If it is given f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².
To solve this problem we have to know more about mathematical functions.
What is a mathematical function?
A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.
Example: f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.
Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.
g(x) = 2- x².
f(x) = 3x - 6.
Therefore,
f(g(x)) = 3( 2- x² ) - 6. [where g(x) = 2- x²]
So, f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²
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The complete question:
Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))
Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule.
Given that the series is 1, 3, 9, 27, ............
The common ratio will be
[tex]Common\text{ ratio=}\frac{2nd\text{ term}}{1st\text{ term}}=\frac{3}{1}=3[/tex]So the common ratio is 3.
The explicit formula uses starting term and the recursive formula uses the previous term.
As
[tex]\begin{gathered} Explicit\text{ form} \\ a_n=3^{n-1} \\ Recursive\text{ form} \\ a_n=a_{n-1}\times3 \end{gathered}[/tex]These are the required forms.
what is the result of processing the set of numbers in a domain called
Answer:
the output
Step-by-step explanation:
output
on the unit circle., in standard position an angle of which measure is coterminal with an angle that measures 3pi/5 radians
Coterminal angles are angles with the same terminal sides.
[tex]\theta\rightarrow\theta+2\pi\rightarrow\theta-2\pi[/tex]For the given angle, the coterminal angles are;
[tex]\begin{gathered} \theta=\frac{3\pi}{5} \\ \theta+2\pi=\frac{3\pi}{5}+2\pi=\frac{3\pi}{5}+\frac{10\pi}{5}=\frac{13\pi}{5} \\ \theta-2\pi=\frac{3\pi}{5}-2\pi=\frac{3\pi}{5}-\frac{10\pi}{5}=-\frac{7\pi}{5} \\ \theta+2(2\pi)=\frac{3\pi}{5}+4\pi=\frac{3\pi}{5}+\frac{20\pi}{5}=\frac{23\pi}{5} \end{gathered}[/tex]From the given answer choices, the coterminal angle is;
[tex]\frac{23\pi}{5}[/tex]I need help on what the question is asking. Can you help me solve it step by step?
Given:
The total number of tamiliies is N = 30.
The objective is to find the mean number of gallons of milk consumed by 30 families.
Explanation:
The total number of milk consumed consumed by 30 families can be calculated as,
[tex]\begin{gathered} T=(8\times3)+(9\times2)+(13\times5) \\ =24+18+65 \\ =107 \end{gathered}[/tex]To find mean:
The mean number of gallons of milk can be calculated as,
[tex]M=\frac{T}{N}[/tex]On plugging the obtained values in the above equation,
[tex]\begin{gathered} M=\frac{107}{30} \\ =3.56666\ldots\text{.} \\ =3.6 \end{gathered}[/tex]Hence, the mean number of milk consumed by 30 families is 3.6 gallons.
NEED HELP ASAP‼️‼️‼️‼️‼️‼️‼️‼️‼️
simplify 3xy³ + x²y⁵ over xy²
PLEASE SEND QUICK DUE IN 10-15 MINUTES ‼️‼️‼️
Answer:
[tex]4xy^3[/tex]
Step-by-step explanation:
3xy^3 + x^2y^5/xy^2
How do I write this in function notation part b
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
Total rice bought is 75kg
Each week, he used 4.5kg, this means in w weeks, he will use:
[tex]4.5\times w=4.5w[/tex]STEP 2: Get the remaining kilograms of rice after w weeks
This will be gotten by using the function below:
[tex]75-4.5w[/tex]Hence, the function will be gotten as:
[tex]r(w)=75-4.5w[/tex]I need help with this question please?
[tex]t=100 \left(1-\frac{V}{50} \right)^2\\\\\frac{t}{100}=\left(1-\frac{V}{50} \right)^2[/tex]
Since time is positive, we take the positive square root.
[tex]\frac{\sqrt{t}}{10}=1-\frac{V}{50}\\\\\frac{\sqrt{t}}{10}-1=-\frac{V}{50}\\\\50-5\sqrt{t}=V\\\\\therefore f^{-1}(V)=\boxed{50-5\sqrt{V}}[/tex]
Question 7Simplity 663x - 5) + (2x - 1). Show each step on a separate line and tell what you did in that step. Write your answer in factored form.
