Answers
The values for the composition of the functions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate the Composition of Functions?To evaluate the composition of a function, the first thing to do is to evaluate the inner function, then use the output as an input to evaluate the outer function of the composition.
Given the following functions:
f(x) = x² + 5
g(x) = 3x
We are required to find (f o g)(x) and (g o f)(x).
To find (f o g)(x), replace g(x) for x in the outer function f(x):
(f o g)(x) = (3x)² + 5
(f o g)(x) = 9x² + 5
To find (g o f)(x), replace f(x) for x in the outer function g(x):
(g o f)(x) = 3(x² + 5)
(g o f)(x) = 3x² + 15
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Related Questions
Compute the square root of 532 to the nearest tenth. Use the "divideand average method.
Answers
ANSWER:
[tex]\sqrt[]{532}\cong23.065[/tex]STEP-BY-STEP EXPLANATION:
We have the following square root
[tex]\sqrt[]{532}[/tex]We calculate by means of the divide and average method.
The first thing is to look for exact roots between those two values
Step 1 estimate
[tex]\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}[/tex]Step 2 divide
[tex]\frac{532}{23.5}=22.63[/tex]Step 3 average:
[tex]\frac{23.5+22.63}{2}=\frac{46.13}{2}=23.065[/tex]Therefore:
[tex]\sqrt[]{532}\cong23.065[/tex]The average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.1. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediate z value calculations to two decimal places.Find the probability that the mean of a sample of 25 people is less than 10.Find the probability that the mean of a sample of 25 people is greater than 10.Find the probability that the mean of a sample of 25 people is between 11 and 12.
Answers
The z-score is given by the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where x is the data point, μ is the mean, and σ is the standard deviation.
First
Solve for w.4w+6= -22Simplify your answer as much as possible.W8DDХ5?
Answers
w= -7
Explanation
[tex]\begin{gathered} 4w+6=-22 \\ \end{gathered}[/tex]
Step 1
The addition property of equality and subtraction property of equality are similar. Adding or subtracting the same number to or from both sides of an equation keeps both sides equal, so we can use this fact to isolate w
a) subtract 6 in both sides of the equation
[tex]\begin{gathered} 4w+6=-22 \\ 4w+6-6=-22-6 \\ 4w=-28 \\ \end{gathered}[/tex]Step 2
The division property of equality states that when we divide both sides of an equation by the same number, the two sides remain equal.so
b) divide both sides by 4
[tex]\begin{gathered} 4w=-28 \\ \frac{4w}{4}=\frac{-28}{4} \\ w=-7 \end{gathered}[/tex]therefore, the answer is
w= -7
I hope this helps you
What is the answer for 5p+10 = 8p+1
Answers
The equation is given to be:
[tex]5p+10\: =\: 8p+1[/tex]We can solve for p using the following steps:
Step 1: Subtract 10 from both sides of the equation
[tex]\begin{gathered} 5p+10-10=8p+1-10 \\ 5p=8p-9 \end{gathered}[/tex]Step 2: Subtract 8p from both sides of the equation
[tex]\begin{gathered} 5p-8p=8p-9-8p \\ -3p=-9 \end{gathered}[/tex]Step 3: Multiply both sides by -1
[tex]\begin{gathered} -1\times(-3p)=-1\times(-9) \\ 3p=9 \end{gathered}[/tex]Step 4: Divide both sides by 3
[tex]\begin{gathered} \frac{3p}{3}=\frac{9}{3} \\ p=3 \end{gathered}[/tex]ANSWER:
[tex]p=3[/tex]The function g is defined as follows for the domain given g(x) = 3x - 2 , omain = \{- 2, - 1, 0, 1\} Write the range of g using set notation. Then graph g
Answers
Given: The function below
[tex]\begin{gathered} g(x)=3x-2 \\ Domain:\lbrace-2,-1,-0,1\rbrace \end{gathered}[/tex]To Determine: The range and the graph of g
Solution
The range is as given below
[tex]\begin{gathered} x=-2 \\ g(-2)=3(-2)-2=-6-2=-8 \\ x=-1 \\ g(-1)=3(-1)-2=-3-2=-5 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ g(0)=3(0)-2=0-2=-2 \\ x=1 \\ g(1)=3(1)-2=3-2=1 \end{gathered}[/tex]Hence, the range is
{-8, -5, -2, 1}
Let us form a table showing the domain(x) and the range (g(x))
Let us use the table to plot graph of the domain(x) against the range(g(x)) as below
Ethan and Evan are twins. They each deposit $3,000 into separate bank accounts.Their accounts each accrue interest annually as shown in the tables below.
Answers
Part A.
