Answers
Part A.
The composition of f ang g is given by
[tex](f\circ g)(x))=f(g(x))=\frac{(3x+7)-7}{3}[/tex]where we have inserted 3x-7 in the place of x in function f. Then, we have
[tex](f\circ g)(x))=f(g(x))=\frac{3x+7-7}{3}=\frac{3x}{3}=x[/tex]Therefore, the answer is
[tex](f\circ g)(x))=x[/tex]Part B
Similarly to the previous case, we have
[tex](g\circ f)(x))=g(f(x))=3(\frac{x+7}{3})-7[/tex]which gives
[tex](g\circ f)(x))=g(f(x))=x+7-7=x[/tex]then, the answer is
[tex](g\circ f)(x))=x[/tex]Part C.
In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.
Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).
Related Questions
Julianne needs 7 yards of string for her kite. She has 5/8 yards. How many more yards does Julianne need for her kite?
Answers
Find out the difference between 7 yards and 5/8 yards
[tex]7-\frac{5}{8}=\frac{8*7-5}{8}=\frac{51}{8}\text{ yd}[/tex]Convert to a mixed number
51/8=(48/8)+(3/8)=6+3/8=6 3/8 yd
therefore
The answer is 6 3/8 ydKwan had 16 3/4 inches of wire. He cut of 4 2/4 inches of wire to use in a craft project how much wire does kwan have left
Answers
We know that the total is 40 students, and 24 of them are girls, then the fraction that represents it is
[tex]\frac{24}{40}[/tex]But we must simplify the fraction, let's divide the denominator and numerator by 4
[tex]\frac{24}{40}=\frac{6}{10}[/tex]Now we can do it again by 2
[tex]\frac{24}{40}=\frac{6}{10}=\frac{3}{5}[/tex]Therefore the correct answer is the letter B.
[tex]\frac{3}{5}[/tex]Answer: 12 1/4
Step-by-step explanation: 16 =4 is 12, and 3/4 - 2/4 is 1/4
hope this helps :)
Solve the following(1) 8(11 + 2r) = 12(4/3 r + 22/3)(2) -8(10 + 7k) + 8k = 9 + 4(6 - 12k)
Answers
Answers:
(1) r = 0
(2) The equation has no solution
Explanations:
(1) Given the expression:
[tex]8(11+2r)=12(\frac{4}{3}r+\frac{22}{3})[/tex]Removing the brackets, we have:
[tex]88+16r=\frac{48}{3}r+\frac{264}{3}[/tex]Multiply both sides by 3
[tex]\begin{gathered} 264-48r=48r+264 \\ \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} 48r+48r=264-264 \\ 48r=0 \end{gathered}[/tex]Divide both sides by 48
[tex]r=\frac{0}{48}=0[/tex](2) Given the expression:
[tex]-8(10+7k)+8k=9+4(6-12k)[/tex]Remove brackets
[tex]-80-56k+8k=9+24-48k[/tex]Collect like terms
[tex]\begin{gathered} -56k+8k+48k=9+24+80 \\ \end{gathered}[/tex]Simplifying this, the variable k vanishes, leaving us with nothing to find. Therefore, the equation has no solution.
Find the value of k that makes f(x) continuous at x = 3
Answers
Given:
The function is,
[tex]f(x)=f(x)=\begin{cases}\frac{x-3}{x^2+2x-15},x\ne3 \\ k,x=3\end{cases}[/tex]As the given function is continous at x= 3 ,
[tex]\begin{gathered} \lim _{x\to3}f(x)=k \\ \lim _{x\to3}(\frac{x-3}{x^2+2x-15})=k \end{gathered}[/tex]Shade in 4 of the picture. Shade in 1 of the picture. Shade in 3-4 of the picture.
