The correct inverse of F(x) = 6x is y = x/6 according to given question
To find the inverse of a function, we need to interchange the roles of the dependent variable (x) and the independent variable (F(x)) and solve for the new dependent variable.
Given that F(x) = 6x, to find the inverse, we can follow these steps:
Replace F(x) with y: y = 6x.
Swap x and y: x = 6y.
Solve for y: Divide both sides by 6 to isolate y: y = x/6.
Therefore, the inverse function of F(x) = 6x is given by y = x/6.
Out of the options provided:
A. F(x) = 6x: This is the original function, not the inverse.
B. F(x) = x-6: This is not the correct inverse function.
C. F(X): This option is incomplete; it does not provide an equation for the inverse.
D. F(x) = x + 6: This is not the correct inverse function.
Therefore, the correct inverse of F(x) = 6x is y = x/6.
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Write the given number in expanded form. 3.724 = (3 × ) + (7 × ) + (2 × ) + (4 × )
Answer:
3.724
Step-by-step explanation:
3.724 =
3
+ 0.7
+ 0.02
+ 0.004
3.724 =
3 × 1
+ 7 × 0.1
+ 2 × 0.01
+ 4 × 0.001
answer this please pretty please
Answer:
Wassup Obito
Step-by-step explanation:
I would have done it if you had asked for only 1 question but you have asked someone to do more than 10 q
You must be mad to think someone will do the entire thing
Mark me brainliest
A rectangle piece of metal has an area of 32 square centimeters. Its perimeter is 24 centimeters. What are the dimensions of the piece
The dimensions of the piece are l = 8 and b =4.
What are dimensions?
The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. Because only one coordinate is required to specify a point on a line, it has a dimension of one.
Here,
Let the length of a rectangular piece of metal = l cm
And the breadth of a rectangular piece of metal = b cm
Perimeter of a rectangular piece of metal = 2(l+b) = 24 cm
Or, l+b = 24/2
Or, l+b = 12 -------- (1)
Area of a rectangular piece of metal = l×b = 32 cm²
Or, l×b = 32 ------- (2)
We know that,
(l - b)² = (l+b)² - 4×l×b
(l - b)² = (12)² - 4×32
(l - b)² = 144 - 128
(l - b)² = 16
(l - b)² = 4
l - b = 4 --------- (3)
Adding equations (1) and (3), we get
l+b+l-b = 12 + 4
2l = 16
l = 8
Now, we put the value of l in equation(1) and we get
8 + b = 12
b =4
Hence, the dimensions of the piece are l = 8 and b =4.
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PLEASE ANSWER WILL MARK BRAINLIEST!!
The table shows the soil density of several soil samples at different depths.
(a) Write the quadratic regression equation that models the data. Let x = depth below the surface
and let y = soil density.
(b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Show your work.
Answer:
(a) y = -0.4931x² + 23.3798x + 996.0289
(b) x = 20
y = -0.4931x² + 23.3798x + 996.0289
y = -0.4931(20)² + 23.3798(20) + 996.0289
y = -0.4931(400) + 467.596 + 996.0289
y = -197.24 + 467.596 + 996.0289
y = 1266.3849
Write a system of equations to represent the scenario.
2) Clark and Bruce went to Taco Hut for lunch. Clark bought 4 burritos and 5 tacos, which cost him $6.71. Bru
bought 5 burritos and 3 tacos, which cost him $7.12.
Answer:
Step-by-step explanation:I need the same answer lol
Answer:
Step-by-step explanation:
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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Please help me!
For a certain company, the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0.5x^2.
The profit that the company makes is how much it takes in (revenue) minus how much it spend (cost). In economic models, one typically assumes that a company wants to maximize its profit or at least wants to make a profit:
Set up an expression for the profit from producing and selling x items
Find two values of x that will create a profit of $300
Using the profit concept, we have that:
The expression is: P(x) = -0.5x² + 40x - 300.A profit of $300 is found with x = 20 and x = 60.What is the profit concept?Profit is given by revenue subtracted by costs.
In this problem, we have that:
The revenue is: R(x) = 90x - 0.5x².The costs are: C(x) = 50x + 300.Hence the expression for the profit is given as follows:
P(x) = R(x) - C(x)
P(x) = 90x - 0.5x² - 50x - 300
P(x) = -0.5x² + 40x - 300.
A profit of $300 is found when P(x) = 300, hence:
300 = -0.5x² + 40x - 300
0.5x² - 40x + 600 = 0.
x² - 80x + 1200 = 0.
(x - 60)(x - 20) = 0.
Hence the values are:
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To solve a(b + c) = d for a in 1 step:
Answer:
a = \(\frac{d}{b+c}\)
Step-by-step explanation:
a(b + c) = d
isolate a by dividing both sides by b + c
a = \(\frac{d}{b+c}\)
Solve by graphing. x2 + 2x – 3 = 0
By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.
We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.
1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:
0 = x^2 + 2x - 3.
