The value of the functions for the condition is,
1. f(x + h) = 3(x + h)² - (x + h) + 5,
2. (fog)(x) = 27x² -33x + 15,
3. f(g(h(-1))) = 16,060.
What is the function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
Given f(x) = 3x² - x + 5
g(x) = -3x + 2
h(x) = -5x³
1. Find f(x + h),
so f(x) = 3x² - x + 5
substitute x = x+ h
f(x + h) = 3(x + h)² - (x + h) + 5
2. (fog)(x),
f(g(x))
g(x) = -3x + 2
f(-3x + 2) = 3(-3x + 2)² - (-3x + 2) + 5
f(g(x)) = 3(9x² + 4 - 12x) - 2 + 3x + 5
f(g(x)) = 27x² + 12 - 36x - 2 + 3x + 5
f(g(x)) = 27x² -33x + 15
3. Find f(g(h(-1)),
h(x) = -5x³
g(x) = -3x + 2
g(h(x)) = -3(-5x³)² + 2
g(h(x)) = -75x⁶ + 2
f(x) = 3x² - x + 5
f(g(h(x))) = 3(-75x⁶ + 2)² - (-75x⁶ + 2) + 5
f(g(h(x))) = 3(5625x¹² + 4 - 300x⁶) + 75x⁶ - 2 + 5
f(g(h(x))) = 16875x¹² + 12 - 900x⁶ + 75x⁶ -2 + 5
f(g(h(x))) = 16875x¹² - 825x⁶ + 10
substitute x = -1,
f(g(h(-1))) = 16875(-1)¹² - 825(-1)⁶ + 10
f(g(h(-1))) = 16,060
Hence f(x + h) = 3(x + h)² - (x + h) + 5,
2.f(g(x)) = 27x² -33x + 15,
3. f(g(h(-1))) = 16,060.
Learn more about functions;
https://brainly.com/question/12431044
#SPJ1
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
If a large equilateral triangle pyramid stands in front of the city's cultural center. The time it take the painter to paint 75% of the pyramid is 10.8 hours.
How to find the time?The area of the base is:
(1/2) * 40 * 40
= 800 square feet
The area of one lateral face is:
(1/2) * 50 * 40
= 1000 square feet
So, the total area of all four lateral faces is:
4 * 1000
= 4000 square feet
The total surface area of the pyramid is:
800 + 4000 = 4800 square feet
To paint 75% of the pyramid, the painter needs to paint:
0.75 * 4800
= 3600 square feet
Time it will take them is:
3600 / 100 * 18
= 648 minutes or 10.8 hours
Therefore painter will take approximately 648 minutes, or 10 hours and 48 minutes, to paint 75% of the pyramid.
Learn more about time here:https://brainly.com/question/26046491
#SPJ1
Find the value of c. Round to the nearest tenth
The value of x is 16.2.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
Perpendicular = 18
Base = x
Tan Ф = Perpendicular / Base
Tan 48 = 18 / x
1.11 = 18/x
Solve for x.
1.11 = 18/x
x = 18/1.11
x = 16.22
x = 16.2
Thus,
x is 16.2
Learn more about trigonometric identities here:
https://brainly.com/question/14746686
#SPJ1
two negative integers have a sum of -17 and a product of 70 what are the integers?
Answer:
-10 and -7
Step-by-step explanation:
Notice that (-10) + (-7) = -17, and (-10)(-7) = 70, so these are the integers.
Answer:
-7 & -10
Step-by-step explanation:
-7 + -10 = -17
-7 x -10 = +70
When you arrive at the family reunion, Uncle Mandla has already eaten 5 mini hot dogs. He continues to eat them at a rate of 4 hot dogs per minute. y = 4x + 5 models this situation. Make a graph of this situation
The graph of y = 4x + 5 that models this situation is added as an attachment
How to determine the graph of the situationFrom the question, we have the following parameters that can be used in our computation:
Already eaten = 5 mini hot dogs
Rate = 4 hot dogs per minute
So, the equation is
y = 4x + 5
A linear equation is represented as
y = mx + c
Where
slope = m = 4
y-intercept = c = 5
See attachment for the graph
Read more about linear equation at
https://brainly.com/question/2030026
#SPJ1
Suppose the original quantity is $30 and the new quantity is $39. Estimate the percent change. Is this an example of a percent increase or a percent decrease?