Answers
The first one is correct
In the second one you have to shade one complete circle plus
In the third one you need to shade three complete triangles plus
thank you for viewing my question I seem to be stuck on this and need help thank you
Answers
ANSWER
[tex]\begin{gathered} A=\frac{1}{4} \\ B=\frac{1}{2} \\ C=\frac{1}{4} \end{gathered}[/tex]EXPLANATION
From the given data;
Event A; Alternating even and odd numbers means;
EOE and OEO
Number of favourable outcome is 2 while number of possible outcome is 8
Hence, the probability of Event A IS;
[tex]\begin{gathered} Prob(A)=\frac{2}{8} \\ =\frac{1}{4} \end{gathered}[/tex]In Event B; More even numbers than odd means having;
EEE,OEE,EEO and EOE
[tex]\begin{gathered} EEE,OEE,EEOandEOE \\ Prob(B)=\frac{4}{8} \\ =\frac{1}{2} \end{gathered}[/tex]For Event C; an even number on both the first and the last rolls;
EEE and EOE
[tex]\begin{gathered} EEEandEOE \\ Prob(C)=\frac{2}{8} \\ =\frac{1}{4} \end{gathered}[/tex]Find the interest earned on a $50,000 deposited for six years at 4 1/8% interest, compounded continuously.
Answers
For the given principal $50,000 which was deposited for six years at
4 1/8% interest rate compounded continuously is $14040.97.
As given in the question,
Deposited amount is equal to $50,000
Time period 't' is equal to 6 years
Interest rate 'r' compounded continuously is equal to 4 1/8%
Compounded continuously formula is
A = P[tex]e^{rt}[/tex]
P is the initial amount deposited
P = $50,000
r = 4 1/8%
= 33/8 %
= 0.04125
Substitute the value in the formula we get,
A = ( 50,000 ) × [tex]e^{0.04125 \times 6}[/tex]
⇒ A = 50,000 × [tex]e^{0.2475}[/tex]
⇒ A = 64040.97
Interest =Amount - Principal
⇒ Interest = 64040.97 - 50,000
⇒ Interest = $14040.97
Therefore, For the given principal $50,000 which was deposited for six years at 4 1/8% interest rate compounded continuously is $14040.97.
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4/3x+2/3=1 can someone help me
Answers
Given the expression 4/3x+2/3=1, we are to find the value of x from the expression. This is as shown below;
4/3x+2/3=1
subtract 2/3 from both sides
4/3x+2/3-1/3=1-1/3
4/3x = (3-1)/3
4/3x = 2/3
cross multiply
2(3x) = 4(3)
6x = 12
Divide both sides by 6
6x/6 - 12/6
x = 2
Hence the value of x is 2
Write an equation of the line perpendicular to the line –4x + 3y = –15 and passes through the point (–8, –13)
Answers
4y = -3x - 76
Explanations:The given equation is:
-4x + 3y = -15
Make y the subject of the formula to express the equation in the form
y = mx + c
[tex]\begin{gathered} -4x\text{ + 3y = -15} \\ 3y\text{ = 4x - 15} \\ y\text{ = }\frac{4}{3}x\text{ - }\frac{15}{3} \\ y\text{ = }\frac{4}{3}x\text{ - 5} \end{gathered}[/tex]Comparing the equation with y = mx + c
the slope, m = 4/3
the y-intercept, c = -5
The equation perpendicular to the equation y = mx + c is:
[tex]y-y_1\text{ = }\frac{-1}{m}(x-x_1)[/tex]The line passes through the point (-8, -13). That is, x₁ = -8, y₁ = -13
Substitute m = 4/3, x₁ = -8, y₁ = -13 into the equation above
[tex]\begin{gathered} y\text{ - (-13) = }\frac{-1}{\frac{4}{3}}(x\text{ - (-8))} \\ y\text{ + 13 = }\frac{-3}{4}(x\text{ + 8)} \\ y\text{ + 13 = }\frac{-3}{4}x\text{ - 6} \\ y\text{ = }\frac{-3}{4}x\text{ - 6 - 13} \\ y\text{ = }\frac{-3}{4}x\text{ - 19} \\ 4y\text{ = -3x - }76 \end{gathered}[/tex]A tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas would be needed to cover the tepee?
