-2)x³-2x²-64x+128The required polynomial is "x³-2x²-64x+128".To learn more about polynomials, visit :
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Triangle BCD is similar to triangle EFG. Find the measure of side EF. Round youranswer to the nearest tenth.
Answers
Triangle BCD is similar to triangle EFG.
x2Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.Degree:. Leading Coefficient
Answers
Given the following question:
(incomplete question)
To determine the degree of a polynomial we have to find the highest power IN the polynomial.
Example:
[tex]\begin{gathered} 4x^2+5^6-9 \\ \text{Degree of the polynomial is 6 } \end{gathered}[/tex]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:
[tex]\begin{gathered} 4x^2+5^6-9 \\ \text{ Leading coefficient is 4} \end{gathered}[/tex]Since 4 is the first coefficient in the polynomial.
Example two:
[tex]\begin{gathered} x^2+3x-7 \\ \text{ Leading coefficient is 3} \end{gathered}[/tex]Since 3 is the first coefficient in the polynomial.
find volume of hemisphere who’s great circle has an area of 12.5 ft squared
Answers
The surface area of a hemisphere is given as 12.5 square feet. It is required to find the volume of the hemisphere.
To do this, equate the given surface area to the formula, find the radius, and then substitute the radius into the volume formula to find the volume.
The surface area of a hemisphere radius, r is given as:
[tex]S=3\pi r^2[/tex]Substitute S=12.5 into the formula and solve for r in the resulting equation:
[tex]\begin{gathered} 12.5=3\pi r^2 \\ \Rightarrow3\pi r^2=12.5 \\ \Rightarrow\frac{3\pi r^2}{3\pi}=\frac{12.5}{3\pi} \\ \Rightarrow r^2=\frac{25}{6\pi} \\ \Rightarrow r=\sqrt{\frac{25}{6\pi}} \end{gathered}[/tex]The volume of a hemisphere is given as:
[tex]V=\frac{2}{3}\pi r^3[/tex]Substitute the calculated value of r into the volume formula:
[tex]\begin{gathered} V=\frac{2}{3}\pi\left(\sqrt{\frac{25}{6\pi}}\right)^3 \\ \text{ Substitute }\pi=3.14\text{ into the equation:} \\ \Rightarrow V=\frac{2}{3}(3.14)\left(\sqrt{\frac{25}{6(3.14)}}\right)^3\approx3.2\text{ square feet} \end{gathered}[/tex]The required volume is about 3.2 square feet.
A journal on how to determine a quadratic equation given the roots
Answers
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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How much commission will jack make on the sale of a $160,700 house if he receives 4.7% of the selling price His commission will be …?
Answers
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.
What is percentage?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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A student incorrectly simplifies an expression. The expression and work is shown below.
-(-6)(-3) - 2/3 (22 - 7)
3/5
Step 1: -(-6) (-3) - 2/3 (15)
3/5
Step 2: 18 - 2/3 (15)
3/5
Step 3: 18 - 10
3/5
Step 4: 8_3_5
Answer they got: 4 4/5
Idetnfiy which step is incorrect.
.
PLSSS HELP MEEEEEE
Answers
Answer:
so in the second step you see how the 18 is a positive
its supposed to be a negative
in the step 1, the part is -(-6)(-3), right?
so the negative symbol outside the negative 6 cancels out the negative, making it a positive number
it becomes 6(-3), which them multiplies into -18
so, i think the explanation is "the person forgot to change the 18 to a negative in the second step"
yea lol i think thats it
help pls for my freind!!!
Answers
A rectangular garden has one side with a length of x + 7 and another with a length 2x + 3. Find the perimeter of the garden.
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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
[tex]P=2(W+L)[/tex]Where W is the width and L is the length of the rectangular garden
Let us substitute the given values into the above formula
[tex]P=2(x+7+2x+3)[/tex]Now simplify the equation
[tex]\begin{gathered} P=2(x+2x+7+3) \\ P=2(3x+10) \\ P=6x+20 \end{gathered}[/tex]Therefore, the perimeter of the rectangular garden is equal to 6x + 20.
