Domain and range of the composite function (gof)(x) formed by given f(x) and g(x) is equal to all positive real numbers and y > 6 , y ∈R respectively.
Function f(x ) is :
f(x) = e^x
Function g(x) is :
g(x) = x + 6
To find the range of composite function (gof)(x) simplify the function .
(gof)(x)
= g ( f(x))
Substitute f(x) = e^x we get
= g ( e^x )
Replace x by e^x in g(x) we get,
= e^x + 6
Domain of the composite function is given by all the value based on e^x that is all positive real numbers.
Range is translated by 6.
y > 6 , y∈ R ( positive real numbers)
Therefore, the domain and range of composite function (gof)(x) is all positive real numbers and y > 6 , y∈ R ( positive real numbers) respectively.
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PLS HELPPPPPOOOOPPPP
Answer:
if there anything you dont understand ask me
Indirect proportional question please answer
Answer:
y = 250x
Step-by-step explanation:
y = 1/[tex]x^{3}[/tex](k) Solve for k
2 = 1/[tex]5^{3}[/tex](k)
2 = 1/125 (k) Multiply both sides by 125
250 = k
y = 250x
A car sales person makes $7.00 per hour plus $100.00 for every car sold. Which expression represents the amount in dollars the salesperson makes, before taxes, if x cars are sold in 40 hours?
The expression represents the amount in dollars the salesperson makes, before taxes, would be 7x + 100 = 40.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We are given that car sales person makes $7.00 per hour plus $100.00 for every car sold.
Therefore, we have;
7x + 100 = 40
The expression represents the amount in dollars the salesperson makes, would be 7x + 100 = 40.
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The graph shows a relationship between two quantities.
2000
1800
1600
1400
1200
1000
800
600
400
200
STA
y = 1500x + 150
ALONS
JUMA
1 HOUT
TOU
8-6-4-2 0
N
Hilber
2 4
6 8
Which equation best represents the relationship between x and y in the graph?
y = 1500 + 150x, this is correctly represents the relationship between x and y in the graph. This can be solved using the slope formula.
What is slope?Slope, An evaluation of a line's inclination with respect to the horizontal using numbers. The slope of any line, ray, or line segment in analytical geometry is defined as the proportion of the vertically to the horizontally distance between the two points on the line ("slope equals rise over run").
(0, 1500) to (2, 1800)
thus, slope = (y₂ - y₁) / (x₂ - x₁)
or, slope = 300 / 2
or, slope = 150
So, y - 1500 = 150x
thus, y = 1500 + 150x
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The complete question is as follows:
The first gardener can finish the job in 6 hours, and the second gardener can do the same job in 7 hours. How long will it take to finish the same job if they work together
Explanation Please
Answer:
3 3/13 hours
Step-by-step explanation:
you will first find out how many hours it will take for each gardener to do 1 part of the job. gardener 1 is 1/6 and the second is 1/7. you will next add the two fractions. this will equal 13/42. you will then multiply by the reciprocal to get 1, this stands for the whole job done together. The reciprocal is the answer, 42/13. You will then simplify that to 3 3/13 hours.
Marisa divides a number by a power of ten and the quotient is 1.4. She says that if she multiplies the number by the same power of ten, the product is 14,000. What was the dividend in Marisa's original
problem? Use patterns to explain your thinking.
Help
The required number is 140 and it is divided by 10²
Finding the number:Assume the given numbers with 2 different variables and form the mathematical expressions according to the given conditions in the problem. Now solve the resultant equations by substitution method for the values of both variables.
Here we have
Marisa divides a number by a power of ten and the quotient is 1.4.
If she multiplies the number by the same power of ten, the product is 14,000.
Let 'x' be the number and the power of 10 is 'a'
By the given data,
=> x/10ᵃ = 1.4 ---- (1)
=> 10ᵃx = 14000 ---- (2)
From (1)
=> x = 1.4 × 10ᵃ --- (3)
From (3) and (2)
=> 10ᵃ(1.4 × 10ᵃ) = 14000
=> [tex]10^{2a} = \frac{14000}{1.4}[/tex]
=> [tex]10^{2a} = 10000[/tex]
=> [tex]10^{2a} = 10^{4}[/tex]
=> 2a = 4
=> a = 2
From (3)
=> x = 1.4 × 10²
=> x = 140
Therefore,
The required number is 140 and it is divided by 10²
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A rabbit starts at 10 along a number line and then makes three jumps. First the rabbit jumps 4 units, then 2 units, and finally makes a jump of 1 unit. We don't know the direction of any jump.What are the possibilities
Answer:
Step-by-step explanation:
Pedro tiene como proyecto de construir la casa de sus sueños, estuvo ahorrando dinero, pero no fue suficiente ya que para hacer la casa al 100% necesita 60.000.0000$ lo que quiere decir que le faltan 35.000.0000$ para poder juntar todo el dinero. Contemplo la posibilidad de prestar en un banco los 35.000.000$ para pagarlos en 10 años con una tasa de interés del 8%. Preguntas. ¿Cuánto dinero había reunido Carlos antes de pensar en prestar con el banco? 25.000.000$ ¿Cuánto dinero pagaría Carlos en total al finalizar los 10 años? 37.800.000 ¿Qué precio tendría cada cuota mensual durante los 10 años? 315.000$
Pedro había reunido 25.000.000$ antes de pensar en prestar con el banco. Al finalizar los 10 años, Carlos pagaría 37.800.000$ en total, lo que significa que tendrá que pagar una cuota mensual de 315.000$ durante los 10 años para poder cumplir con el préstamo.
