The inverse function returns the original value for which the output of a function was given.
The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3)
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
A function's inverse is not always a function! To ensure that the inverse function is also a function, the original function must be a one-to-one function. A one-to-one function is one in which each second element corresponds to exactly one first element. (Each x and y value is only used once).
The inverse of a function is thought to be a reflection of the original function along the line y = x. Simply put; the inverse function is obtained by swapping the original function's (x, y) values.
Let the function be y = 4 - 3x
f(x) = 4 - 3x
y = 4 - 3x
simplifying the value of x, we get
x = 4 - 3y
x - 4 = -3y
x - 4/-3 = y
[tex]f^{-1[/tex]= - (x - 4/3)
The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3).
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Please help I really need help
Add
3/4 +(-1/4)
3/8+(-3/8)
[tex]{\huge\color{yellow}{\boxed{\fcolorbox{blue}{black}{꧁ANSWER ꧂}}}} \\ \\ \frac{3}{4} + ( - \frac{1}{4} ) \\ \\ = \frac{9 - 3}{12} = \frac{6}{12} = \frac{2}{4} \\ \\ \frac{3}{8} + ( - \frac{3}{8}) = 0(cancel \: \: out)[/tex]
Answer:
3/4 + (-1/4)
-1/4 = -0.25
3/4 = 0.75
0.75+-0.25 = 0.53/8 + (-3/8)
-3/8 = -0.375
3/8 = 0.375
0.375+-0.375 = 0I SWEAR ON MY MOMMY IF I DONT GET NO HELP
Answer:
Step-by-step explanation:
w(t) = F(t) - D(t) = water into (or out of the pool)
= t^2 + 8t+9 - (t^2 +11t+4)
w(t) = -3t + 5 <===== shows all of the water will leak out after 5/3 hr
the two functions intersect at 5/3 hr this is where water in = water out = dry pool
which pairs of figures below are congruent
Answer:
In the first image, the triangles are congruent because each side measures equally to the other. The circles are not because they are not the same size. The big circle is 4 by 4 squaes and the small circle is 2 by 2.
In the second image the first image is congruent, and in the second image the figures are not congruent because the image to the right is thinner than the left.
Step-by-step explanation:
Hope it helps! =D
Answer: Ok for the first screen shot (the one with the triangles) its yes then the circles no
the upside down L 's yes
and the quadrilaterals no
Step-by-step explanation: congruent means the same or identical.
Hope it helped :D
18 is what fraction of 144?
Answer:
1/8
Step-by-step explanation:
144 ÷ 18 = 8
so, it 1/8
Use the properties of logarithms to simplify and solve each equation. Round to the nearest thousandth.
ln (2 x-1)²=7
The simplification of the given logarithmic functions ln (2x-1)² = 7 is 17.055.
What are called the logarithmic functions?The logarithm of a number is the exponent by which a fixed value referred as the base should always be raised to generate a certain number. For instance, because 1000 is 10 to the third power, a log of 1000 to base 10 is 3.
The y-intercept doesn't really exist.A vertical asymptote is x = 0. *Mention: An asymptote is a line that a graph moves as the absolute value of x and otherwise y increases.A logarithmic function does not have a horizontal asymptote.The x-intercept is one.The function is spreading across the domain.If the base is between 0 and 1, the function diminishes out across domain.Some properties of the logarithmic functions are defined as-
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xAs, for the stated log or ln function ln (2 x-1)²=7
Use the power rule on the left side of the equation.
2 ln (2 x-1) = 7
Simplifying the equation.
ln (2 x-1) = 7/2
ln (2 x-1) = 3.5
Using the exponential property of the log.
e∧[ln (2 x-1)] = e∧3.5
2x-1 = 33.11
2x = 33.11 + 1
2x = 34.11
x = 34.11/2
x = 17.055
Therefore, the value of the x for the stated logarithmic functions ln (2x-1)² = 7 is calculated as 17.055.
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Which two integers is 37 between?
Integers are positive and negative whole number digits, where the set of integers is denoted by capital Z.
Z={-n,...,-2,-1,0,1,2,...,36,37,38,39,...,n}
So 37 is in between 36 and 38
Help me with 1-5 i really need it
Answer:
1. E K H and F K G
2. E K F and H K G
3. E K F or G K H
4. F K G and G K J
5. G K J
Step-by-step explanation:
On a fishing trip, you catch two fish. The weight of the first fish is 1.2 pound. The second fish weighs at least 0.5 pound more than the first fish. Write an inequality that represents the possible weights w (in pounds) of the second fish.