The expression is given as
[tex]6(3x-5)+5(2x-1)[/tex]STEP 1
Expand the first parenthesis by multiplying all the terms there by 6.
[tex]18x-30+5(2x-1)[/tex]STEP 2
Expand the second parenthesis by multiplying all the terms there by 5.
[tex]18x-30+10x-5[/tex]STEP 3
Collect the like terms.
[tex]18x+10x-30-5[/tex]STEP 4
Perform the arithmetic operations (addition and subtraction) to get the final answer.
[tex]28x-35[/tex]The final answer is 28x - 35
A client of Susan's has asked her to create a new wood floor for his living room. The design will be created by laying wood strips in different directions, as shown on the coordinate grid. Determine whether Quadrilateral can best be described as a trapezoid, a rhombus, a rectangle, or a square. Explain your reasoning.
Answer: Where's the graph
Step-by-step explanation:
13) y = 4x - 3 -8x + 6y = 14
Replacing y in the second equation
[tex]\begin{gathered} -8x+6(4x-3)=14_{} \\ -8x+24x-18=14 \\ 16x=14+18 \\ 16x=32 \\ x=\frac{32}{16} \\ x=2 \end{gathered}[/tex]Then
[tex]\begin{gathered} y=4(2)-3 \\ y=8-3 \\ y=5 \end{gathered}[/tex]Just checking our answer
[tex]-8(2)+6(5)=-16+30=14[/tex]So the correct answer is x=2 and y=5
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How many ounces of yogurt does the carton hold? (Hint: 1 ounce equals 1.805 in.³) round to the nearest tenth as needed
The carton holds 8.9 ounces of yoghurt
Explanation:The upper diameter, D = 2 in
R = D/2
R = 2/2
The upper radius, R = 1 inch
[tex]\begin{gathered} \text{The lower diameter, d= 2}\frac{7}{16}\text{ in = }2.4375 \\ \text{The lower radius, r = }\frac{d}{2}=\text{ }\frac{2.4375}{2}in\text{ = }1.22\text{ in} \end{gathered}[/tex]The height, h = 3 in
The volume of the cone frustrum is:
[tex]\begin{gathered} V=\frac{1}{3}\pi h(R^2+r^2+Rr) \\ V=\frac{1}{3}\times3.142\times3(1^2+1.22^2_{}+1.22(1)) \\ V=3.142(3.7084)) \\ V=11.65in^3 \end{gathered}[/tex]1.805 in.³ = 1 ounce
11.65in.³ = 11.65/1.805 ounce
11.65in.³ = 6.5 ounces
The carton holds 6.5 ounces of yoghurt
what is 42/100 of x over 35?
The value of x in 42/100 of x over 35 based on the computation is 14.7.
How to calculate the fraction?It should be noted that a fraction simply means a number that's not a whole number.
Based on the information, we want to calculate 42/100 × x/35. This will be illustrated thus:
= 42/100 × x/35.
Cross multiply
(100 × x) = (42 × 35)
100x = 1470
Divide through by 100
100x / 100 = 1470 / 100
x = 14.7
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Suppose that the function f is defined, for all real numbers, as follows.
f(x)= {5x-4 if x≤1
-x+4 if x>1
Graph the function f. Then determine whether or not the function is continuous.
Answer:
F(x)
Step-by-step explanation:
hope it helps
Given the function [tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex], the function is not continuous at x = 1.
A function is said to be continuous if it can be drawn without picking up the pencil. Otherwise, a function is said to be discontinuous.
Given function,
[tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex]
We need to check the continuity of the function f(x) at x = 1. At all other points, it is continuous.
f(x) at x = 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x < 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x > 1 : -x + 4 = -1 + 4 = 3
Since, f(x) at x < 1 ≠ f(x) at x > 1, therefore, f(x) is not continuous at x = 1.
The same is also visible from the graph attached below. There is a disruption at x = 1, the graph is not a smooth line.
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HELP PLSSSSSSSSSSSSS
Answer:
the volume of the toy house is 66cm3
Solve each problem below by writing an equation that matches the situation. Then solbe your equation to find the solution to the problem. (It's been almost a day and these two questions baffled me.)