Answers
To find:
The area of canvas needed to cover the tepee.
Solution:
Given that the tepee is in the shape of a right cone, with slant height 18.5 feet and diameter of 20 feet then the radius is 10 feet.
The area of canvas is equal to the curved surface area of the tepee. It is known that the curve surface area of the cone is given by:
[tex]CSA=\pi rl[/tex]Where, r is the radius of the cone and l is the slant height of the cone. So,
[tex]\begin{gathered} CSA=3.14\times10\times18.5 \\ =580.9ft^2 \end{gathered}[/tex]Thus, the approximate canvas that would be needed to cover the tepee is 580.9 ft^2.
581Answer:
Step-by-step explanation:
there are 64 hamburgers and 52 hot dogs at the picnic. what is the ratio of the number of hamburgers to the total number of lunch items?
Answers
Answer: The ratio of hamburgers to the total lunch items is 16 : 29
Number of hamburgers = 64
Number of hot dogs = 52
Total number of items for lunch = number of hamburgers + number of hot dogs
Total number of items for lunch = 64 + 52
Total number of items for lunch = 116
The ratio of number of hamburgers to the total number of lunch items
64/116
16 : 29
Therefore, the ratio of hamburgers to the total lunch items is 16 : 29
Graph the system of linear inequalities and shade in the solution set. If there are no solutions, graph the corresponding lines and do not shade in any region X - y > 2 Y < - 1/3x + 1
Answers
We need to graph the following inequality system:
[tex]\begin{cases}x-y>2 \\ y<-\frac{1}{3}x+1\end{cases}[/tex]Now we need to isolate the y-variable on the left side for the first equation:
[tex]\begin{cases}yNow we have to graph the boundary lines, which are:[tex]\begin{gathered} y=x-2 \\ y=-\frac{1}{3}x+1 \end{gathered}[/tex]We need to points to graph these equations. We will use the points that have x equal to 0 and y = 0.
For the first equation:
[tex]\begin{gathered} y=0-2 \\ y=-2 \end{gathered}[/tex]The first point is (0,-2).
[tex]\begin{gathered} 0=x-2 \\ x=2 \end{gathered}[/tex]The second point is (2, 0).
For the second equation:
[tex]\begin{gathered} y=-\frac{1}{3}\cdot0+1 \\ y=1 \end{gathered}[/tex]The first point (0,1).
[tex]\begin{gathered} 0=-\frac{1}{3}x+1 \\ \frac{1}{3}x+1 \\ x=3 \end{gathered}[/tex]The second point is (3, 0).
Now we can trace both boundary lines:
Finally we can shade the solution set, which is the region that is below both lines, since both have an "<" signal.
suppose each cube in this right rectangular prism is a 1/2-in unit cube
Answers
Answer:
The length of each cube is given below as
[tex]l=\frac{1}{2}in[/tex]Concept:
To figure out the dimension of the prism, we will calculate the number of cubes to make the length,width and height and multiply by 1/2
To figure out the length of the prism,
we will multiply 1/2in by 5
[tex]\begin{gathered} l=\frac{1}{2}in\times5 \\ l=2.5in \end{gathered}[/tex]To figure out the width of the prism,
we will multiply 1/2in by 4
[tex]\begin{gathered} w=\frac{1}{2}in\times4 \\ w=2in \end{gathered}[/tex]To figure out the height of the prism,
we will multiply 1/2 in by 3
[tex]\begin{gathered} h=\frac{1}{2}in\times3 \\ h=\frac{3}{2}in=1.5in \end{gathered}[/tex]Hence,
The dimensions of the prism are
Length = 2.5in
Width = 2in
Height = 1.5 in
2.5in by 2in by 1.5in
Part B:
To figure out the volume of the prism, we will use the formula below
