Answers
The solution of the composite function is as follows:
(f + g)(x) = 9x + 1(f - g)(x) = -7x - 17 (f. g)(x) = 8x² - 55x - 72(f / g)(x) = x - 8 / 8x + 9How to solve composite function?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
Therefore,
f(x) = x - 8
g(x) = 8x + 9
Hence,
(f + g)(x) = f(x) + g(x) = x - 8 + 8x + 9 = 9x + 1
(f - g)(x) = f(x) - g(x) = x - 8 - ( 8x + 9 ) = x - 8 - 8x - 9 = -7x - 17
(f. g)(x) = f(x) . g(x) = (x - 8)(8x + 9) = 8x² + 9x - 64x - 72 = 8x² - 55x - 72
(f / g)(x) = f(x) / g(x) = x - 8 / 8x + 9
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Related Questions
Franklin is drawing a model of a rectangular swimming pool. He marks two points, A and B, on the coordinate plane and connects them to represent one side of the pool. Points C and D are reflections of B and A, respectively, across the x- axis. Each unit in the coordinate plane represents 1 meter. Draw a rectangle in the coordinate plane yo model the swimming pool. What is the area of the swimming pool?
Answers
Area = base x height
A = 8 x 6 = 48 m²
the triangle in the figure had a hypotenuse equal to 40 units what is the approximate length of x
25.7 units
30.6 units
47.7 units
52.2 units
(Srry I’m spamming I know nothing on this test)
Answers
If the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
The length of the hypotenuse = 40 units
The angle = 50 degrees
Here we have to apply the trigonometric function
we know
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
Here we have to use the equation of sin θ
Substitute the values in the equation
sin 50 = x/40
x = 40×sin 50
x = 30.64 units
Hence, if the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
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The figure shown represents a triangular window design. If ΔIKL ≅ ΔJOP, which of the following statements must be true?
Answers
The most appropriate choice for congruency of triangles will be given by
[tex]\bar{IL} \cong \bar{JP}[/tex]
Third option is correct.
What are congruent triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are equal.
There are five axioms of congruency. They are
SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom.
Here,
ΔIKL ≅ ΔJOP [Given]
[tex]\bar{IL} \cong \bar{JP}[/tex] [Corrosponding parts of congruent triangles are congruent]
Third option is correct.
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Complete Question
The diagram with the question has been attached below
Classify the triangle with side lengths 8,13,20. a) Acute b) Right c) Obtuse
Answers
for right angles triangle,
hyposenuse square should be equal to sum of square of other two sides
it fails that law so its not right angled triangle
Find all numbers whose absolute value is .4]
Answers
The numbers 4 and - 4 have an absolute value equal to 4.
What numbers are associated to a given absolute value?
In this question we need to find all the numbers such that absolute value is equal to 4. This can be found by using the definition of absolute value:
|x| = x for x ≥ 0.|x| = - x for x < 0.Absolute values are functions that contains only the magnitudes of the numbers, that is, their distances with respect to zero. Then, if the absolute value is 4, then, the number may be 4 or - 4.
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The absolute value is 4, then, the number may be 4 or - 4.
What are Absolute values?Absolute value describes the distance from zero that a number is on the number line, without considering direction
To find all the numbers such that absolute value is equal to 4.
By definition of absolute value we have
|x| = x for x ≥ 0.
|x| = - x for x < 0.
Absolute values contains magnitude which does not have direction.
|4|=4 for 4≥ 0.
|4| = -4 for x < 0.
Then, if the absolute value is 4, then, the number may be 4 or - 4.
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give the answer as a mixed number and as an improper fraction (number 1)
Answers
Answer:
Jossie has filled 59/30 of the 3 baskets.
Step-by-step explanation:
If Jossie has filled 3/5 of one, 7/10 of another, and 2/3 for the last one. The proportion of the total baskets:
[tex]\frac{3}{5}*\frac{2}{2}+\frac{7}{10}+\frac{2}{3}=\frac{6}{10}+\frac{7}{10}+\frac{2}{3}[/tex]Compute.
[tex]\frac{13}{10}+\frac{2}{3}=\frac{39+20}{30}=\frac{59}{30}[/tex]Jossie has filled 59/30 of the 3 baskets.
