Part 1
f(x) + g(x)
3x+2 + 4x
(3x+4x) + 2
7x+2
Therefore, f(x)+g(x) = 7x+2
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Part 2
f(x) = 3x+2
f( g(x) ) = 3( g(x) ) + 2 ... replace every x with g(x)
f( g(x) ) = 3(4x) + 2 .... plug in g(x) = 4x
f( g(x) ) = 12x + 2
================================================
Part 3
Let's say x is the number of minutes.
Furthermore, let's say f(x) and g(x) are phone plan costs. Computing f(x)+g(x) will give the total cost of both plans combined. This is one example where it's useful to add the functions.
---------
As for a second example, let's say g(x) = 4x represents the total cost to fill up your car when you use x gallons of gas. The 4 out front means gas is $4 per gallon.
When we compute f( g(x) ) = 3*g(x) + 2, we could have 3 different cars that use the same amount of gas (x). The +2 at the end could be something like we have to pay $2 for parking.
Overall, f( g(x) ) = 12x + 2 is the total cost of filling up 3 cars and paying for the extra $2 parking.
Notice the output of g(x) is fed directly as the input of f(x). Think of it like a chain reaction.
This is one example of many where function composition is useful.
please help! I need to give this by today
Answer:
About 26.67 percent.
Solve 11x+10y=32..... Will mark the brainliest!
The equation 11x + 10y = 32 is a linear equation, and the solution to the linear equation 11x + 10y = 32 is [tex]y = \frac{32 - 11x}{10}[/tex]
How to solve the equation?The equation is given as:
11x + 10y = 32
Subtract 11x from both sides
10y = 32 - 11x
Divide both sides by 10
[tex]y = \frac{32 - 11x}{10}[/tex]
Hence, the solution to the linear equation 11x + 10y = 32 is [tex]y = \frac{32 - 11x}{10}[/tex]
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Instead of using the values {1, 2, 3, 4, 5, 6} on dice, suppose a pair of dice have the following {1, 2, 2, 3, 3, 4} on one die and {1, 3, 4, 5, 6, 8} on the other. Find the probability of rolling the sum of 7 with these dice. Be sure to reduce.
The dice will show a sum of 7 if you roll
• 1 and 6
• 2 and 5 (2 ways)
• 3 and 4 (3 ways)
so there are 6 ways of rolling a sum of 7. Out of 6 × 6 = 36 possible outcomes, the probability of rolling a sum of 7 is 6/36 = 1/6.
What is the volume of the rectangular prism?
PLEASE HELP ASAP
Answer:
7yd^2
Step-by-step explanation:
Calculate for volume as if its 1yd for cube, divide it by a third because each cube is 1/3 of a yard, square it.
Result: 7yd^2
The printing company wants to minimize costs. What is the objective function? p = 45x 20y p = 25x 45y p = 25x 10y p = 25x 20y
The objective function of the printing company in a bid to minimize cost is; p = 25x + 20y.
What is the objective function of the company?The objective function in a linear programming problem is the real-valued function whose value is to be either minimized or maximized dependent on the constraints defined on the given linear programming problem over the set of feasible solutions. The objective function of a LPP is a linear function of the form z = ax + by in which case, z is the parameter to be optimised.
It therefore follows from the complete question that the objective function is; p = 25x + 20y. This follows from the fact that Supplier X charges $25 per case. Supplier Y charges $20 per case and the parameter to be optimised is price.
Remarks;
The complete question is as follows;
A printing company orders paper from two different suppliers. Supplier X charges $25 per case. Supplier Y charges $20 per case. The company needs to order at least 45 cases per day to meet demand and can order no more than 30 cases from Supplier X. The company needs no more than 2 times as many cases from Supplier Y as from Supplier X. Let x = the number of cases from Supplier X and y = the number of cases from Supplier Y.
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Answer:
D
Step-by-step explanation:
right on edge
Name the largest and the smallest angle
A certain commercial jet plane uses a mean of 0.15 gallons of fuel per passenger-mile, with a standard deviation of 0.01 gallons. Find the mean number of gallons the plane uses to fly 8000 miles if it carries 210 passengers.
Answer:
I do not know I am very sorry brother now begone
625 x 625 = ? What is the answer?
