Answers
The composite functions are evaluated and simplified as:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate a Composite Function?To evaluate a composite function, the inner function is evaluated first using the given input. After then, the output of the inner function is used as the input to evaluate the outer function.
Given the following:
f(x) = x² + 5g(x) = 3xTherefore:
a. (f o g)(x) = f(g(x))
Substitute g(x) for x into f(x) = x² + 5
f(g(x)) = (3x)² + 5
Simplify the function
f(g(x)) = 9x² + 5
b. (g o f)(x) = g(f(x))
Substitute f(x) for x into g(x) = 3x:
g(f(x)) = 3(x² + 5)
Simplify the function
g(f(x)) = 3x² + 15
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Related Questions
Square meters of ceiling Number of tiles 1 10.75 10 100.75 9.3 100 What is the value of the red X? Write your answer as an algebraic expression using variable "a".
Answers
x = 9a + 1.75
slope = (100.75 - 10.75)/(10 - 9) = 90/9 = 9
offset: 10.75 = 9(1) + b
10.75 - 9 = b
1.75 = b
b = 1.75
y = mx + b
in this case: x = 9a + 1.75
y + 7x= 11; x= -1,0, 4
Answers
We have an expression with 2 unknowns, and we have values for one unknown. We have to calculate then the other unknown value:
Expression:
[tex]\begin{gathered} y+7x=11 \\ y=11-7x \end{gathered}[/tex]Then, when x=-1
[tex]y=11-7x=11-7(-1)=11+7=18[/tex]When x=0
[tex]y=11-7(0)=11[/tex]When x=4
[tex]y=11-7(4)=11-28=-17[/tex]Given 5x + 2y=22 and that y=1, find x
Answers
In a linear equation both variables are dependent on each other
Then to find x
first reorder and put x as one term only
x = (22- 2y)/5
now replace y by its given value y= 1
then x= (22- 2•1)/5 = 20/5= 4
In a class of 30 students, 14 take tea and 20 take coffee. How many take both tea
and coffee?
Answers
Answer:
4
Step-by-step explanation:
[tex]20 + 14 = 34[/tex]
[tex]34 - 30 = 4[/tex]
What types of solutions will a quadratic equation have when the discriminant b2 − 4ac in the quadratic formula is negative?
Answers
Explanation
When the discriminant is negative, this implies that
[tex]b^2-4ac<0[/tex]Answer: In this case, the equation has no real solutions;
What is the equation of the circle with endpoints (5,7) and (1,3)
Answers
Explanation:
endpoints (5,7) and (1,3)
The equation of circle formula:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ radius\text{ =r and (a, b) are the coordinates of the centre} \end{gathered}[/tex]To find the centre(a, b), we need to find the midpoint of the two given points:
[tex]\begin{gathered} \text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2) \\ \text{Midpoint = 1/2(5+1), 1/2(7+3)} \\ \text{Midpoint = 3, 5} \\ \text{centre = (a, b) =(3, 5)} \end{gathered}[/tex]The radius is the distance between the centre of the circle and any of the two points.
We will apply the distance formula:
[tex]\begin{gathered} dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ (3,5)\text{ and (1, 3)} \\ \text{Distance =}\sqrt[]{(3-5)^2+(1-3)^2} \\ \text{Distance =}\sqrt[]{4+4} \\ \text{Distance =}\sqrt[]{8}\text{ = 2}\sqrt[]{2} \\ \text{radius = distance = 2}\sqrt[]{2} \end{gathered}[/tex]Using the equation of circle:
[tex]\begin{gathered} (x-3)^2+(y-5)^2=(2\sqrt[]{2)}^2 \\ (2\sqrt[]{2)}^2=\text{ }2\sqrt[]{2)}\times2\sqrt[]{2)}\text{ = 4(}\sqrt[]{2})^2\text{ = 4(2) = 8} \\ (x-3)^2+(y-5)^2=\text{ 8} \end{gathered}[/tex]Nikki and four friends had lunch at their favorite restaurant. The total bill was $29.00, and they wanted to leave a 15% tip. Which amount of money is closest to the 15% tip? A $3.00 B $3.50C $4.00D $4.50
Answers
Total bill = $29
Tip left = 15%
The valu of the tip = 15% of $29
[tex]\begin{gathered} \frac{15}{100}\text{ x 29} \\ \\ =\text{ \$4.35} \end{gathered}[/tex]The value of the tip = $4.35
Let us consider the options given
$4.35 - $3 = $1.35
$4.35 - $3.5 = $0.85
$4.35 - $4 = $0.35
$4.5 - $4.35 = $0.15
Looking t the deviation from the real value of the tip ($4.35), the least deviation is $0.15. Hence, we can conclude that $4.5 is the closest to the tip.