[tex]\begin{gathered} V_{prism}=base\text{ area}\times height \\ V_{prism}=l\times w\times h \\ l=2.5in,w=2in,h=1.5in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V_{pr\imaginaryI sm}=l\times w\times h \\ V_{pr\mathrm{i}sm}=2.5in\times2in\times1.5in \\ V_{pr\mathrm{i}sm}=7.5in^3 \end{gathered}[/tex]Alternatively, we will calculate below by calculate the volume of each cube and then multiply by the total number of cubes
[tex]\begin{gathered} volume\text{ of each cube=} \\ =l^3=(\frac{1}{2})^3=\frac{1}{8}in^3 \\ The\text{ total number of cubes =} \\ =5\times4\times3 \\ =60cubes \\ Volume\text{ of the prism } \\ =\frac{1}{8}in^3\times60 \\ =7.5in^3 \end{gathered}[/tex]Hence,
The volume of the prism is = 7.5in³
x^2-18x-57=6 solve each equation by completing the square
Answers
x=-3
x=21
Which of the following is equivalent to –(–5.25) ? 5 5.25 –5 –5.25please answer fast
Answers
the given expression is,
= - ( - 5.25)
= 5.25
thus, the answer is 5.25
I need to simplify this equation 7b + 3x − 5b + 21x
Answers
Answer:
2b + 24x
Step-by-step explanation:
The equation is,
→ 7b + 3x − 5b + 21x
Simplifying the given equation,
→ 7b + 3x − 5b + 21x
→ (7b - 5b) + (3x + 21x)
→ 2b + 24x
Hence, the answer is 2b + 24x.
In x - In(x + 1) = 2
Answers
Answer: no solution
Step-by-step explanation:
f(x)=-x+5;g(x)=2f(x) i need to know the horizontal stretch and by. also f(x)=2x+3; g(x)=f(x)+3
Answers
For the first equation:
[tex]f(x)=-x+5,g(x)=2f(x)[/tex]That's a vertical stretch by 2. If you change f(x) for 'y' you'll see that more clearly:
[tex]y=-x+5,g(x)=2y[/tex]All 'y' coordinates of the function are now twice as before. This means that the function is stretched vertically.
For the second:
[tex]f(x)=x-4,g(x)=-f(x)[/tex]We'll change f(x) for 'y' too:
[tex]y=x-4,g(x)=-y[/tex]That is a reflection over the x axis. This is because in order to go from y to -y all 'y' coordinates of the points on the function have to change from possitive to negative and from negative to possitive. In a graph:
4. Given the degree and zeros of a polynomial function, find the standard form of the polynomial.
Degree: 4; zero: -i, 5i
The expanded polynomial is:
x4+
x3 +
x2 +
x +
Answers
The equation of the polynomial equation in standard form is P(x) = x⁴ + 6x² + 5
How to determine the polynomial expression in standard form?The given parameters are
Degree = 4
Zero = -i, 5i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = -5i and i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = 1 * (x - (-5i)) * (x + 5i) * (x - (-i)) * (x - i)
This gives
P(x) = 1 * (x² + 5) * (x² + 1)
Evaluate the products
P(x) = (x² + 5)(x² + 1)
Express in standard form
P(x) = x⁴ + x² + 5x² + 5
Evaluate the like terms
P(x) = x⁴ + 6x² + 5
Hence, the equation is P(x) = x⁴ + 6x² + 5
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[tex]7 \sqrt{5 |4| } [/tex]3+6-4÷36×59099m
Answers
how do I multiplely negative mixed numbers step by step
Answers
According to the given data we have the following expression:
(2/5)x -2*4/6
The calculation would be as follows:
1) (2/5)x -8/6
2)(2/5)x=8/6
2x=8/6*5
2x=20/3
x=20/3 / 2
x=3.33333
The value of the x would be x=3.33333
1) multiply -2 times 4/6=-8/6
2)Move -8/6 to other side. Would change sign and would be positive
using the box and whisper plot shown, find the quartile values Q1 and Q3
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
box-and-whisker plot
Step 02:
quartile values:
We must analyze the plot to find the solution.