This quadratic equation can be factored as (x + 3)(x - 1) = 0.
Therefore, x = -3 or x = 1.
2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.
3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).
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for small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: g-l=al(t-t), where g is the length of the object at temperature t, and l is the length at temperature t, and a is a constant which depends on the type of metal. a rod is 135 cm long at 115 degrees f and made of a metal with a=10^-3. write an equation giving the length of this rod at temperature t(because a=10^-3 is very small, give an exact answer: do not round expand multiplied numerical products to get rounded decimals).
Equation giving the length of this rod at temperature is g = 0.000085t + 84.991075 cm.
What is temperature ?
A temperature is a unit used to represent voguishness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter( body with an advanced temperature) to a colder( body with a lower temperature)( one at a lower temperature).Given that,
Temperature denoted by T
G - L = aL(t - T)
G = aLt + L(1 - aT)
Slope = aL
Intercept = L(1 - aT)
g = 0.000085t + 84.991075 cm
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help pls I need help
please answer this question
The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.
What is integration?It is the reverse of differentiation. The differentiation is the rate of change of the function with respect to variables.
The integration is given below.
\(\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{(1 +x)^{2022}} \ dx\)
Then the integration can be written as
\(\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{[(1 +x)^{1011}]^2} \ dx\)
Let (1 + x)¹⁰¹¹ = t. Then 1011x¹⁰¹⁰ dx = dt.
Then we have
\(\rightarrow \int_{1}^{\infty } \dfrac{dt}{1011 \ t^2}\)
Then integrate
\(\rightarrow \dfrac{1}{1011} \left [ \dfrac{-1}{t} \right ]_{1}^{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ \dfrac{1}{t} \right ]^{1}_{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ 1- 0 \right ]\\\\\\\rightarrow \dfrac{1}{1011}\)
The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.
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solve the following quadratic equation using the quadratic formula and then choose the correct solution set 8x2-6x+1=0
Answer:
The solutions to the quadratic equation using the quadratic formula will be:
\(x=\frac{1}{2},\:x=\frac{1}{4}\)
Step-by-step explanation:
Given the equation
\(8x^2-6x+1=0\)
solving with the quadratic formula
\(\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\)
\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
\(\mathrm{For\:}\quad a=8,\:b=-6,\:c=1\)
\(x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}}{2\cdot \:8}\)
as
\(\sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}=2\)
so
\(x_{1,\:2}=\frac{-\left(-6\right)\pm \:2}{2\cdot \:8}\)
Separating the solution
\(x_1=\frac{-\left(-6\right)+2}{2\cdot \:8},\:x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}\)
solving
\(x_1=\frac{-\left(-6\right)+2}{2\cdot \:\:8}\)
\(=\frac{6+2}{2\cdot \:8}\)
\(=\frac{8}{16}\)
\(=\frac{1}{2}\)
and
\(x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}\)
\(=\frac{6-2}{2\cdot \:\:\:8}\)
\(=\frac{4}{16}\)
\(=\frac{1}{4}\)
Therefore, the solutions to the quadratic equation using the quadratic formula will be:
\(x=\frac{1}{2},\:x=\frac{1}{4}\)
Answer:
1/4 1/2
Step-by-step explanation:
5 The price of a bag of bagels is equal to 0.9 times the number of bagels. Model the price as p, and the number of bagels as n. Which could be the proportional relationship between quantity and price? С c A n = 0.9p B. n = 9.0p C. p = 0.9n c D. p = 9.On 0 O Type here to search
Let the price of a bag of bagels be P
Let the number of bagels be n
Since we have been told that the price, P is 0.9 times the number of bagels
=> P = 0.9 x n
=> P = 0.9n
A point has been translated left and down. Based on the graph, which could be true? Check all that apply. A is the image of C. A is the image of D. B is the image of D. B is the image of E C is the image of A. C is the image of D. D is the image of E. please please hurry with the answers.
From the image that we have here, the translation of the image would be:
B is the image of D. B is the image of E.C is the image of D.What is translation in mathematics?In the field of mathematics, this is the type of transformation which would take points in an image and move it in similar distance and direction.
It has to do with the movement of points in an horizontal manner or in a vertical manner.
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Factor this polynomial expression. X2 – 16 O A. (x - 16)(x - 16) O B. (x + 4)(x – 4) C. (x + 16)(x - 16) D. (x-4)(x - 4)
Answer is: (x+4)(x-4)
Answer:
Yeah that's the answer. Nice job
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table below shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function which best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
Which statement about the slopes of the functions is true?
Answer:
A or D
Step-by-step explanation:
I'm pretty sure its D
A bicycle has a listed price of $794.95 before tax. if the sales tax rate is 8.75% find the total cost of the bicycle with sales tax included.
round your answer to the nearest cent, as necessary.