The answer is option D ($4.50)
Find slope and y-intercept of the line. Compare the values to equation y=3x-8
Answers
The slope of a line graph, we need to pick two point on the line.
It is better to pick points that meet the grids, so we can have its exactly coordinates.
Also, since we will need the y-intercept, one of the points can be this.
The y-intercept is the point where the line intercepts the y-axis, its x value is always 0, and we can see that it happens, in this case, at y = -8, so the point is (0, -8), and the y-intercept is -8.
Now, we can look at any other point. We can see that one point that meets the grids is the point at x = 3 and y = 1, so at point (3, 1).
The slope, m, can be, then, calculated as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-(-8)}{3-0}=\frac{1+8}{3}=\frac{9}{3}=3 \end{gathered}[/tex]So, the slope is 3.
Answers:
Slope: 3
y-intercept: (0, -8)
The line in the slope-intercept form is:
[tex]y=mx+b[/tex]where m is the slope and b is the y value of the y-intercept.
So, in this case, we have:
[tex]\begin{gathered} m=3 \\ b=-8 \\ y=3x-8 \end{gathered}[/tex]Which is exactly the same as the equation given, y = 3x - 8, so the equation given corresponds to the graph given.
help me please.......
Answers
Let
x -----> the larger room
y -----> the smaller room
we have that
x=2y
we have
y=25 3/4 ft
Convert to an improper fraction
25 3/4=25+3/4=103/4 ft
Find the value of x
x=2y
x=2(103/4)
x=103/2 ft
Convert to mixed number
103/2=51.5=51+0.5=51 1/2 ft
the answer is51 1/2 fthe larger roomhe larger room
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
YOU WILL GET 70 POINTS!
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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what's the answer for proportions 4/n+2=7/n
Answers
Explanation
[tex]\frac{4}{n+2}=\frac{7}{n}[/tex]we need to solve for n
Step 1
cross multiply
[tex]\begin{gathered} \frac{4}{n+2}=\frac{7}{n} \\ 4\cdot n=7(n+2) \\ 4n=7n+14 \\ \end{gathered}[/tex]Step 2
subtract 4n in both sides
[tex]\begin{gathered} 4n=7n+14 \\ 4n-4n=7n+14-4n \\ 0=3n+14 \end{gathered}[/tex]Step 3
subtract 14 in both sides,
[tex]\begin{gathered} 0=3n+14 \\ 0-14=3n+14-14 \\ -14=3n \end{gathered}[/tex]Step 4
Finally, divide both sides by 3
[tex]\begin{gathered} \frac{-14}{3}=\frac{3n}{3} \\ n=-\frac{14}{3} \end{gathered}[/tex]I hope this helps you
which property justifies the following statement if 3x=9,then x=3.
Answers
Answer:
Multiplication Property
Division Property
This can be justified using multiplication property and division property:
Multiplication property:
If both sides of equation:
3x = 9
are multiplied by 1/3, we have:
x = 3
Division property
Divide both sides of the equation:
3x = 9 by 3, we have:
x = 3
If f (x)- VX-3, complete the following statement:x + 219) =
Answers
Given that;
[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]To get f(19), let's substitute 19 for x in the function f(x);
[tex]\begin{gathered} f(x)=\frac{3}{x+2}-\sqrt{x-3} \\ f(19)=\frac{3}{19+2}-\sqrt{19-3} \\ f(19)=\frac{3}{21}-\sqrt{16} \\ f(19)=\frac{1}{7}-4 \\ f(19)=-3\frac{6}{7} \end{gathered}[/tex]Therefore, the value of f(19) is;
[tex]f(19)=-3\frac{6}{7}[/tex]An advertising company plans to market a product to low-income families. A study states that for a particular area the mean income per family is $25,174 and the standard deviation is $8,700. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. Assume the variable is normally distributed.
Answers
18. Yvonne paid $18.72 for 8 gallons of gas. How much would she have spent on gas if she had only needed 5 gallons of gas?
Answers
As given by the question
There are given that $18.72 for 8 gallons of gas.
Now,
Since, $18.72 for 8 gallons of gas;
Then,
First calculate the price of one-gallon gas
So,
[tex]\frac{18.72}{8}=2.34[/tex]The price og one g
tell whether the fractions are equivalent
Answers
Step 1:
Equivalent fractions are fraction that are equal in ratio.