El préstamo que Carlos está considerando es una forma común de financiamiento para proyectos de construcción de viviendas. Esta forma de financiamiento le permite a Carlos acceder a fondos que de otro modo no tendría, permitiéndole construir su casa de los sueños. El préstamo a largo plazo también le ofrece la flexibilidad de pagar el préstamo en cuotas mensuales durante un período de 10 años.
Versión en inglés:
Peter had raised $25,000,000 before he thought about lending with the bank. At the end of the 10 years, Carlos would pay $37,800,000 in total, which means he will have to pay a monthly payment of $315,000 over the 10 years in order to make good on the loan.
The loan Carlos is considering is a common form of financing for home construction projects. This form of financing allows Carlos to access funds he would not otherwise have, allowing him to build his dream home. The long-term loan also offers him the flexibility to repay the loan in monthly installments over a 10-year period.
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what is what is 9+10+12+13+18+17+21+98+207
Answer:
405
Step-by-step explanation:
Answer: 405
Step-by-step explanation:
given the graph of y = -3/2x - 1 and y = -x + 4 which of the following is a solution to both equations
pls help!
(1, -1) is the solution to both equations.
How to find the solution to the graph of system of linear equations?
A system of equations is a collection of two or more equations with the same variables. The goal is to find values for the variables that simultaneously satisfy all the equations in the system. There are different methods to solve a system of equations, including substitution, elimination, and graphing
The solution to both equations can found be determine by picking the x and y values of the point of intersection of the two lines. That is:
At the point of intersection of the lines:
x = 1 and y = -1
Thus, the solution to both equations is (1, -1)
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3/4(24x+28)-(4x-1)
I don't understand how to get the answer.
The expression evaluates to 14x + 22.
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
3/4(24x + 28) - (4x - 1)
We can start by simplifying the expression inside the parentheses:
3/4(24x + 28) - (4x - 1)
Remove the brackets
18x + 21 - 4x + 1
Evaluate the like terms
14x + 22
So, the value of the expression evaluates to 14x + 22.
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how to determine if vectors are linearly independent
The value of c is zero and a and b can be something else, because the vector are linearly independent.
A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others (i.e., is in the span of the other vectors). A set of vectors is linearly independent if no vector can be expressed as a linear combination of those listed before it in the set.
Assume the following:
[tex]a\left[\begin{array}{ccc}2\\2\\0\end{array}\right] + b\left[\begin{array}{ccc}1\\-1\\1\end{array}\right] +c\left[\begin{array}{ccc}4\\2\\-2\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]
Determine if a=b=c=0
[tex]2a+b+4c =0 (1)\\ 2a-b+2c =0 (2)\\b-2c=0(3)\\[/tex]
Subtract (2) from (1)
[tex]b+c = 0\\b-2c=0[/tex]
Substitute (5) into (4), we get c=0.
So now what do I do with this fact? I'm tempted to say that only c=0, and a and b can be something else.
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intuitively, what do we expect to have when the error term's variance increases when we estimate a simple linear regression model?
When the variance of the error term increases in a simple linear regression model, it indicates a less accurate model with a high degree of uncertainty in its predictions.
Regression is a statistical method used to model the relationship between two variables, where one of the variables is dependent on the other.
Simple linear regression is a type of regression where the relationship between the dependent variable and the independent variable is modeled as a linear equation.
Mathematically, let's consider the simple linear regression equation as:
Y = β0 + β1X + ε
Where Y is the dependent variable, X is the independent variable, β0 and β1 are the coefficients of the regression equation, and ε is the error term.
The variance of the error term, Var(ε), is a measure of the spread of the residuals. A large variance of the error term indicates that the residuals are spread out over a large range, and thus, the regression model's predictions may not be very accurate.