Answer:
Step-by-step explanation:
$794.95(1.0875) = 864.508125 = $864.51
Emma has 16 markers. She gave Jack some, Seven markers are left. How many
markers did Emma give Jack?
what is 20 squared 2 + 6(9 + 3)
Answer:
\(\sf 872\)
Step-by-step explanation:
Parentheses
\(9 + 3 = 12\)
\(=20^2\cdot \:2+6\cdot \:12\)
Exponents
\(20^2=400\)
\(=400\cdot \:2+6\cdot \:12\)
M/D(Multiply/Div.)
\(6\cdot \:12 = 72\)
\(=800+72\)
A/S(Add/Sub.)
\(800+72=872\)
\(\sf Thus,\\= 872\)
The equation y=195(1.10)x can be used to represent growth in the number of Salad Supreme restaurants since 2005. Which is the most reasonable conclusion based on this information? A. Salad Supreme had 110 restaurants in 2005. B. Salad Supreme is increasing the number of restaurants by 10% each year. C. Salad Supreme is increasing the number of restaurants by 195 each year. D. Salad Supreme is increasing the number of restaurants by 110% each year.
The most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year. Option B
How to determine the most reasonable conclusionBased on the given equation y = 195(1.10)^x, where x represents the number of years since 2005 and y represents the number of Salad Supreme restaurants, we can draw the following conclusions:
A. Salad Supreme had 110 restaurants in 2005: This conclusion is not supported by the given equation.
B. Salad Supreme is increasing the number of restaurants by 10% each year: This conclusion is supported by the equation.
C. Salad Supreme is increasing the number of restaurants by 195 each year: This conclusion is not supported by the equation.
D. Salad Supreme is increasing the number of restaurants by 110% each year: This conclusion is not supported by the equation. The growth factor of 1.10 (or 10%) indicates a 10% increase each year, not 110%.
Therefore, the most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year.
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1. Prove ~ (Pvq) <=> (~P^~9).
Algebra of propositional variables
2. P^ q = q^q
P v q = q v p
show that both are commutative
Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
How to explain the commutative property.It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property
From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.
In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.
Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
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A bag contains 5 red marbles, 8
green marbles, 6 orange marbles, and
11 yellow marbles. What is the
probability of randomly choosing
an orange marbles
Answer:
1/5
Step-by-step explanation:
First you need to find the total amount of marbles
5+8+6+11= 30
There are 6 orange marbles
So the probability is 6/30 which reduces to 1/5
Evaluate the expression for x^2×x^1 for x=9
Answer:
729
Step-by-step explanation:
x^2*x^1 = (9)^2 * (9)^1
= (9)^3
= 729
Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase under her bed, modeled by the function s(x) = 450. She is able to babysit to earn extra money and that function would be a(x) = 6(x − 2), where x is measured in hours. Explain to Tamara how she can create a function that combines the two, and describe any simplification that can be done.
Answer:
Add both of the function together.
Step-by-step explanation:
s(x) + a(x) = 450 + 6(x - 2)
Answer:
1) The function that represents how the money in her suit case is s(x) = 450
The function that represents the amount she is able to make from baby sitting is a(x) = 6(x - 2)
Given that the values of the two function are the same units, dollars, and the amount are to be put to the same use for spending money for her first year of college, the combination of the two functions is the sum of their values given as follows;
f(x) = s(x) + a(x) = 450 + 6(x - 2)
2) For simplification, we expand the second term and add the constant terms as follows;
f(x) = 450 + 6·x - 12
f(x) = 450 + 6·x - 12
f(x) = 438 + 6·x
The sum of the two terms becomes, f(x) = 438 + 6·x
determine the number of significant figures in the measurement 6.07 m . express your answer numerically as an integer.
The total number of significant figures ( numerically as an integer ) in the given measurement 6.07 m is equal to 3.
Significant figures are the count of digit present in the given number.Zeros between two non zero digit of the given number is also significant figure.Leading zeros of the number are not considered as significant figure.Here in the measurement 6.07 m
Zero is in between two non zero digit 6 and 7.
Zero is countable.
Total number of significant figure in 6.07 m is 3.
Therefore, the number of significant figure in the 6.07 m is equal to 3.
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Jack is two years older than bob. If bob is x years old, what is the sum of jacks age and bobs age
Expression 2(x+1) represents the sum of bob and Jacks age.
What is Expression?An expression is combination of variables, numbers and operators.
Given,
Bob is x years old,
Jack is two years older than bob=x+2
we need to find the sum of jacks age and bobs age
x plus x plus two
x+x+2
Two times of x plus two
2x+2
Take two as common, two times of x plus one
2(x+1)
Hence expression 2(x+1) represents the sum of bob and Jacks age.
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Line segment BA¯¯¯¯¯¯¯¯ has endpoints B(−3,0) and A(5,4). What are the coordinates of the point located 14 of the way from B to A?
(1,2)
(3,3)
(−1,1)
(1,−1)
Answer: P'(9, -1), L'(3, 1)
Step-by-step explanation:
I dont have a an explanation but this is the correct answer.