A linear function has a slope of 11. Interpret this slope with a complete sentence using the words“inputs” and “outputs”. (1 point)As the inputs________,_______
Answers
Answer
the inputs increase by 1 and the outputs increase by 11
Step-by-step explanation:
The standard form of a linear function is written as
y = mx + c
where m = slope
Since the slope is 11
y = 11x + c
This implies that the inputs increase by 1 and the outputs increase by 11
Identify the type(s) of symmetry for the graph below.Select all that apply. aSymmetry with respect to the line \small \theta=\frac{\pi}{2} bSymmetry with respect to the polar axis cSymmetry with respect to the pole
Answers
The line θ=π/2 is the vertical line in the polar grid, the polar axis is the horizontal line and the pole is the center of coordinates. Now let's analyze the symmetries:
If the grpah is symmetric with respect to θ=π/2 then the graph at the left of this line has to be the mirrored image of the graph at the right side. This is the case of this graph so it does have symmetry with respect to θ=π/2.
For the polar axis is the same, the graph above the axis has to be the mirrored image of that below the axis. However in this case we have two "petals" above the polar axis and one below so the upper part is not the mirrored version of the lower part so it has no symmetry with respect to this axis.
For the pole we must rotate the graph 180°. If the graph remains unchanged then it is symmetric with respect to it. In this case if we rotate the graph 180° the lower petal ends up in the opposite direction so the graph changes after a 180° rotation and it has no symmetry with respect to the pole.
Then the only type of symmetry is with respect to the line θ=π/2 and the answer is option a.
I need the slope the y intercept is -2 and the x intercept is -1
Answers
The x intercept is the value of x when y = 0
Given that x intercept = - 1, the coordinate is (- 1, - 0)
The y intercept is the value of y when x = 0
Given that y intercept = - 2, the coordinate is (0, - 2)
Slope = (y2 - y1)/(x2 - x1)
x1 = - 1, y1 = 0
x2 = 0, y2 = - 2
Slope = (- 2 - 0)/(0 - - 1)
slope = - 2/1
slope = - 2
which of the following is an integer ) 58/81) π) -11) 27.4444....
Answers
-11 is an integer number
The function f (x) = x+4/3 is in a system with its inverse f-1(x). What is the solution to the system?
Answers
Mrs. Williams estimates that she will spend $65 onschool supplies. She actually spends $73. What is thepercent error? Round to the nearest tenth ifnecessary.
Answers
We can calculate the percent error as the absolute difference between the predicted value ($65) and the actual value ($73) divided by the actual value and multiplied by 100%.
This can be written as:
[tex]e=\frac{|p-a|}{a}\cdot100\%=\frac{|65-73|}{73}\cdot100\%=\frac{8}{73}\cdot100\%\approx11.0\%[/tex]Answer: the percent error is approximately 11.0%
After adding the two equations to eliminate x you are left with 4y=-8
Answers
solve for y
[tex]\begin{gathered} \frac{4y}{4}=-\frac{8}{4} \\ y=-2 \end{gathered}[/tex]then, solve for x
[tex]\begin{gathered} 2x-2=4 \\ 2x-2+2=4+2 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]x = 3
y = -2
What is the greatest common factor of 9 and 72?
Answers
The Greatest Common Factor of 9 and 72 is: 9
SOLUTION
Problem Statement
The question asks us to find the greatest common factor of 9 and 72.
Method
In order to solve this question, we just need to follow these steps:
1. Write out the prime factors of 9 and 72
2. Choose the common factors from both expressions.
3. Multiply the common factors.
Implementation
1. Write out the prime factors of 9 and 72:
[tex]\begin{gathered} 9=1\times3\times3 \\ \text{The common factors of 9 are: 3 and 3} \\ \\ 72=1\times2\times2\times2\times3\times3 \\ \text{Common factors of 72 are: 1,2, 2, 2 and 3, 3} \end{gathered}[/tex]2. Choose the common factors from both expressions.:
We need to examine the two expressions for 9 and 72 above. Choose the common values.
[tex]\begin{gathered} 3\times3\text{ is common to both 9 and 72} \\ i\mathrm{}e\text{.} \\ 9\text{ is common to both 9 and 72} \\ 3\text{ is common to both 9 and 72 as well} \\ 1\text{ is also common to both 9 and 72} \end{gathered}[/tex]3. Multiply the common factors.:
[tex]\begin{gathered} \text{Thus, choosing the greatest values from 1,3 and 9.} \\ \therefore\text{The Greatest Common Factor = 9} \end{gathered}[/tex]Final Answer:
The Greatest Common Factor of 9 and 72 is: 9
The lower quartile for wages at a coffee shop is $8.25, and the upper quartile is $10.75. What can you conclude? a. Half the workers earn between $8.25 and $10.75. b. The median is $9.50. c. The range is $2.50 H COR B
Answers
A)Half the workers earn between $8.25 and $10.75.