Step 1:
Let the number of hours = m
Flat fee = $25
Fees charge per hour = $30
Step 2:
Money Ronnie made from his first customer = $175
Write an equation.
30m + 25 = 175
Step 3:
Solve the equation.
[tex]\begin{gathered} 30m\text{ + 25 = 175} \\ 30m\text{ = 175 - 25} \\ 30m\text{ = 150} \\ \text{Divide through by 30} \\ m\text{ = }\frac{150}{30} \\ \text{m = 5 hours} \end{gathered}[/tex]Final answer
5 hours
A pizza is taken out of an oven and placed on a counter. The temperature, T, in degrees Fahrenheit, of the pizza after m minutes is modeled by the function Which graph represents the model?
The graph of the exponential function that represents the temperature of the pizza after m minutes is given at the end of the answer.
Which model represents the temperature of the pizza?The model that represents the temperature of the pizza m minutes after it is taken out of the oven and placed on the counter is given by:
[tex]T(m) = 72 + 200e^{-0.0445m}[/tex]
The number e is the Euler number, and the function is the exponential function translated 72 units up, hence the minimum value that the pizza obtains is of 72 degrees Fahrenheit.
Due to the negative exponent, the temperature is decaying over time, but it never gets less than 72 ºF.
The time cannot be negative, hence the domain of the graph is given as follows:
m ≥ 0.
Then, considering this, the graph of the function is given at the end of the answer.
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Answer:
Step-by-step explanation:
a
Finding Slope From Two Points
Find the slope of the line through each pair of points.
1) (19,-16), (-7, -15)
The slope of a line from given points (19,-16), (-7, -15) is - 1/26
Slope :
In Mathematics, Slope of a line defined as the direction of the line and the change in y-coordinate with respect to x - coordinate. Slope of a line is denoted by 'm'
The formula for slope of a line which passes through the points (x₁, y₁) and (x₂, y₂) is given by Slope (m) = (y₂– y₁)/(x₂ – x₁)
Here, we have pair of points (19,-16), (-7, -15)
Take (x₁, y₁) = (19,-16) and (x₂, y₂) = (-7, -15)
Slope (m) = [-15 -(-16) ] / [ -7 -19 ]
= [ - 15+16] / [ -26 ]
= [ 1 ] / [ -26 ]
= - 1/26
Therefore,
The slope of line from given points (19,-16), (-7, -15) is - 1/26
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Finding a difference quotient for a linear or quadratic function
Given the function
[tex]f(x)=-2x^2-3x+6[/tex]We are to look for the difference quotient:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Get f(x + h)
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-3(x+h)+6 \\ f(x+h)=-2(x^2+2xh+h^2)-3x-3h+6 \\ f(x+h)=-2x^2-4xh-2h^2-3x-3h+6 \\ \end{gathered}[/tex]Given f(x) expressed as:
[tex]f(x)=-2x^2-3x+6[/tex]Substitute both functions into the difference quotient;
[tex]\begin{gathered} \frac{-2x^2-4xh-2h^2-3x-3h+6-(-2x^2-3x+6)}{h} \\ \frac{-\cancel{2x^2}-4xh-2h^2-\cancel{3x}-3h+\cancel{6}+\cancel{2x^2}+\cancel{3x}-\cancel{6}}{h} \\ \frac{-4xh-2h^2-3h}{h} \end{gathered}[/tex]Factor out "h" from the result to have
[tex]\begin{gathered} \frac{\cancel{h}(-4x-2h-3)}{\cancel{h}} \\ -4x-2h-3 \end{gathered}[/tex]This shows that the simplified form of the expression is -4x - 2h - 3
if h(x, y) moves 12 units to the left and 4 units up. what is the rule that describes this translation .
Answer:
(x,y) -> (x-12, y+4)
Step-by-step explanation:
(x,y) -> (x-12, y+4)
Suzanne's salary grew from $40,000 in 2000 to $56,000 in 2021. during the same time period, Mike's salary grew form $38,000 to $53,000. Whose salary grew more in absolute change? In percentage change?