Answer:
390625 = 625 x 625
Step-by-step explanation:
calculator
The Line plot below shows the lengths of bolts Mr.Slivka found in his drawer He needs 16 bolts that are longer than 1 inch for a projector he is working on. Does he have enough bolts for his project. (Bolt Lengths) 2/8 4/8 6/8 1 whole 1 2/8 1 4/8 (Inches) A. yes there are 16 Bolts that have lengths greater then 1 inch, which is just enoguh. B. Yes. there are 18 Bolts that have lengths greater then 1 inch, which is more than enough. C. No there are only 3 bolts with lengths greater than 1 inch, which is not enough. D. No, there are only 12 bolts that have lengths greater than 1 inch, which is not enough.
Thank you if you answered this u get a good Answer :)
Answer:
the answer is D
Step-by-step explanation:
Avery bought stock in a company two years ago that was worth x dollars. During the first year that she owned the stock, it increased by 40%. During the second year the value of the stock decreased by 10%.
Answer:
The value of the stock can be found by: x × 1.26.
Step-by-step explanation:
The value of the stock in year one can be found by multiplying x by 1.4. This will represent a 40% increase in value. The following year, the stock decreases in value by 10%; this is represented by multiplication by 0.9. For example, if the value of the stock was $5:
5 × 1.4 = 7 (A 40% increase in value)
(5 × 1.4) * 0.90 = 6.3 (A further 10% decrease in value)
Rather than writing out the long version, we can simplfify by multiplying 1.4 by 0.9 to get 1.26 .We can also replace 5 with x to get a more general equation.
Haiiiii i need help with this question pls!! what is the distance between (3,3) and (-5,-2)
tysm!!!
A company which employs 10 unskilled and 8 skilled workers produce two models of a toy, Model A and Model B. • Model A requires 20 hours of unskilled labour while Model B requires 15 hours of unskilled labour • Model A requires 10 hours of skilled labour while Model B requires 25 hours of skilled labour Each worker provides 40 hours of labour per week. (a) Calculate the maximum number of hours available per week for (i) unskilled labour
The Maximum number of hours available for unskilled labour
= 400 hours
Maximum number of hours available for skilled labour be, = 320 hours
What is Unitary Method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
The company employs 10 unskilled workers and each worker provides 40 hours of labour per week.
The company also employs 8 skilled workers and each worker provides 40 hours of labour per week.
Maximum number of hours available for unskilled labour be,
= 40 × 10
= 400 hours
Maximum number of hours available for skilled labour be,
= 40 × 8
= 320 hours
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Elliot has a total of 26 books. he has 12 more fiction books than nonfiction books. let x represent the number of fiction books and y represent the number of nonfiction books. which system of linear equations represents the situation? x y = 26 and x y = 12 x y = 26 and x – y = 12 x y = 26 and –x y = 12 x – y = 26 and x y = 12
Answer:
X+Y=26
X-Y=12
Step-by-step explanation:
fiction books= X
non fiction books= Y
then,
fiction books= X
non fiction books = X-12
but Y= X - 12
from. the statement,
X+Y = 26
X-Y=12
simplify the expression (2x+3y)+y=?
Answer: [tex]2x+4y[/tex]
Step-by-step explanation:
[tex]2*(x+2y)[/tex]
[tex](2x+3y)+y[/tex]
Apply rule: [tex](a)=a[/tex]
[tex](2x+3y)=2x+3y[/tex]
[tex]=2x+3y+y[/tex]
Add similar elements: [tex]3y+y=4y[/tex]
[tex]=2x+4y[/tex]
[tex]2x+4y~is~the~answer[/tex]
What are the solutions for the following system of equations?
−2x2 + y = 6
4x² + 3y = 28
(0, 6) and (1, 8)
(0, 6) and (-1, 8)
(-1, 4) and (1,4)
(-1, 8) and (1,8)
The solution of the system of equation are (1,8) and (0, 6)
How to find solution of a system of equation?-2x² + y = 6
4x² + 3y = 28
Therefore,
-4x² + 2y = 12
4x² + 3y = 28
5y = 40
y = 40 / 5
y = 8
Therefore,
-2x² + 8 = 6
-2x² = -2
x² = 1
x = 1
2(0)² + y = 6
y = 6
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Answer:
D. (-1, 8) and (1,8)
Step-by-step explanation:
I took the math exam
The longest straw that can fit inside a 5-inch cylindrical cupm if the straw is placed at the angle in the cup, is 6- inches.
what is the approximate length of the cylinder's radius?