Answer:
Step-by-step explanation:original quantity = $30
New quantity = $39
increase amount = 39-30 = 9
Percent change:
30 x = 9
x = 9/30
x = 0.3
0.3x 100 = 30%
Since the quantity grows, it's a percent increase.
The product of one-fourth and the quantity of the sum of x and eight
Answer:
Step-by-step explanation:
Are you asking to have this sentence put into a mathematical expression? If so, I think the answer is:
y = (1/4)(x + 8) = 1/4 x + 2
10. La exigencia mínima para un cargamento de grava es que 85% de la grava pueda pasar a través de un colador de cierto tamaño. Al probar una carga de 6 yardas cúbicas se observó que solo un 65% cumple. ¿Cuánta grava de 90% se deberá agregar a las de 65% para que sea aceptable?
Se requiere agregar un volumen adicional de 24 yardas cúbicas para obtener una concentración de grava de 85 %.
¿Cuánta grava se debe agregar para mejorar concentración?
Este problema es un caso de aplicación de promedios ponderados, en donde se mezcla un volumen de un porcentaje menor de grava con otro volumen de un porcentaje mayor de grava para obtener una mezcla con un porcentaje deseado. Esta situación queda descrita en la siguiente ecuación:
(6 yd³) · 65 + x · 90 = (6 yd³ + x) · 85
Donde x es el volumen del cargamento de grava al 90 %, en yardas cúbicas. A continuación, procedemos a determinar el volumen requerido:
390 + 90 · x = 510 + 85 · x
5 · x = 120
x = 24 yd³
ObservaciónNo aparecen problemas verificados en español sobre promedios ponderados. Se ha agregado un problema en inglés por defecto.
Para aprender más sobre promedios ponderados: https://brainly.com/question/28419561
#SPJ1
Need assistance here looking REAL Answer and Solution please so i can understand. Please help math expert there.
The value of y'(2) is 135/16.
The correct option is A.
What is differentiation?Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.
Given:
y = (x - 1/x)³
Differentiating the function with respect to x,
y' = 3x² +3/x⁴ - 3 - 3/x²
y'(2) = 12 + 3/16 - 3 -3/4
y'(2) = 135/16
Therefore, the value is 135/16.
To learn more about the differentiation;
https://brainly.com/question/24898810
#SPJ1
Let f(t) be the outside temperature (°F) t hours after 3 A.M. Explain the meaning of f(4) <ƒ(5).
The temperature at
than the temperature at
The temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.
What is the temperature?
Temperature is a physical property of matter that measures the degree of hotness or coldness of an object. It is a scalar quantity that is expressed in units such as Celsius, Fahrenheit, or Kelvin.
The statement "f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M."f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.
To learn more about temperature, Visit
https://brainly.com/question/25677592
#SPJ1
Fill in the blank with the value that makes the
number sentence true:
36 +27= 88 - O
The number 25 is the value at which the number sentence is true. An enumerated (numbered) list can be presented in sentence form in a variety of ways.
How should numbered sentences be written?An enumerated (numbered) list can be presented in sentence form in a variety of ways. The number (not the number word) can be placed in parentheses in the following manner: I listed the following three causes: Here is my first justification, this is my second justification, and this is my third justification. A number sentence compares two numerical expressions and states their equivalence (or inequality).
Let the value be x
now 36 + 27 = 88 - x
36 + 27 = 88 - x
63 = 88 - x
x = 88 - 63
x = 25
To know more about number sentence visit:-
https://brainly.com/question/13349953
#SPJ1
I need help
Grinding
Answer: 500
Step-by-step explanation:
25 x 20 = 500
Select the correct answer. Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? A. f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial. B. f(x) and g(x) are closed under subtraction because when subtracted, the result will be a polynomial. C. f(x) and g(x) are closed under subtraction because when subtracted, the result will not be a polynomial. D. f(x) and g(x) are not closed under subtraction because when subtracted, the result will not be a polynomial.
f(x) and g(x) are closed under subtraction because when subtracted, the result is also a polynomial.