1) We must remember that the First Quartile responds to 25% of the data points, as well as the Third Quartile responds to 75% of the data points within this dataset.
2) Since the first quartile and the third quartiles were given, then we can tell that
Half the workers earn between $8.25 and $10.75
The median will present exactly what is the value.
Because the difference between the third and the first quartile corresponds to 50%.
Moreover to that, there's not much information about the dataset to figure the range (Highest minus lowest data point) or the median.
there are twelve inches in one foot,creating the equation y=12x. if a door frame is 6.5 feet tall,how many inches tall is it
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 12in=1ft \\ y=12x \end{gathered}[/tex]The height of the door frame is 6.5 feet. To convert to inches, we have:
[tex]\begin{gathered} y=12(6.5)=78inches \\ y=78inches \end{gathered}[/tex]I have no idea what the answer is or how to do it,A certain state uses the following progressive tax rate for calculating individual income tax0-3000 2% tax rate3001-5000 3% tax rate5001-17,000 5% tax rate17,001 and up 5.75% tax rateCalculate the state income tax owed on a 60,000 per year salary
Answers
SOLUTION
From the table given, the progessive income tax for salaries of $17,001 and above is 5.75% of the income.
So, for $60,000, it will also be 5.75% of the income.
This becomes
[tex]\begin{gathered} \frac{5.75}{100}\times60,000 \\ =3450 \end{gathered}[/tex]Therefore, the answer is $3,450
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Answers
There are two families who visit a park and pay the entrance fee. The distribution of each family and the total cost paid at the entrance by each are given:
Family 1:
[tex]\begin{gathered} NumberofAdults(A_1\text{ )= 2} \\ NumberofChildren(B_{1\text{ }})\text{ = 3} \\ TotalEntryCost(C_1)\text{= }20\text{ pounds} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} NumberofAdults(A_2\text{ ) = 1} \\ NumberofChildren(B_2\text{ )= 4} \\ TotalEntryCost(C_2\text{ )= 15 pounds} \end{gathered}[/tex]Now we will define the ticket rates for adults and children at this park:
[tex]\begin{gathered} \text{Adult Rate = x} \\ \text{Children Rate = y} \end{gathered}[/tex]Next step is to express the total entry cost born by each family. This is done by multiplying the rate of each age group with the respective distribution of age group comprising each family.
Family 1:
[tex]\begin{gathered} C_1\text{ = x}\cdot A_1\text{ + y}\cdot B_1 \\ 20\text{ = 2}x\text{ + 3}y\text{ }\ldots.\text{ Eq1} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} C_2\text{ = x}\cdot A_2\text{ + y}\cdot B_2 \\ 15\text{ = x + 4y }\ldots Eq\text{ 2} \end{gathered}[/tex]We have two equation with two unknowns representing the cost charged for adults ( x ) and cost charged for children ( y ) at the park entrance.
We will solve the equation simultaneously ( Eq1 and Eq2 ) by using the process of Elimination:
[tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -2\cdot(15\text{ = x + 4y) = -30 = -2x -8y} \end{gathered}[/tex][tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -30\text{ = -2x -8y} \\ ========== \\ -10\text{ = 0 -5y} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 2}} \end{gathered}[/tex]Plug the value of ( y ) in either of the two equations and solve for ( x ):
[tex]\begin{gathered} 15\text{ = x + 4(2)} \\ x\text{ = 15 - 8} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 7 }} \end{gathered}[/tex]Therefore, the rates charged for each age group are:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Adult ticket = x = 7 pounds}} \\ \text{\textcolor{#FF7968}{Child ticket = y = 2 pounds}} \end{gathered}[/tex]Answer:yes
Step-by-step explanation:
y = -2x + 5a. What is the slope? b. What is the vertical intercept? c. What is the horizontal intercept? d. Graph the equation
Answers
Given: The equation below
[tex]y=-2x+5[/tex]To Determine: The slope, the vertical and horizontal intercept, and the graph of the equation
Solution
The general slope-intercept form of a straight line is as shown below
[tex]\begin{gathered} y=mx+c \\ Where \\ m=slope \\ c=vertical-intercept \end{gathered}[/tex]Let us compare the general slope-intercept form of a straight line to the given
[tex]\begin{gathered} y=mx+c \\ y=-2x+5 \\ slope=m=-2 \end{gathered}[/tex]The vertical intercept is the point where the x values is zero
[tex]\begin{gathered} y=-2x+5 \\ x=0 \\ y=-2(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]The vertical intercept is y = 5, with coordinate (0, 5)
The horizontal intercept is the point where the y value is zero
[tex]\begin{gathered} y=-2x+5 \\ y=0 \\ 0=-2x+5 \\ 2x=5 \\ x=\frac{5}{2} \end{gathered}[/tex]The horizontal intercept is x = 5/2, with coordinate (5/2, 0)
The graph of the equation is as shown below
Answer Summary
(a) slope = -2
(b) Vertical intercept, y = 5
(c) Horizontal intercept, x = 5/2
This is from my prep guideI will provide the answer options in another picture
Answers
In order to determine the corresponding graph to the given function f(x), consider the y-intercept of the function (the value of the y-coordinate of the curve when x = 0).