1/3 is equivalent to 4/12
4/12 can be simplify to 1/3 because 4 is a highest common factor of 4 and 12
When you divide by numerator ( 4) and denominator (12) by 4, the fraction result to 1/3.
Hence, 1/3 is equivalent to 4/12.
Final answer
[tex]\frac{1}{3}\text{ = }\frac{4}{12}[/tex]
Is this correct?
Or please provide an explanation.
Answers
Answer:
The answer selected is correct
Step-by-step explanation:
When talking about balance, having -X (being X in the negative) , means owing X.
Dylan owes $19.25
Elise owes $42.75
Francesca owes $23
Jamaal owes $35.50
So naturally, Dylan owes the least.
I will show you the question
Answers
Given a coordinate plane
For each point, we will make a rotation about the origin
A: ( 9, 3) Clockwise by 90
The rule of rotation will be:
[tex](x,y)\rightarrow(y,-x)[/tex]So, the image of A will be A' = ( 3, -9)
B: ( -4, 7 ) counterclockwise 90
the rule of rotation will be:
[tex](x,y)\rightarrow(-y,x)[/tex]So, the image of B will be B' = ( -7, -4)
C: ( 6, -5) by 180
The rule of rotation will be:
[tex](x,y)\rightarrow(-x,-y)[/tex]so, the image of C will be C' = (-6, 5)
D: ( -8, -2) clockwise by 90
So, the image of D will be D' = ( -2, 8)
Find the measure of each angle in the triangle. F R 6x 15x 15x O 02
Answers
Answer:
R = 75
O = 75
F = 30
Step-by-step explanation:
15x + 15x + 6x = 180
add like terms
36x = 180
divide
x = 5
The measure of angle P is 30°, angle R is 75° and angle O is 75° in triangle POR.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
From the given triangle POR, ∠R=15x, ∠O=15x and ∠P=6x.
By using angle sum property, we get
∠P+∠O+∠R=180°
6x+15x+15x=180
36x=180
x=180/36
x=5
So, ∠R=15x=75°, ∠O=15x=75° and ∠P=6x=30°
Therefore, the measure of angle P is 30°, angle R is 75° and angle O is 75° in triangle POR.
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Since January 1, 1960, the population of Slim Chance has been described by the formula P = 27000(0.95)^t, where P is the population of the city t years after the start of 1960. At what rate was the population changingon January 1, 19702?numerical rate of change= ___ people per year
Answers
We have to calculate the rate of change of the population P(t) at January 1, 1970 (t = 10).
The expression for P(t) is:
[tex]P(t)=27000\cdot0.95^t[/tex]The rate of change will be given by the first derivative of P(t):
[tex]\frac{dP}{dt}=27000\cdot\ln (0.95)\cdot0.95^t[/tex]Then, we can calculate the value of the rate of change when t = 10, by replacing t with 10 in the last expression. We then will get:
[tex]\begin{gathered} \frac{dP}{dt}(100)=27000\cdot\ln (0.95)\cdot0.95^{10} \\ \frac{dP}{dt}(100)\approx27000\cdot(-0.0513)\cdot0.5987 \\ \frac{dP}{dt}(100)\approx-829 \end{gathered}[/tex]The population, on January 1st 1970, is decreasing at a rate of 829 people per year.
Answer: numerical rate of change= -829 people per year
The diameter of the Milky Way is 2 x 10²⁰ meters. The radius of Earth is 6.37 x 10⁶meters. About how many times as great is the diameter of the Milky Way than the radius of Earth? The diameter of the Milky Way is about
Answers: 4.37 X 10¹⁴
3.1 X 10¹⁴
4.37 X 10¹³
3.1 X 10¹³
(blank) times as great as the radius of Earth.
Answers
Answer:
3.1 x [tex]10^{13}[/tex]
Step-by-step explanation:
[tex]\frac{2x10^{20} }{6.37x10^{6} }[/tex]
3/6.37 is about .31
When you are dividing with powers, you subtract the exponents
20 - 6 = 14
.31 x [tex]10^{14}[/tex] This is not in scientific notation because .31 is less than 1
3.1 x [tex]10^{-1}[/tex]x[tex]10^{14}[/tex] When we multiply powers with the same base we add the exponents
3.1 x [tex]10^{13}[/tex]
want to graph xdont you need to find out what x is?-3x-6y=0
Answers
We have a equation of a line in the form:
[tex]-3x-6y=0[/tex]This goes through the point (0,0).
With another point, we can graph the line.