Ethan's account can be model as a linear equation since it is increasing at a constant rate of the form:
[tex]y=240x+3000[/tex]And Evan's account can be model as a exponential equation of the form:
[tex]y=3000(1.08)^x[/tex]Part B:
Evaluate the 1st and 2nd equation for x = 5:
[tex]\begin{gathered} y=240(5)+3000=4200 \\ y=3000(1.08)^5=4407.98 \\ so\colon \\ \frac{4407.98}{4200}=1.05 \end{gathered}[/tex]It would be 1.05 higher
two integers a and b have a product of 36 what is the least possible answer
Answers
Answer:
the answer is 12
Step-by-step explanation:
In short, a = 6 and b = 6. We can make a table of various values to help confirm that 12 is the smallest sum.
Answer: 1
Step-by-step explanation: 1 is the least possible answer because an integer is any number and 1x36 would be the least possible answer for the product.
Can someone help me with 7? I’m desperate
Answers
Solve 2x - 8 < 7...........................................................................
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
2x - 8 < 7
Step 02:
inequality:
2x - 8 < 7
2x - 8 + 8 < 7 + 8
2x / 2 < 15 / 2
x < 15 / 2
The answer is:
x < 15 / 2
(-oo , 15/2)
Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) forinifinity and a U for union as needed.-- 5x + 4 >I 19 OR – 22 - 15 – 3-8 -7 -6 -5-4-3-2-] 022345678Clear All Draw:Interval notation for the above inequality and graph is
Answers
- 5x + 4 > 19
1st step let us move 4 to the other side by subtracting both sides by 4
- 5x + 4 - 4 > 19 - 4
- 5x > 15
2nd step is move - 5 to the other side by dividing both sides by -5, BUT when we divide the sides of an inequality by a negative number we must reverse the sign of inequality
[tex]\frac{-5x}{-5}<\frac{15}{-5}[/tex]x < -3
The solution is all values smaller than -3
On the number, line draw an empty circle at -3 then draw from it an arrow pointing to the left ( - ve infinity)
The solution is {x : x < -3} or (-00, -3)
How do I use the calculator to find log10 6, to 3 decimal places please?
Answers
Your calculator uses base 10 for its logs
There should be a button that says log
That is a base 10 log
log 6 = .77815125
To 3 decimal places
log 6 = .778
The base 10 is implied
A committee must be formed with 4 teachers and 4 students. If there are 7 teachers to choose from, and 9 students, how many different ways could the committee be made?
Answers
ANSWER
4,410
EXPLANATION
The number of ways we can choose 4 teachers from 7 teachers is,
[tex]_7C_4=\frac{7!}{(7-4)!\times4!}=\frac{7\times6\times5\times4!}{3!\times4!}=\frac{7\times6\times5}{3\times2}=\frac{7\times6\times5}{6}=7\times5=35[/tex]There are 35 ways of choosing 4 teachers out of 7.
And the number of ways we can choose 4 students from 9 students is,
[tex]\begin{gathered} _9C_4=\frac{9!}{(9-4)!\times4!}=\frac{9\times8\times7\times6\times5\times4!}{5!\times4!}=\frac{9\times8\times7\times6\times5}{5\times4\times3\times2} \\ _9C_4=\frac{9\times8\times7}{4}=\frac{9\times(2\times4)\times7}{4}=9\times7\times2=126 \end{gathered}[/tex]There are 126 ways of choosing 4 students out of 9.
The committee is formed by 4 teachers and 4 students. The number of ways it can be made is,
[tex]_7C_4\times_9C_4=35\times126=4,410[/tex]Hence, there are 4,410 ways to choose 4 students and 4 teachers out of 9 students and 7 teachers.
Find the equation of the axis of symmetry of the following parabola using graphingtechnology.y = x^2 – 8x + 32
Answers
Explanation:
If we graph this parabola we can see the vertex at point (4, 16)
The axis of simmetry is a vertical line that passes through the vertex of the parabola.
Any vertical line's equation is:
[tex]x=a[/tex]'a' is any value of x.
Answer:
The equation of the axis of simmetry is x = 4
Which fraction is represented by point A on the numb 0 -1 O- 1 4. 4 1 1
Answers
The fraction that represent the point A is -1/4.
Since there are 4 divition in between -1 and 0.
Thus the length of one division is,
[tex]undefined[/tex]Which is the equation of the line that passes through the points (-4, 8) and (1, 3)?A. Y=x+4B. Y=-x+12C. Y=-x+4D. Y=x+12
Answers
In order to find the equation that passes through both points, we can use the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Using the given points on this equation, we have:
[tex]\begin{gathered} (-4,8)\colon \\ 8=m\cdot(-4)+b \\ b=8+4m \\ \\ (1,3)\colon \\ 3=m+b \\ 3=m+8+4m \\ 5m=3-8 \\ 5m=-5 \\ m=-1 \\ b=8+4\cdot(-1)=8-4=4 \end{gathered}[/tex]Therefore the equation is y = -x + 4 (correct option: C)
There is a stack of plates in the backyard. There are 4 plates in the 1st layer, 8 in the second, 16 in the third, 32 in the fourth, and so on. There are total 10 rows/layers. How many total plates are in the stack?