box-and-whisker plot:
q1 = - 4
q3 = 6
The answer is:
q1 = - 4
q3 = 6
i will send a pick of the problem
Answers
we have that
Verify each statement
1) AE≅DE -----> given ----> is ok
2) BE≅CE ----> given ----> is ok
3) AB=DC----> opposite sides congruent----> is not ok
4) m by vertical angles
5) Δ AEB≅ΔDEC -----> by SAS congruence postulate
therefore
Sarah is not correct
A pizza parlor is considering adding taco pizza and Hawaiian pizza to itsmenu. It surveyed a group of potential customers to find out what theythought, and the results of the survey are shown in the bar graph below, withthe percentage of respondents favoring the addition of each pizza shownabove the corresponding bar.What should we add to our menu?58%47%TacopizzaHawaiianpizzaIf the pizza parlor can make a maximum of 135 pizzas a day, how manyshould they expect will be taco pizzas?
Answers
In order to fins the number of pizzas that correspond to Taco pizzas, we can multiply the number of pizzas that the parlor can make, and then using the percentage that corresponded to the selected flavour.
then
[tex]135\cdot58\%=78.3\rightarrow79\text{ taco pizzas}[/tex]in a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who who. The claim is that among voters the percentage who believe that they voted for the winning candidate is equal to 43%. find a test statistic for the proportion.
Answers
The test statistic is given by
[tex]\frac{\frac{308}{611}-0.43}{\sqrt{\frac{(1-0.43)(0.43)}{611}}}[/tex]The result is 3.699288767
A crop circle discovered in Cambridge, England, covers approximately 44,100 square feet. What is the approximate diameter of this circle?
Answers
We have a circle that has an approximate area of 44100 ft².
We have to calculate the diameter.
We can relate diameter D and area A as:
[tex]A=\frac{\pi}{4}D^2[/tex]We can then calculate D as:
[tex]\begin{gathered} A=\frac{\pi}{4}D^2 \\ D^2=\frac{4A}{\pi} \\ D=\sqrt{\frac{4A}{\pi}} \\ D=\sqrt{\frac{4(44100)}{\pi}} \\ D\approx\sqrt{56149} \\ D\approx237\text{ }ft \end{gathered}[/tex]Answer: the diameter is approximately 237 ft
What is x?5x-35=55-xHow do I get like variables together
Answers
hello
this is a simple equation and to solve this, we should first of all collect like terms together
[tex]5x-35=55-x[/tex]step one
collect like terms together
[tex]\begin{gathered} 5x-35=55-x \\ 5x+x=55+35 \\ 6x=90 \end{gathered}[/tex]step two
divide both sides by the coefficient of x
[tex]\begin{gathered} 6x=90 \\ \frac{6x}{6}=\frac{90}{6} \\ x=15 \end{gathered}[/tex]from the calculations above, the value of x is equals to 15
The product of a number and 3 is the same as the sun of that number and 6
Answers
Answer: 3x = 6x
Step-by-step explanation: After you move the variable over you will move 6x so the opposite of 6x is -6x after you subtract -6-3 you should get 3. Thus, the final answer would be 3.
Find the distance from P to l. Line l contains points (2, 4) and (5, 1). Point P has coordinates (1, 1).
Answers
First we need to find the equation of the line l passing through the points (2, 4) and (5, 1).
The equation of a line is expressed as y = mx+c
m is the slope
c is the intercept
m = y2-y1/x2-x1
m = 1-4/5-2
m = -3/3
m = -1
Get the intercept
Substitute any point (2, 4) and the slope m = -3 into the expression y = mx + c
4 = -3(2)+c
4 = -6 + c
c = 4+6
c = 10
The equation of line l is y = -3x+10
Next is to find the equation of the line w perpendicular to the line l, through P(1, 1).
Since the line w is perpendicular to lin
what is the ratio of sin b
Answers
we have that
sin(B)=56/65 -----> by opposite side angle B divided by the hypotenuse