Option B is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
f(x) = a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex]
g(x) = b(0) + b(1)x + b(2)x² + .......... + b(n)[tex]x^n[/tex]
Now,
f(x) - g(x)
= a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex] - b(0) - b(1)x - b(2)x² - .......... - b(n)[tex]x^n[/tex]
= (a(0) - b(0)) + (a(1) - b(1))x + (a(2) - b(2))x² + ........... + (a(n) - b(n))[tex]x^n[/tex]
This is also a polynomial.
Thus,
f(x) and g(x) are closed under subtraction.
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ1
CAN YALLL HELP ME (sorry bout the caps )
Which of the following is the result of rewriting the formula to solve for l
A.
B.
C.
D.
Step-by-step explanation:
Since we're solving for L, it has to equal L.
Which means C & D are the only options.
Only problem is... we don't have the original formula. Not sure if it was part of #1 or...
Chee is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 4 points. What would be Chee's test score (out of 100) if she got 10 questions wrong? What would be her score if she got a questions wrong? Score with 10 questions wrong. score with x questions wrong
Answer:
i hope this help
Step-by-step explanation:
If each question is worth 4 points, then 100 questions would be worth 400 points.
If Chee got 10 questions wrong, she would have answered 100-10 = 90 questions correctly.
Her score would be 90 x 4 = 360 points out of 400 points.
As a percentage, her score would be 360/400 x 100 = 90%.
If Chee got x questions wrong, her score would be (100-x) x 4 points.
Mayra's brother is driving back from college to visit. His college is 330 miles away. After an hour of
driving, he still has 275 miles to go. If the roads are clear, he'll be able to keep up that pace for the
whole drive. Write a linear function to model how much further he'll have to go over time.
He has 5hrs to drive and 275 miles to drive to cover to arrive at the university.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
His college is 330 miles away.
After an hour of driving, he still has 275 miles to go.
If the roads are clear, he'll be able to keep up that pace for the whole drive.
If he drives 55 miles in 1 hr
he would drive 330 miles in
=6hrs.
his total travel time is 6 hr
He has 5hrs to drive and 275 miles to drive.
To learn more on speed click:
brainly.com/question/28224010
#SPJ1
PLEASE HELP
I dont understand how to get the answer
For the given triangles ΔABC ≈ ΔXYZ, the length of the side AB is, 24
What is similarity of triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"
Given that,
One triangle, ΔABC
Another triangle , which is ΔXYZ
Triangle ΔABC and ΔXYZ similar,
So, we can say ΔABC ≈ ΔXYZ
And it is known that
for similar triangles, ratio of lengths of sides are equal for similar triangles
so, AB/BC = XY/ZY
⇒ X/18 = 16/12
⇒ X = 24
Hence, the value of x is 24
To know more about properties of triangles check:
https://brainly.com/question/8476788
#SPJ1
A medium pizza at Big Time Pizza costs $6.80 plus $0.90 for each topping. The cost of a medium pizza at PizzaPizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a medium pizza from each restaurant in order for the pizzas to cost the same?
Step-by-step explanation:
At Big Time Pizza, you would need to add 5 toppings in order for the pizza to cost the same as a medium pizza from PizzaPizza, which would cost $9.50. At PizzaPizza, you would need to add 8 toppings in order for the pizza to cost the same as a medium pizza from Big Time Pizza, which would cost $9.50.
In May 2003, JP Gas Co. had the following rate schedule for natural gas usage in single-family residences. Gas is
measured in units called therms. All customers pay a monthly charge. They also pay a distribution charge based on
the amount of gas they use and a supply charge that is also based on the amount of gas they use. The fees are as
follows:
Monthly Customer Charge $6.45
Distribution Charge
1st 20 therms $0.20/therm
Next 30 therms $0.11/therm
Over 50 therms $0.04/therm
Gas supply charge $0.73/therm
a) What is the charge for using 40 therms?
b) What is the charge for using 202 therms?
c) Construct a function that gives the monthly charge C for the x therms of gas.