The y-intercept is the value of f(x) for x= 0. Replace x = 0 into the given function:
[tex]f(0)=(\frac{1}{2})^{0+1}+3=\frac{1}{2}+3=\frac{7}{2}[/tex]Then, the point of intersection of the curve with the y-axis is (0 , 7/2) or (0 , 3.5).
You can notice that from the given answer choices, that option two (up right side) has the required y-intercept. Then, that graph matches with the given function.
Use the following function rule to find f(48).
f(x) = 12 + x/4
Answers
Answer:
See image
depending on what is in the numerator of your question:
24 OR 15 SEE IMAGE!
Step-by-step explanation:
f(48) just means to use 48 in place of x in your work.
f(x) = 12 + x/4
f(48) = 12 + 48/4
Hopefully, your text/worksheet/screen is clear on which problem you are doing.
The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.3 mm. Round values to 4 decimal places when possible.
The mean of this distribution is _____
The standard deviation is _____
The probability that the round off error for a jumper's distance is exactly 0.4 is P(x = 0.4) = ____-
The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.3 mm is P(1.2 < x < 3.4) = ____
The probability that the jump's round off error is greater than 4.16 is P(x > 4.16) = ____
P(x > 4.2 | x > 1.8) = ___
Find the 85th percentile____
Find the maximum for the lower quartile. ____
Answers
Using the uniform distribution, it is found that:
The mean is of 2.65 mm.The standard deviation is of 1.53 mm.P(X = 0.4) = 0.P(1.2 < x < 3.4) = 0.4151 = 41.51%.P(X > 4.16) = 0.2121 = 21.51%.P(X > 4.2|x > 1.8) = 0.3257 = 32.57%.85th percentile: 4.505 mm.Lower quartile: 1.325 mm.Uniform probability distributionThe uniform distribution has two bounds, a and b, and all outcomes in the distribution are equally as likely.
In this problem, the bounds are as follows:
a = 0, b = 5.3.
Hence the mean is:
M = (a + b)/2 = (0 + 5.3)/2 = 2.65 mm.
The standard deviation is of:
[tex]S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{5.3^2}{12}} = 1.53[/tex]
The uniform distribution is continuous, hence the probability of an exact value is of 0.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence:
P(1.2 < x < 3.4) = (3.4 - 1.2)/(5.3 - 0) = 0.4151 = 41.51%.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Hence:
P(X > 4.16) = (5.3 - 4.16)/(5.3 - 0) = 0.2121 = 21.51%.
P(x > 4.2 | x > 1.8) makes the lower bound 1.8, hence:
P(X > 4.2|x > 1.8) = (5.3 - 4.16)/(5.3 - 1.8) = 0.3257 = 32.57%.
The 85th percentile is found as follows:
0.85 x (5.3 - 0) = 4.505 mm.
The lower quartile is the 25th percentile, hence:
0.25 x (5.3 - 0) = 1.325 mm.