In other words, a large variance of the error term means that the model has a high degree of uncertainty in its predictions, leading to a larger deviation between the actual and predicted values.
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4. What kind of sequence is the pattern 15, 17, 20, 24, 29,. ? *
is it an arithmetic or geometric sequence?
No, the given sequence is neither an arithmetic nor geometric sequence as there is no common difference nor common ratio.
Pattern for difference is dₙ = dₙ₋₁ + 1.
Pattern of the sequence is :
15, 17, 20, 24, 29,.....
15 + 2 = 17
17 + 3 = 20
20 + 4 = 24
24 + 5 = 29
Next number will be
29 + 6 = 35
35 + 7 = 42 and so on.
Difference of two consecutive terms are related by :
dₙ = dₙ₋₁ + 1
Common difference is not same for all the terms so it is not arithmetic sequence.
Common ratio is also not constant implies it is not geometric sequence.
Therefore, pattern for difference is dₙ = dₙ₋₁ + 1 but sequence is neither an arithmetic nor geometric sequence.
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Please help me!!!! I cannot figure it out
Answer: 12/37
Step-by-step explanation:
sin A= bc/ab = 12/37
The sine of the angle is equal to the ratio of the opposite to the hypotenuse (Ik this probably made 0 sense but I hope it helps! :D)
Jack has $684 in his wallet, which is 6 times as much as Jill has. How much money does Jill have in her wallet?
Answer:
114
Step-by-step explanation:
If jack has 684 which is 6 times jill then divide 645 by 6 and thenmake sure its correct by multiplying 6 times what you got and if the awnser if 684 its correct
Answer:
$4,104
thus : since jack has $684
jill=6*$684=$4104
a room has a floor dimension of 6 meters by 8 meters the height of the basement is 8 meters what is the total area of all four walls
Answer:
224 m^2
Step-by-step explanation:
The dimensions of the four walls are:
6x8, 8x8, 6x8, 8x8
The area of all of these walls is 2(6x8 + 8x8) = 224 m^2
Find the value of the expression
7/8-v
for v =5/8
Write your answer as a fraction or as a whole or mixed number.
Answer:
1/4
Step-by-step explanation:
7/8 - 5/8 = 2/8
2/8 divided by 2/2 is 1/4
Answer:
7/8-5/8
Step-by-step explanation:
7-5/8
2/8
2 into itself and into 8 is equal to 1/4
50 points to whoever can answer with explanation.
Answer:
1/ a, c, d
2/ You are missing the option in the picture.
Step-by-step explanation:
If a relation is a function, one input can only have one output!
1/
b is wrong because 1 has two outputs -3 and 0. So, the answer for 1 is: a, c, d
2/
To test whether the graph is a function, we have to see if one x has 2 y or not! If it has 2 y, then it is not a function.
You are missing the options for question 2! So I can't answer number 2.
based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction?
Based on the boxplot, approximately 50% percent of the people who entered the amusement park met the height requirement for the attraction.
About Box PlotBox-Plot is a summary of the sample distribution presented graphically which can describe the shape of data distribution (skewness), a measure of central tendency and a measure of dispersion (diversity) of observational data. There are 5 statistical measures that we can read from the boxplot, namely:
minimum value: the smallest observed value Q1: lowest quartile or first quartile Q2: median or average value Q3: highest quartile or third quartile maximum value: the largest observed value.In addition, the boxplot can also show whether there are outlier values and extreme values from the observed data.
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Find the sum of 5√25 and √7 in simplest form. Also, determine whether the result
is rational or irrational and explain your answer.
solve these simultaneous equations
4a+3b=-9
2a+5b=-1
The solution to the system of equations 4a + 3b = -9 and 2a + 5b = -1 is a = 12, b = -5, found through substitution method.
Simultaneous equations are a set of equations with multiple variables, and the solution of these equations gives us the values of the variables that make all the equations true at the same time. To solve these equations, we can use elimination, substitution or matrices method.
Here, the given set of simultaneous equations is
4a + 3b = -9
2a + 5b = -1
One way to solve this is by substitution, where we solve one equation for one variable and substitute that expression into the other equation. Solving the first equation for "a", we get:
a = -3b - 3
Substituting this expression into the second equation, we get:
2(-3b - 3) + 5b = -1
Expanding the left-hand side, we get:
-6b - 6 + 5b = -1
Combining the like terms, we get:
-b - 6 = -1
Adding b and 6 to both sides, we get:
-b = 5
Finally, dividing both sides by -1, we get:
b = -5
Substituting the value of b back into the expression for a, we get:
a = -3(-5) - 3 = 15 - 3 = 12
So the solution to the system of equations is:
a = 12, b = -5
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6 divide by 222 long devision
Answer: 37
Step-by-step explanation:
6 divided into 2 is 0.