Answer:
a) $40.05
b) $161.99
c) C(x) = 6.45 + 0.93x, if x ≤ 20
C(x) = 6.45 + 0.84x, if x > 20 and x ≤ 50
C(x) = 6.45 + 0.77x if x > 50
What’s the domain of the function y =2 (2)x +2
Answer: X E R
Step-by-step explanation: y=2 x 2x+2
calculate the product
y=4x+2
The domain of a linear function is the set of all real numbers
x E R
Why has she putten these parentheses? And the first number (xe2) goes from positive to negative ((-2)e2) and then back to positive (4)?
[tex]x=-2\hspace{5em}y=2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^2 - y^3}{x^3 + y^2}\implies \cfrac{(-2)^2 - (2)^3}{(-2)^3 + (2)^2}\implies \cfrac{(-2)(-2)~~ - ~~(2)(2)(2)}{(-2)(-2)(-2)~~ + ~~(2)(2)} \\\\\\ \cfrac{(+4)~~ - ~~(+8)}{(-8)~~ + ~~(+4)}\implies \cfrac{4-8}{-8 + 4}\implies \cfrac{-4}{-4}\implies \text{\LARGE 1}[/tex]
for the sake of clarity, is better to parenthesize all, since plugging in the value for the variable, only includes the variable, no any exponents or signs in front.
that said, let's recall that minus * minus = plus, and that plus * plus = plus, however minus * plus = minus.
so you can think of it this way, if you have a negative value multiplied an "even times", it'll positivize, if you multiply it an "odd times", it'll go back to negative, so is not like it remains negative, it changed a few times and in the end negativized back.
Sunday, Peeta earned $142.20 working at his fmaily's bakery. He earned $5.50 per hour plus $90.20 in tips.
Create an equation that can be used to determine the njmber of hours, h, Peeta worked on Sunday.
Peeta worked 9.41 hours on Sunday. The equation 5.5h + 90.2 = 142.2 can be used to determine the number of hours Peeta worked given his earnings.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let h be the number of hours that Peeta worked on Sunday. We know that he earned $5.50 per hour and $90.20 in tips. So, his total earnings can be represented as:
5.5h + 90.2 = 142.2
Solving for h:
5.5h = 142.2 - 90.2
5.5h = 52
h = 52 / 5.5
h = 9.41 hours
Learn more about models here:
https://brainly.com/question/22591166
#SPJ1
selena erned $4,283.30 last month
The money left from last month's earnings is $1660.35.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be termed as finding difference.
In order to find the money left, we have to find the difference of earnings and expense.
Earnings = $4,283.30
Expense for bills = $4,283.30 × (3/5) = $2569.98
Expense for shirts = $19.99 × 2 = $39.98
Expense for sunglasses = $12.99
Total expense = $2569.98 + $39.98 + $12.99 = $2622.95
Money left = $4,283.30 - $2622.95 = $1660.35
Hence $1660.35 amount of money is left.
To learn more about Subtraction, click :
https://brainly.com/question/13619104
#SPJ1
The complete question is :
Selena earned $4,283.30 last month she used 3/5 of her earnings to pay her bills with the remaining money she bought two shirts $19.99 each and a pair of sunglasses for $12.99 how much money does Selena have left from last month's earnings?
What do you guys think the formula of a circle is?
Answer:
πr2
Step-by-step explanation:
The formula of a circle/finding its area is pi(r)^2
Answer: The formula for the area of a circle is π r squared
2,5 days to 80 hours ratio
The ratio of 2 days to 80 hours and 5 days to 80 hours is 1 day : 40 hours and 1 day : 16 hours respectively.
How to calculate ratio?2, 5 days : 80 hours
So,
2 days : 80 hours
= 2/80
= 1/40
= 1 day : 40 hours
Also,
5 days : 80 hours
= 5/80
= 1/16
= 1 day : 16 hours
Hence, the ratio of days to hours is given by 1 day : 40 hours and 1 day : 16 hours respectively.