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Find the slope, if it exists, of the line containing the pair of points. (−2,−6) and (−15,−7)
Answers
The linear regression for a given data set has the form
[tex]y=a+bx[/tex]where the values a and b can be solved using the equation
[tex]\begin{gathered} a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2} \\ b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2} \end{gathered}[/tex]Based on the given data set, we have n equals 5. We will solve for the values of the summation first. We have the following
[tex]\begin{gathered} \sum y=4+4+6+6+8=28 \\ \sum x=1+3+5+7+9=25 \\ \sum xy=(1\cdot4)+(3\cdot4)+(5\cdot6)+(7\cdot6)+(8\cdot9)=160 \\ \sum x^2=1^2+3^2+5^2+7^2+9^2=165^{} \\ (\sum x)^2=25^2=625 \end{gathered}[/tex]Using these values to compute for the values of a and b, we get
[tex]\begin{gathered} a=\frac{(28\cdot165)-(25\cdot160)}{5(165)-625}=\frac{31}{10}=3.1 \\ b=\frac{5(160)-(28\cdot25)}{5(165)-625}=\frac{1}{2}=0.5 \end{gathered}[/tex]Take note that the problem wants us to reduce the numbers to the nearest tenth. Hence, the linear regression for the given data set is written as
[tex]y=3.1+0.5x[/tex]Farrah borrows $18,000 to purchase a new car. The annual interest rate for the 60-month loan is 4.3%.If she makes all the monthly payments, what is the total amount of interest she will pay on the loan?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Principal = $ 18,000
Time = 60 month = 60/ 12 = 5 years
Interest = 4. 3%
Step 2:
The total amount she will pay at the end of the 5 -year period is given as follows:
[tex]\begin{gathered} A\text{ = P ( 1 + }\frac{R}{100})^t \\ A\text{ = 18000 ( 1 + }\frac{4.3}{100})^5 \\ \end{gathered}[/tex][tex]\begin{gathered} A\text{ = 22,217. 4416} \\ A\text{ }\approx\text{ }22,217.44\text{ dollars} \end{gathered}[/tex]Step 3:
Now, we have that the amount = 22, 217. 44 dollars.
And the Principal = 18,000 dollars
If she makes all the monthly payments,
Then, the total amount of interest she will pay on the loan is:
[tex]22,\text{ 217. 44 - 18,000 = 4,217. 44 dollars}[/tex]CONCLUSION:
The total amount of interest she will pay on the loan = 4, 217. 44 dollars.
In triangle HIJ,△HIJ, overline{HI}cong overline{JH} HI ≅ JH and text{m}angle H = 118^{\circ}.m∠H=118 ∘ . Find \text{m}\angle J.m∠J.
Answers
The measure of angle J in the isosceles triangle is given as follows:
m<J = 31º.
What is an isosceles triangle?An isosceles triangle is a triangle in which:
Two of the angles have equal measures.Two of the sides have equal measures.In the context of this problem, the angles are given as follows:
118º. (angle H).x: angle J.x: angle I.Angles J and I are equal as the triangle is isosceles and the congruent angles are acute, that is, they cannot have measures above 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence we can solve for x as follows:
x + x + 118º = 180º
2x = 62º
x = 62º/2
x = 31º.
Hence the measure of angle J is of 31 degrees.
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f(9) =
(Simplify your answer. Type an integer or a fraction.)
Answers
Answer:
9f
Step-by-step explanation:
f(9) = f * (9)
a) Multiply.
f * (9) = 9f
Used two equations in two variables to solve the application.A 60 m pass around the rectangular garden. The width of the garden is 2/3 its length. Find the area in meters squared.
Answers
From the data provided, we can conclude:
The perimeter of the rectangle is 60m, so:
[tex]60=2w+2l_{\text{ }}(1)[/tex]Where:
w = width
l = length
The width of the garden is 2/3 its length, therefore:
[tex]w=\frac{2}{3}l_{\text{ }}(2)[/tex]Replace (2) into (1)
[tex]60=2(\frac{2}{3}l)+2l[/tex]Solve for l:
[tex]\begin{gathered} 60=\frac{4}{3}l+2l \\ 60=\frac{10}{3}l \\ l=\frac{180}{10} \\ l=18 \end{gathered}[/tex]Replace l into (2):
[tex]\begin{gathered} w=\frac{2}{3}(18) \\ w=12 \end{gathered}[/tex]Consider the function, Find the zeros or x-intercepts of f(x).
Answers
To find the x-intercepts, equate the function with zero as follows:
[tex]\begin{gathered} f(x)=0 \\ -16x^2+25x+10=0 \\ x=\frac{-25\pm\sqrt[]{(25)^2-4\times10\times-16}}{2\times-16} \\ x=\frac{-25\pm\sqrt[]{625+640}}{-32} \\ x=\frac{-25\pm35.5668}{-32} \\ x=-0.3302,1.8927 \end{gathered}[/tex]Hence the intercepts are -0.3302 and 1.8927
The intercepts are at points (-0.3302,0) and (1.8927,0)
The sum of two numbers is 164. The second number is 24 less than three times the first number. Find the numbers.
Answers
4x-24=164
4x=188
X=47
The numbers are 47 and 117
Jeremy said I added 3/4+1/5 and got 4/9, does Jeremy’s answer make sense? Explain how you know without calculating the answer
Answers
If
[tex]\frac{3}{4}+\frac{1}{5}=\frac{4}{9}[/tex]That would imply that 9 is a common multiple of 4 and 5, which is false since 9=3^2.
Additionally, 3/4 is greater than 4/9; so 3/4+1/5 has to be greater than 4/9.