Answers
Given that
[tex]\begin{gathered} layer1=4plates \\ layer2=8plates \\ layer3=16plates \\ layer4=32plates \end{gathered}[/tex]Explanation
From the above, it is easy to see that the arrangement of the layers follows a geometric sequence where
[tex]\begin{gathered} first\text{ term = 4} \\ common\text{ ratio = }\frac{second\text{ }term}{first\text{ term}}=\frac{8}{4}=2 \end{gathered}[/tex]Since r>1, therefore the sum of 10 terms, which implies would give the total number of plates that are in the stack can be seen below.
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ therefore; \\ S_{10}=\frac{4(2^{10}-1)}{2-1}=\frac{4(1024-1)}{1}=4(1023)=4092 \end{gathered}[/tex]Answer: 4092
Write the equation of each line in slope intercept form (see attached)
Answers
As we can see we have a horizontal line, the slope of the horizontal line is zero
the form of the equation of the line in slop-intercept form is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
In our case m=0
[tex]\begin{gathered} y=(0)x+b \\ y=b \end{gathered}[/tex]in this case the y-intercept is b=-4
Therefore the equation is
[tex]y=-4[/tex]ANSWER
y=-4
create a system of equations to represent this situation. be sure to explain the meaning of each variable. graph the system of equations. determine the break even point for Chuck E Cheese and Bright Child, Adventure Plex and Bright Child, Adventure Plex and Chuck E Cheese.
Answers
For them, let x = number of children of the party and
A=Adventure Plext cost
B= Bright Child cost
C= Chuck E Cheese cost
So,
[tex]\begin{gathered} A=300+12x \\ B=180+15x \\ C=18x \end{gathered}[/tex]Then, graphing each equation of the system of equations
Now, for determine the break even point for Chuck E Cheese and Bright Child you have
[tex]\begin{gathered} 180+15x=18x \\ 180=18x-15x \\ 180=3x \\ \frac{180}{3}=x \\ 60=x \end{gathered}[/tex]That is, the break even point for Chuck E Cheese and Bright Child occurs when x = 60 children.
For determine the break even point for Adventure Plex and Bright Child you have
[tex]\begin{gathered} 300+12x=180+15x \\ 300+12x-180=180+15x-180 \\ 120+12x=15x \\ 120+12x-12x=15x-12x \\ 120=3x \\ \frac{120}{3}=\frac{3x}{3} \\ 40=x \end{gathered}[/tex]That is, the break even point for Adventure Plex and Bright Child occurs when x = 40 children.
Finally, For determine the break even point for Adventure Plex y Chuck E Cheese you have
[tex]\begin{gathered} 300+12x=18x \\ 300+12x-12x=18x-12x \\ 300=6x \\ \frac{300}{6}=\frac{6x}{6} \\ 50=x \end{gathered}[/tex]That is, the break even point for Adventure Plex and Chuck E Cheese occurs when x = 50 children.
help meeeeeeeeee pleaseee !!!!!
Answers
For the given functions, the two compositions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3*x² + 15
How to find the compositions of the functions?Here we have two functions which are:
f(x) = x² + 5
g(x) = 3x
Now we want to find the compositions:
(f o g)(x) = f( g(x) )
So we just need to evaluate f(x) in g(x), we will get:
f( g(x) ) = g(x)² + 5
f( g(x) ) = (3x)² + 5 = 9x² + 5
The other composition is:
(g o f)(x) = g(f(x))
And we can get this in a similar way:
g(f(x)) = 3*f(x) = 3*(x² + 5) = 3*x² + 15
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Drag the factors to the correct locations on the image. Not all factors will be used.What is the factored form of this expression?27 m 3 + 125n39m + 25n9m2 - 15mn + 25n23m + 5n9m2 + 15mn + 2523m2 – 8mn + 5123m - 5n
Answers
Express the sum of the angles of this triangle in two different waysX3/2X1/2X
Answers
1) Since the sum of these angles is written in terms of x, we can write it out:
[tex]\begin{gathered} x+\frac{3}{2}x+\frac{1}{2}x\text{ } \\ \frac{2x+3x+x}{2} \\ \frac{6x}{2} \\ 3x \end{gathered}[/tex]Notice that to sum these fractions we had to take the LCM(2, 1) = 2 and rewrite it as a sum.
2) Another way of writing the sum of these angles is writing it as a sum of decimal numbers since we can rewrite fractions as decimal numbers.