Since the straw is 6 inches long, the approximate length of the cylinder's radius is 3.32 in
To find the radius of the cylinder, we need to apply Pythagoras' theorem.
What is Pythagoras' theorem?Pythagoras' theorem states that in any right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.
Mathematically, c² = a² + b² where
c = hypotenusea and b = other sides.Now, since the 6 inch straw inclined at an angle forms a right angle with the radius,r and length of the cylinder, h.
Since the length of the straw is the hypotenuse side, L we have that
L² = h² + r²
Radius of the cylinderMaking r the radius of the cylinder subject of the formula, we have
r = √(L² - h²)
Given that
L = 6 in and h = 5 inSubstituting the values of the variables into the equation,we have
r = √(L² - h²)
r = √(6² - 5²)
r = √(36 - 25)
r = √11
r = 3.316 in
r ≅ 3.32 in
So, the approximate length of the cylinder's radius is 3.32 in
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Evaluate h(x)=-2x+9 when x=-2,0, and 5 .
h(-2)=
h(0)=
h (5)=
Answer:
The answer is 13, 9 and (-1)
Step-by-step explanation:
Given;h(x) = (-2x + 9)To Find;h(x) = (-2x + 9) when x = (-2), 0 and 5.For x = (-2)
h(x) = (-2x + 9)
h(-2) = [-2(-2) + 9]
h(-2) = (4 + 9)
h(-2) = 13
For x = 0
h(x) = (-2x + 9)
h(0) = [-2(0) + 9]
h(0) = (0 + 9)
h(0) = 9
For x = 5
h(x) = (-2x + 9)
h(5) = [-2(5) + 9]
h(5) = [(-10) + 9]
h(5) = (-1)
Thus, The answer is 13, 9 and (-1) when x = (-2), 0 and 5 respectively.
Solve for x.
4(5+x) = 2x + 2
3
Please help me
Step-by-step explanation:
4(5 + x) = 2x + 2
that is my understanding of the given problem.
if you made a typo, please adapt the following solution.
4×5 + 4×x = 2x + 2
20 + 4x = 2x + 2
20 + 2x = 2
2x = -18
x = -9
Rockport had 5,620 residents at the time of its founding. Currently there are 3,934 residents. What is the percent of decrease in Rockport's population?
Answer:
30%
Step-by-step explanation:
percent decrease = (new - old) / old * 100 = (3934-5620)/5620 * 100 = 30%
the probability that the coin shows tails and is the number 2
Answer:
50%
Step-by-step explanation:theres only 2 sides on a coin
Answer: 50% , as likely as not .
Step-by-step explanation:
The probability of a 2 on the die is 1/6. The probability of a heads on the coin is 1/2. That means that (on average) half the time you roll a 2 you'll also get heads and the other half you'll get tails. What's half of 1/6?
The possibilities are:
1H 2H 3H 4H 5H 6H
1T 2T 3T 4T 5T 6T
So, it's 1/12 that you'll get a 2 and heads (on average).
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Can someone please tell me if this is right!
Answer:
the leading coefficient of a polynomial is the coefficient of the term with the highest degree of the polynomial
so the answer should be the second one -7+6x+5x^2
Please i need help, i have to clean my room before my dad gets home a but first i have to do my homework and he is on his way home!!!
tino works at a retail clothing store as a sales clerk and part of his paycheck is based on commission, meaning that it is determined by the value of the clothes that he sells. each week, he earns $7 an hour plus 15% of his total sales. if tino works for 18 hours and sells $538 in clothes in a certain week, what is the amount of his commission? what is his total pay for that week?
I found the answer for you
describe the transformations from the parent function f(x)=x2 to the function g(x)=(x-2)^2+5
A. 2 units down, 5 units to the left
B. 2 units down, 5 units to the right
c. 2 units to the right, 5 units up
D. 2 units to the left, 5 units up
Answer:
C.) 2 units to the right, 5 units up
Step-by-step explanation:
The graph shifts left or right when a number modifies the "x" value before it is affected by any other number/function in the equation. This number is within parentheses with the "x". Subtracting a value moves the function to the right, whereas adding a value moves the function to the left. Therefore, since 2 is being subtracted from "x", the function has been shifted 2 units to the right.