0 multiplied by 6 is 0.
2-0=2
bring down the other 2
6÷22=3
3×6= 18
23-18= 4
bring down the 3rd 2
now we have 44
44÷6 =43
42-42= 0
hence the answer is 37
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = 40
Step-by-step explanation:
We have to find,
→ the value of x in the equation.
The equation is,
→ (x/2) + 3 = 23
Now the value of x will be,
→ (x/2) + 3 = 23
→ x/2 = 23 - 3
→ x/2 = 20
→ x = 20 × 2
→ [ x = 40 ]
Hence, the value of x is 40.
help i will give alot of points
Put the following integers in order from least to greatest:
1, 4, and −3.
Answer:
Hi there! The answer is -3, 1, 4.
Step-by-step explanation:
4 is the greatest and -3 is the least.
Hope this helps!
Brainiest? Can click the crown on this answer? Thanks!
When rolling a die (number cube), what is the probability of rolling a 2 or a 3?
OA. //
OB.
0C. 1/1/0
OD. 1/1/2
OE. 5/10
Answer:
1/3
Step-by-step explanation:
6 faces in a die
1/6 of rolling each side
1/6 of rolling 2 or 3
2/6 chance, 1/3 (simplified)
Choose a second initial value that is 0. 01 greater than the initial value from question 9. Iterate it using the function, f, ten times. If necessary, you can round your results to the nearest ten-thousandth. (my initial value from question 9 is 2 btw. )
The result of the 10th iteration is 1.689, rounded to the nearest ten-thousandth.
The initial value for this question is 2 + 0.01 = 2.01. If we iterate this initial value using the function "f" ten times, we get the following sequence:
1st iteration: f(2.01) = 3.07 - [tex](2.01)^{2}[/tex]= 0.1599
2nd iteration: f(0.1599) = 3.07 - [tex](0.1599)^{2}[/tex]= 2.868201
3rd iteration: f(2.868201) = 3.07 - [tex](2.868201)^{2}[/tex]= 0.34459799
4th iteration: f(0.34459799) = 3.07 - [tex](0.34459799)^{2}[/tex] = 2.46306801
5th iteration: f(2.46306801) = 3.07 - [tex](2.46306801)^{2}[/tex] = 0.86121799
6th iteration: f(0.86121799) = 3.07 - [tex](0.86121799)^{2}[/tex] = 2.11255201
7th iteration: f(2.11255201) = 3.07 -[tex](2.11255201)^{2}[/tex] = 1.47511099
8th iteration: f(1.47511099) = 3.07 -[tex](1.47511099)^{2}[/tex] = 1.87593299
9th iteration: f(1.87593299) = 3.07 -[tex](1.87593299)^{2}[/tex] = 1.28972499
10th iteration: f(1.28972499) = 3.07 -[tex](1.28972499)^{2}[/tex] = 1.68900499
So, the result of the 10th iteration is 1.689, rounded to the nearest ten-thousandth.
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Evaluate 1/5r + 9/20 when r = 1/4
1/5 ( blank) + 9/20 = blank + 9/20= Answer?
please answer asap
The value of the equation is A = 1/2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 1/5 )r + 9/20 be equation (1)
On simplifying the equation , we get
when r = ( 1/4 )
Substituting the value of r in the equation , we get
A = ( 1/5 ) ( 1/4 ) + 9/20
A = ( 1/20 ) + ( 9/20 )
On further simplification , we get
A = 10/20
A = 1/2
Hence , the equation is A = 1/2
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Please help me I’m a bit stuck
Answer:
Step-by-step explanation:
The Answer would be -4x
Because 3-7= -4
F(x)=-6x^4x+2x^2+12 G(x)=-2x^3+6x^2-x-1
The value of the expression,
F(x) + G(x) is -6x⁴ -2x³ + 8x² -x + 11.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
An expression,
F(x) = -6x⁴ + 2x² + 12
And G(x) = -2x³ + 6x² - x - 1
To solve F(x) + G(x):
F(x) + G(x)
= -6x⁴ + 2x² + 12 -2x³ + 6x² - x - 1
Simplifying,
= -6x⁴ -2x³ + 8x² -x + 11
Therefore, the value is -6x⁴ -2x³ + 8x² -x + 11.
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The complete question:
F(x) = -6x⁴ + 2x² + 12
And G(x) = -2x³ + 6x² - x - 1
Find out, F(x) + G(x)?