3/2 = 3÷2 = 1.5
1/2 = 1÷2 =0.5
1
[tex]\begin{gathered} x+1.5x+0.5x \\ x+2x \\ 3x \end{gathered}[/tex]The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgets forceditoral and sales combined is12,500,000, what is the total annual budget
Answers
Explanation
We are asked to find the total annual budget given that the combined amount for sales and editorial is $12,500,000
To do so, let the total combined amount be x
If we check for the combined percentages for the amount for sales and editorial, we will have
[tex]21\text{ \%}+4\text{ \% = 25\%}[/tex]Thus, we can set up the equation
[tex]25\text{ \% of x = 12,500,00}[/tex]Solving for x
[tex]\begin{gathered} \frac{25}{100}\times x=12500000 \\ \\ \frac{x}{4}=12500000 \\ \\ x=4\times12,500,000 \\ \\ x=50,000,000 \\ \end{gathered}[/tex]Therefore, the total annual budget will be $50,000,000
Chloe's car used 15 gallons to travel 570 miles. How many gallons of gas would she need to travel 380 miles?
Answers
Answer:
10
Step-by-step explanation:
I divided 570 by 15 to see how many miles she can travel per gallon of gas which came out to be 38.
After that i divided the 380 by the 38. 380÷38 is 10.
Answer:
Need:
10 gallons
Step-by-step explanation:
Proportions:
15 gallons ⇒ 570 miles
A gallons ⇒ 380 miles
A = 15gallons * 380miles / 570miles
A = 10 gallons
0.4(2-) 0.2(9 + 7) A)-3 B - 1 C) 3 D) all real numbers
Answers
Let us solve the equation to arrange the steps
[tex]-3(4+3x)+5x=-16[/tex]In the first step, we must multiply the bracket by -3 (distributive property)
[tex](-3)(4)_{}+(-3)(3x)=-12-9x[/tex]Then the equation is
[tex]-12-9x+5x=-16[/tex]Now add the like terms on the left side
[tex]\begin{gathered} -12+(-9x+5x)=-16 \\ -12x+(-4x)=-16 \\ -12-4x=-16 \end{gathered}[/tex]Next step, add 12 to both sides
[tex]undefined[/tex]simplify x⁹ divided by x^5
Answers
Answer:
[tex]x^{4}[/tex]
Step-by-step explanation:
Whenever it comes to the division of the same variable, we subtract their powers in order to get the correct answer:
[tex]x^{9}/x^{5}[/tex]
[tex]x^{9-5}[/tex]
[tex]x^{4}[/tex]
que es el producto para (x+5) (2x-1)?
Answers
the given expression is,
(x+ 5) (2x -1)
so the answer is
[tex]\begin{gathered} \mleft(x+5\mright)(2x-1)=2x^2-x+10x-5 \\ \end{gathered}[/tex][tex]=2x^2+9x-5[/tex]so the answer is
2x^2 + 9x - 5
The drama club was selling ticketsto the school play. Adult ticketscost $8.00 each, and studenttickets cost $5.00 each. The littletheater holds 142 people and wassold out for both Friday andSaturday. The total sales for thetwo days was $1,948.00.1. How many adult tickets weresold out over the two days?2. How many student tickets weresold out over the two days?
Answers
We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:
[tex]A+S=284,(1)[/tex]This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:
[tex]8A+5S=1948,(2)[/tex]To solve this equation we will solve for A in equation (1), by subtracting S to both sides;
[tex]\begin{gathered} A+S-S=284-S \\ A=284-S \end{gathered}[/tex]Now we will replace this value in equation (2):
[tex]8(284-S)+5S=1948[/tex]Now we will apply the distributive property:
[tex]2272-8S+5S=1948[/tex]Addins like terms:
[tex]2272-3S=1948[/tex]Subtracting 2272 to both sides;
[tex]\begin{gathered} 2272-2272-3S=1948-2272 \\ -3S=-324 \end{gathered}[/tex]Dividing both sides by -3:
[tex]S=-\frac{324}{-3}=108[/tex]Now we replace this value in equation (1), where we have already solved for A:
[tex]\begin{gathered} A=248-108 \\ A=140 \end{gathered}[/tex]Therefore, there were sold 108 student tickets and 140 adult tickets.
write a quadratic equation in the form of ax²bx+c=0
Answers
The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
In order to write the equation, we would substitute values for a, b and c. If a = 3, b = 8, c = 25, the equation would be
3x^2
You have 1/4 of a quiche left over from lunch. If you sent 4/6 of the leftover quiche home with your brother, how much of the quiche do you have left in the dish?
Answers
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
If the brother took home 4/6, that means that you still have 2/6.
[tex]\frac{1}{4}[/tex] x [tex]\frac{2}{6}[/tex] = [tex]\frac{2}{24}[/tex] which is the same as 1/12
For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
Answers
Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]