The graph shifts up or down when the y-intercept changes. The y-intercept is the "b" value in a standard function. You can identify this value by plugging in zero to "x". If this number is positive, the function is shifted upwards, and if this number is negative, the function is shifted downwards. Therefore, since there is a 5 added to the equation, the function is shifted 5 units up.
How to convert it to an inequality
Find x. Give your answer in the simplest form
2. Juliet coaches soccer and softball. She coaches both sports for a total of 18 hours each day. The soccer practice lasts 1.5 hours more than twice times as long as the softball practice.
(a) Write a system of equations to model the situation. Be sure to define your variables.
(b) How many hours each day does Juliet spend coaching each sport?
Show your work. Be sure to label appropriately.
An equation is formed of two equal expressions. Juliet teaches softball for 5.5 hours, while she teaches football for 12.5 hours.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) Let the amount of time spent on soccer be represented by y, while the amount of time spent on softball is represented by x. Therefore, we can write,
x+y=18
y=2x+1.5
Hence, the system of equations to model the situation is x+y=18 and y=2x+1.5.
B.) Substitute the value of y from the second equation in the first equation, therefore,
x+y=18
x+2x+1.5=18
3x = 16.5
x = 5.5 hours
Substitute the value of x in the second equation, we will get,
y=2x+1.5
y=2(5.5)+1.5
y=11+1.5
y=12.5 hours
Hence, Juliet teaches softball for 5.5 hours, while she teaches football for 12.5 hours.
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A pack of six pencils costs 5 times as much as a single pencil. A single pencil costs 9 cents. How much does the pack of six pencils cost?
Answer:
im sorry I dont know
Write and solve an equation to convert 0.38 m to centimeters
Hi Student!
In the problem statement we are given a number of 0.38 meters which it then tells us to write and solve an equation to convert that to centimeters. The first step would be to write an equation that would perfectly incapsulate what we are trying to do.
[tex]x = meters\ *\ \frac{100\ centimeters}{1\ meter}[/tex]
This equation can now be used for any amount of meters where we can input the amount of meters that we have and that will cancel with the meters on the bottom while multiplying by 100 to which we then will receive our value of x in centimeters. Let's solve the equation using 0.38 meters.
Input the values
[tex]x = meters\ *\ \frac{100\ centimeters}{1\ meter}[/tex][tex]x = 0.38\ meters\ *\ \frac{100\ centimeters}{1\ meter}[/tex]Cancel the meters
[tex]x = \frac{0.38\ meters\ *\ 100\ centimeters}{1\ meter}[/tex][tex]x = 0.38*100\ centimeters[/tex]Simplify the expression
[tex]x =38\ centimeters[/tex]Therefore, our final answer is that 0.38 meters can be converted to centimeters which would then get 38 cm as the result.
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The slope of the line through ( -2 , -5 ) and ( -6 , 7 ) is -3
Solution:Correct option is
Slope of the line [tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]x_1=-2,y_1=-5[/tex] and [tex]x_2=-6,y_2=7[/tex]
∴ [tex]m=\frac{7-(-5)}{(-6)-(-2)}=\frac{12}{-4}=-3[/tex]
Therefore, the slope of the line through ( -2 , -5 ) and ( -6 , 7 ) is -3
What angles are coterminal to an angle measuring 2π3 or −11π7?
By definition of coterminal angles, the angle 2π/3 has two coterminal angles: θ' = 14π/3 and θ' = - 4π/3. The angle - 11π/7 has no coterminal angles.
How to find coterminal angles
Two angles are coterminal when their terminal ends have the same direction. By the fact that two consecutive coterminal angles have a difference of 2π, we find the following definition:
θ' = θ ± 2π · i, i ∈ [tex]\mathbb{N}_{O}[/tex] (1)
Now we proceed to determine the coterminal angles for each case:
a) θ = 2π/3
θ' = 14π/3, θ' = - 4π/3
b) θ = - 11π/7
There are no coterminal angles.
By definition of coterminal angles, the angle 2π/3 has two coterminal angles: θ' = 14π/3 and θ' = - 4π/3. The angle - 11π/7 has no coterminal angles.
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