The wholesale price for a bookcase is $144. A certain furniture store marks up the wholesale price by 23%. Find the price of the bookcase in the furniture store.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
177.12
Step-by-step explanation:
multiply 144 by 0.23 = 33.12
add 33.12 to 144
awnser is 177.12
If each quadrilateral below is a trapezoid, find the missing measures.
#5
Answers
Applying the definition of the adjacent angles of a trapezoid, the value of x in quadrilateral TUVS is: x = 4.
What are the Adjacent Angles of a Trapezoid?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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Mary and two of her friends shared the cost of gas for a road trip if the total amount that they paid for gas was $546 and they shared it equally what amount did mary pay
Answers
Answer:
182
Step-by-step explanation:
It’s literally 546 divided by 3
List the common factors of 4, 36, 58, and 1000.
Answers
factors of 4 are: 1, 2, 4
factors of 36 (up to 4) are: (1, 2, 3, 4), 6, 9, 12, 18, 36
factors of 58 (up to 4) are: (1, 2), 29, 58
Factors of 1,000 (up to 4) are: (1, 2, 4), 5, 8, 10, etc…
Common factors mean that each number must have that factor, like each number having a common factor of 1. If only two of the listed numbers have a common factor, we won’t include it.
The largest factor of 4 is 4, so we cannot go higher than that for the possible common factors.
4, 36, 58, and 1,000 have common factors of:
1 and 2.
Find the rates of change in population for both parks between 2009 and 2014, and determine which park showed faster population growthduring those years.
Answers
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:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]Calculate the rate of change for park A:
Substitute a=4 and b=9 into the formula:
[tex]\frac{f(9)-f(4)}{9-4}[/tex]Substitute f(9)=2870 and f(4)=2370 from the table for park A into the expression for the rate of change:
[tex]\frac{2870-2370}{9-4}=\frac{500}{5}=100\text{ swallows per year}[/tex]Calculate the rate of change for park B:
[tex]\frac{f(9)-f(4)}{9-4}[/tex]Substitute f(9)=2800 and f(4)=2200 from the graph of park B:
[tex]\frac{2800-2200}{9-4}=\frac{600}{5}=120\text{ swallows per year}[/tex]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.
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
Answers
From the graphs we can conclude:
[tex]undefined[/tex]Scale 15/25 by the factor of 0.2.
Answers
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.
Working with Law of Sines. I have attached a picture.
Answers
..
SOLUTION
[tex]\begin{gathered} Sine\text{ rule is given as;} \\ \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC} \end{gathered}[/tex][tex]Where\text{ the capital letters represent the angles and the small letters stand for the sides facing each angle.}[/tex]From our question;
[tex]\frac{13}{sin68}=\frac{x}{sin83}[/tex][tex]\begin{gathered} x=\frac{13sin83}{sin68} \\ x=13.9 \end{gathered}[/tex]x = 13.9
Questions 24-25
The scores of a standardized IQ test are normally distributed with a mean score of 100 and a standard deviation of 15.
Question 24 2
Find the probability that a randomly selected person has an IQ score higher than 105.
Question options:
0.9522
0.3694
-1.15
0.6306
Question 25
A random sample of 55 people is selected from this population. What is the probability that the mean IQ score of the sample is greater than 105?
Question options:
0.0067
0.3694
0.6306
0.9933
Answers
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.
Normal Probability DistributionThe 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 z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/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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АD✓32What points in Triangle 2 correspond to points A, B,and C in the original triangle?BSubin7:4610/5
Answers
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
The graph below plots the values of y for different values of x: plot the ordered pairs 1, 3 and 2, 4 and 3, 9 and 4, 7 and 5, 2 and 6, 18 What does a correlation coefficient of 0.25 say about this graph? (1 point) x and y have a strong, positive correlation x and y have a weak, positive correlation x and y have a strong, negative correlation x and y have a weak, negative correlation
Answers
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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