For example, for x=2, we have:
[tex]\begin{gathered} -3(2)-6y=0 \\ -6-6y=0 \\ -6y=6 \\ y=-1 \end{gathered}[/tex]So the point (2,-1) belongs to the line.
We can graph the line passing through those points:
A taxi service charges $3 for the first mile and then $2.25 for every mile after that. The farthest the taxi will travel is 35 miles. If X represents the number of miles traveled, and Y represents the total cost of the taxi ride, what is the most appropriate domain for the solutions?
Answers
Solution:
Given:
[tex]\begin{gathered} A\text{ taxi service charges \$3 for the first mile} \\ \text{ \$2.25 for every mile after that.} \\ \text{The farthest the taxi will travel is 35 miles.} \end{gathered}[/tex]Since x represents the number of miles traveled
y represents the total cost of the taxi ride
From the description, the number of miles the taxi will travel is between 0 and 35miles since 35 miles is the farthest it could go.
This means the domain which refers to the set of possible input values will be;
[tex]\begin{gathered} x>0\text{ because the service is charged once a certain distance is covered.} \\ \text{when no distance is covered, no charge is made.} \\ \text{Also,} \\ x\le35\text{ because the farthest is 35miles. This means the ta}\xi\text{ can not travel beyond 35miles.} \\ \\ \text{From the descriptions made, the domain will be:} \\ 0Therefore, the most appropriate domain for the solutions is;
[tex]0 The correct answer is OPTION B.If TRAP is an isosceles trapezoid, what is the value of x?A. 1B. 22C. 12D. 23E. 11F. Cannot be determined
Answers
In an Isosceles trapezoid, it is known that the base angles have equal measures, and non-congruent angles are supplementary.
The non-congruent angles ∠RAP and ∠APTfrom the figure have measures 6x° and (2x+4)°, respectively.
Since they must be supplementary, it follows that their sum is 180°:
[tex]\begin{gathered} 6x+2x+4=180 \\ \Rightarrow8x+4=180\Rightarrow8x=180-4 \\ \Rightarrow8x=176\Rightarrow\frac{8x}{8}=\frac{176}{8} \\ \Rightarrow x=22 \end{gathered}[/tex]Hence, the value of x is 22. The correct option is B.
Answer:B
Step-by-step explanation:just took the test
15= x/6-1 help me with this im just using it to study so show step by step because i forgot
Answers
The value of x after solving the expression, 15 = (x/6)-1, step by step is 96.
According to the question,
We have the following expression:
15 = (x/6)-1
Now, we can change the sides because it will not make any difference to the overall answer.
(x/6)-1 = 15
Now, we will move 1 from the left hand side to the right hand side. So, the sign will change from minus to plus.
x/6 = 15+1
x/6 = 16
Now, we will move 6 from the left hand side to right hand side. 6 is in the division on the left hand side then it will be in multiplication on the right hand side.
x = 16*6
x = 96
Hence, the value of x after solving the expression step by step is 96.
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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
Find the value of x. Round tothe nearest tenth.27°Х34°11=x = [?]Law of Sines: sin AAsin Bbsin CIIaС
Answers
Using the law of Sines
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Consider the given triangle
Let A = 27°, the a = 11
Let B = 34°, the b = x
Substitute the values into the sine rule formula
This gives
[tex]\frac{\sin27}{11}=\frac{\sin 34}{x}[/tex]Cross multiply
[tex]x\times\sin 27=11\times\sin 34[/tex]Divide both sides by sin 27
This gives
[tex]x=\frac{11\times\sin 34}{\sin 27}[/tex]Solve for x
[tex]\begin{gathered} x=\frac{11\times0.5592}{0.4540} \\ x=\frac{6.1512}{0.4540} \\ x=13.55 \end{gathered}[/tex]Therefore, the value of x is approximately 13.55
R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Answers
Statement Problem: R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Solution:
R'S'T'U' is a dilation of RSTU by;
[tex]\frac{1}{3}[/tex]because it is reduced by that factor.
CORRECT OPTION: a reduction with scale factor
[tex]\frac{1}{3}[/tex]Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the equation.
Answers
Answer:
I don’t know if I can send it answer
Step-by-step explanation:
11. Jarrod's favorite movie is now on video at 15% off the originalprice. If he pays $17, what was the original price?
Answers
original price = x
discount = 15%
price after discount = $17
Write an equation:
x (1-15/100) = 17
x (1-0.15 ) = 17
0.85x = 17
Solve for x:
x = 17/0.85
x = $20