Absolute change (AC) refers to the simple difference in the indicator over two periods. that is
[tex]\begin{gathered} \text{AC (Suzanne)=56000-40000} \\ \text{AC (Suzanne)=16000} \end{gathered}[/tex]and, for Mike:
[tex]\begin{gathered} \text{AC (Mike)=53000-3}8000 \\ \text{AC (Mike)=1}5000 \end{gathered}[/tex]Whose salary grew more in absolute change? Suzanne's salary.
The relative change (RC) express the absolute change as a pencentage of the value of the indicator in the earlier period:
[tex]RC=\frac{value\text{ 2nd period - value 1st period}}{\text{value 1st period}}\times100[/tex]For Suzanne, we have
[tex]\begin{gathered} RC(\text{Suzzane)}=\frac{56000-40000}{56000}\cdot100 \\ RC(\text{Suzzane)}=\frac{16000}{56000}\cdot100 \\ RC(\text{Suzzane)}=0.286\cdot100 \\ RC(\text{Suzzane)}=28.6 \end{gathered}[/tex]and for Mike, we have
[tex]\begin{gathered} RC(\text{Mike)}=\frac{53000-28000}{53000}\cdot100 \\ RC(\text{Mike)}=\frac{15000}{53000}\cdot100 \\ RC(\text{Mike)}=0.283\cdot100 \\ RC(\text{Mike)}=28.3 \end{gathered}[/tex]In percentage change? For Suzanne is 28.6% and for Mike 28.3%
Answer: Mike's salary grew from $ 38,000 to $ 53,000.
Step-by-step explanation:
Simplify −3(x+4)+5x Write your answer in factored form
Answer:-3x - 12 + 5x
Step-by-step explanation:
Social Security is 6.2% of the first $97,500. Medicare is 1.45% of all income.
The state tax is 2% of gross pay, and the local tax is 1.5% of gross pay.
7.) Orville Staples is a painter who earns $30,000.00 a year. He is single and claims 3 allowances. Weekly deductions include $34.50 for medical insurance and union dues of $15.00.
Please calculate Federal Income Tax, Social Security Tax, Medicare Tax, State Tax & Local tax. Please show work.
The deductions for the taxes are given as follows:
Federal Income Tax: $4,626.27.Social Security Tax: $1,860.Medicare Tax: $435.State Tax: $600.Local Tax: $450.What are his deductions?To calculate the taxes, we have to consider his gross pay, which is given in the text as follows:
Gross pay = $30,000.
The Federal Income Tax for people in his income range is of $1,027.50 plus 12% of the amount over $10,275, hence:
Federal Income Tax = 1027.50 + 0.12 x (30000 - 10.275) = $4,626.27.
The Social Security tax is of 6.2% of his salary, hence:
Social Security Tax = 0.062 x 30000 = $1,860.
The Medicare tax is of 1.45% of his salary, hence:
Medicare Tax = 0.0145 x 30000 = $435.
The State Tax is of 2% os his salary, hence:
State Tax = 0.02 x 30000 = $600.
The Local Tax is of 1.5% of his salary, hence:
Local Tax = 0.015 x 30000 = $450.
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a survey was given to people who owned a certain type of car.what percent of the people surveyed were completely satisfied with the car.blue:compleletely satisfiedpurple: somewhat satisfiedgreen:not satisfied
The percent of people that were completely satisfied (%PS) can be calculated with the formula:
[tex]\text{ \%PS=}\frac{PS}{TP}\times100\text{\%}[/tex]Where PS is the number of persons that were completely satisfied and TP is the total number of persons, in this case, the total number of persons is the sum of each number of persons from each category:
[tex]TP=160+740+1100=2000[/tex]And as we can see from the figure, the number of completely satisfied people is 1100, then the percent of people that were completely satisfied is:
[tex]\begin{gathered} \text{\%PS=}\frac{PS}{TP}\times100\text{\%} \\ \text{\%PS=}\frac{100}{2000}\times100\text{\%} \\ \text{\%PS=}0.55\times100\text{\%}=55\text{\%} \end{gathered}[/tex]The percent of people that were completely satisfied is 55%
You just have to divide 1100 by the total people which is 2000, and then just multiply by 100, and that's it
many of these boxes do you need to buy?you need to buy 40 packsExample 2.At a restaurant one day. 60 sandwiches were sold in all, some on rye bread and 28 onwhite bread. The number of sandwiches sold on try bread was twice the number soldthe day before. How many sandwiches on rye bread were sold the day before"?
rye bread sandwiches + white bread sandwiches = total number of sandwiches
rye bread sandwiches + 28 = 60
rye bread sandwiches = 60 - 28
rye bread sandwiches = 32
This number, 32, is twice the day before, that is, the day before was half of 32 sandwiches, which is 32/2 = 16.