Read more on ratio:
https://brainly.com/question/2328454
#SPJ1
PLEASE HELP!!!
identify the lengths of KL and LW
Answers:
A- KL=2.4, LW=3.6
B- KL=6, LW=2.4
C- KL= 3.6, LW=2.4
D- KL=12, LW=18
Applying the angle bisector theorem, the lengths are:
A. KL = 2.4, LW = 3.6
What is the Angle Bisector Theorem?The Angle Bisector Theorem states that in a triangle, the ratio of the length of a side to the length of another side is equal to the ratio of the length of the angle bisector of one of the angles to the angle bisector of the corresponding angle.
In other words, if two angles of a triangle have angle bisectors of lengths x and y, then x/y = a/b where a and b are the lengths of the sides of the triangle corresponding to the bisected angles.
Based on the angle bisector theorem, we have:
(6 - x)/(x) = 4/6
Cross multiply:
4x = 6(6 - x)
4x = 36 - 6x
4x + 6x = 36
10x = 36
x = 36/10
x = 3.6
LW = x = 3.6
KL = 6 - x = 6 - 3.6 = 2.4
Learn more about angle bisector theorem on:
https://brainly.com/question/2478436
#SPJ1
11-12÷4+3(6-2)...anyone?
Answer:
the answer is 20
Step-by-step explanation:
.........
Answer:
20
Step-by-step explanation:
Do it one step at a time using the correct order of operations.
11 - 12 ÷ 4 + 3(6 - 2) =
= 11 - 3 + 3 × 4
= 8 + 12
= 20
A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an experiment, the spinner will be spun 5 times. If Event A = the spinner lands on numbers all less than 3, what is an outcome of Event A?
Any sequence of five spins that consists only of numbers 1 and 2 would be an outcome of Event A.
What is an outcome of Event A?From the question, we have the following parameters that can be used in our computation:
Event A = the spinner lands on numbers all less than 3
An outcome of Event A would be a sequence of five spins on the spinner that result in numbers all less than 3,
For example: 1, 2, 1, 2, 1.
See that each number in the above sequence is less than 3
Hence, the event A represents outcomes less than 3
Read more about probability at
https://brainly.com/question/251701
#SPJ1
The time required to complete a job varies inversely as the number of people working. It took 10 brick masons 300 hours to brick a new home. How long would it have taken 25 brick masons to complete the same job?
the 25 brick masons complete the same job in 120 hours.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
It took 10 brick masons 300 hours to brick a new home.
1 brick mason will take 300*10 =3000 hours
So 25 brick masons will take 3000/25 = 120 hours.
Hence the 25 brick masons complete the same job in 120 hours.
Learn more about arithmetic, by the following link.
https://brainly.com/question/13181427
#SPJ1
Sebastian is preheating his oven before using it to bake. The initial temperature of the oven is 75° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 17 minutes after being turned on? What is the temperature of the oven
t minutes after being turned on?
Temp after 17 minutes:
Temp after t minutes:
Answer: The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven is 75° and it will increase at a rate of 25° per minute after being turned on.
The equation to model the temperature of the oven t minutes after being turned on is:
Temp = 75 + 25t
Where Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.
For example, if we want to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:
Temp = 75 + 25 * 17 = 75 + 425 = 500°
So, the temperature of the oven 17 minutes after being turned on is 500°.
In general, the temperature of the oven t minutes after being turned on can be found by substituting the value of t into the equation:
Temp = 75 + 25t.
Step-by-step explanation:
The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven will be; 75° and it will increase at a rate of 25° per minute after being turned on.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation to model the temperature of the oven t minutes is:
Temp = 75 + 25t
Where, Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.
For example, if we need to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:
Temp = 75 + 25 * 17 = 75 + 425
Temp = 500°
Thus, the temperature of the oven 17 minutes after being turned on is 500°.
In general, the temperature of the oven t minutes after being turned on can be find by substituting the value of t into the equation:
Temp = 75 + 25t.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2