The day before, 16 sandwiches on rye bread were sold.
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⇒For m=2 and n=-3 in the equation 3m-4n In the place of m plug in 2 and in the place of n plug in -3 and simplify.
[tex]=3(2)-4(-3)\\=6+12\\=18[/tex]
Option C is the answer.
A pizza shop specializes in deep-dish pizzas. They sell a 14 -inch pizza that is 3 inches deep and a 16-inch pizza that is 2 inches deep. The 14 -inch pizza is cut into 8 slices and the 16-inch pizza is cut into 7 slices, and each slice is sold for the same price. If you are purchasing one slice of pizza, which size should you choose to get the most food? Show all of your work to justify your response.
Answer:
The 14-inch pizza cut into 8 slices.
Explanation:
The deep-dish pizza forms a cylindrical shape.
To make comparisons, we find the volume of each slice of pizza in each case.
[tex]\text{Volume of a cylinder=}\pi r^2h[/tex]Case 1
A 14-inch pizza that is 3 inches deep.
Radius = 14/2 = 7 inches
Height = 3 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times7^2\times3 \\ =147\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 8 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{147\pi}{8} \\ =18.375\pi\text{ cubic inches} \end{gathered}[/tex]Case 2
A 16-inch pizza that is 2 inches deep.
Radius = 16/2 = 8 inches
Height = 2 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times8^2\times2 \\ =128\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 7 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{128\pi}{7} \\ \approx18.285\pi\text{ cubic inches} \end{gathered}[/tex]Conclusion
The volume of a slice of pizza in the first case (the 14 -inch pizza cut into 8 slices) is larger, therefore it should be chosen to get the most food.
jerry had 3409 pieces of marble he swallowed 1290 then is mom brought his 3456 more. How much does jerry have?
Answer: 5575 Marbles
Step-by-step explanation:
This can be solved simply by subtracting and adding.
3409-1290=2119
2119+3456=5575
A basketball player scores 14, 16, 20, 5, 22, 30, 16, and 28 points during a
tournament. Make a box-and-whisker plot for the points scored by the player.
The diagram attached shows the box-and-whisker plot for the points scored by the player.
How to Make a Box-and-whisker Plot for a Data Set?A box-and-whisker plot displays the maximum and minimum data values, the upper and lower quartiles, and the median of the data. They are called the five-number summary.
Given the data for the number of points scored by a basketball player is: 14, 16, 20, 5, 22, 30, 16, and 28, the five-number summary for the data would therefore be:
Minimum: smallest data point, which is 5.First Quartile: center of the first part of the data set when ordered, which is 15.Median: The middle data point, which is 18.Third Quartile: center of the second part of the data set, which is, 25Maximum: this represents the highest data point, which is, 30The box-and-whisker plot is shown below.
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mr. Smith took out a 54200 car loan at 10.2% compounded annually what would the interest be after 4 years
The compounded loan means that in the first year the 10.2% of interest is add to the initial 54200 and that value generate the next year the 10.2%
then in the first year the interest will be:
You use a rule of three:
[tex]\text{1st}=\frac{54200\cdot10.2}{100}=5528.4[/tex]As the first year the interest is 5528.4
To the second year that sum is added to the 54200 to get the interest:
[tex]54200+5528.4=59728.4[/tex][tex]2nd=\frac{59728.4\cdot10.2}{100}=6092.3[/tex]Third year:
[tex]59728.4+6092.3=60820.7[/tex][tex]3rd=\frac{60820.7\cdot10.2}{100}=6203.7[/tex]Fourth year:
[tex]60820.7+6203.7=67024.4[/tex][tex]4th=\frac{67024.4\cdot10.2}{100}=6836.5[/tex]After 4 years:
[tex]67024.4+6836.5=73860.9[/tex][tex]=\frac{73860.9\cdot10.2}{100}=7533.8[/tex]After 4 years the interest will be: 7533.8