Answer: 1.7
Step-by-step explanation:
Expand each logarithm.
log a²b³ / c⁴
The answer to the present question is: log(a²b³/c⁴) = 2log(a) + 3log(b) - 4log(c)
For solving this kind of question, we are going to use these three identities:
log(x*y) = log(x) + log(y) ....(1)
log(x/y) = log(x) - log(y) ....(2)
log(xⁿ) = nlog(x) ....(3)
So, using (2), log(a²b³/c⁴) may be written as: log(a²b³) - log(c⁴) ....(4)
Again, using (1), log(a²b³) are often written as: log(a²) + log(b³) ....(5)
Now, Putting equation (4) in equation (3), we get:
log(a²) + log(b³) - log(c⁴) ....(5)
Now, using (3), expanding all the terms, we get:
log(a²) = 2log(a)log(b³) = 3log(b)log(c⁴) = 4log(c)
Putting of these in equation 5, we get:
2log(a) + 3log(b) - 4log(c)
Therefore, log(a²b³/c⁴) = 2log(a) +3log(b) - 4log(c)
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Help ASAP!! DOUBLE POINTS!
Answer: 8c + 40
Step-by-step explanation: i did this on OW
Charlotte has appointed a chairperson to lead a city beautification project. the first act is to install statues and fountains in one of the city's parks. a statue is to be placed in the center of the park. the area of the base of the statue is 4x2 + 12x + 9 m2. factor the area of the base of the statue.
The base lengths are (2x + 3) and (x - 4) meters if the area of the base of the statue is 4x² + 12x + 9.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that:
The quadratic polynomial is:
= 4x² + 12x + 9
After using factor method:
= 2x² - 4x + 3x - 12
= 2x(x + 4) + 3(x - 4)
= (2x + 3)(x - 4)
Thus, the base lengths are (2x + 3) and (x - 4) meters if the area of the base of the statue is 4x² + 12x + 9.
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Woke out the value of (10^4)^2
Answer: 100 million or 100,000,000
Step-by-step explanation:
Do the exponent in the brackets. Then the one outside of the brackets.
10 to the power of 4=10000(which is 10 x 10 x 10 x10)
Then figure out 10000 the the power of 2.
10000 x 10000 = 100,000,000
Therefore the value of this is 100 million.
Find the area of a cement walkway of width x meters around a 50m by 25m pool.
The area of a rectangular cement walkway of width x meters around a 50m by 25m pool is 4x²+150x sq. meters.
What is an area of a rectangle?Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A rectangle is a form of a quadrilateral, a two-dimensional object with four sides and four vertices. The four angles of the rectangle are all perfectly right angles or 90 degrees. The opposing sides of the rectangle are equal and parallel.
Area of Rectangle = Length × Breadth
In the given question,
The width of the walkway is x meters.
Width of the pool= 25+2x meters
and the Length= 50+2x.
So the area of the walkway with the pool is
= (25+2x)+(50+2x)
= 1250+100x+50x+4x²
= 4x²+150x+1250 sq. m
Area of the pool= 50x25
= 1250 sq. m
Area of the walkway= 4x²+150x+1250-1250
= 4x²+150x sq. meters.
Hence, the answer is 4x²+150x sq. meters.
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What is the quotient of (x³ + 8) = (x + 2)?
Ox²+2x+4
Ox²-2x+4
O x² +4
Ox²-4
12
The correct option is (x²- 2x + 4) for the quotient.
What is termed as the quotient?The quotient is the result of dividing one number by the other. For instance, if we divide 6 by 3, the result is 2, which represents the quotient. The quotient can be either an integer or a decimal.For the given question;
The equations are given as;
(x³ + 8) = (x + 2)
For finding the quotient; this could be written as,
(x³ + 8)/ (x + 2) = 1
Thus, we have
= (x³ + 8)/ (x + 2)
Rewriting the equation as;
= (x³ + 2³)/ (x + 2)
Apply the formula of (a³ + b³) = (a+b)(a² - ab + b²) at the numerator;
= (x + 2)(x² -2x + 4)/ (x + 2)
Cancel the value of (x+ 2)
= (x² -2x + 4)
Thus, the quotient of the division is obtained as (x² -2x + 4).
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Please help me out please please please
Expand each logarithm.
log₇ √r+9 / s² t¹/₃
After expanding logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]\frac{log_7(\sqrt{r} )+9}{s^2t^\frac{1}{3} }[/tex]
as, log (√x) = 1/2 log (x), equation becomes
[tex]= \frac{\frac{1}{2} log_7(r) + 9}{s^2t^\frac{1}{3} } \\[/tex]
now, after rationalize this equation
[tex]= \frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]
Thus, after expanding the logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]
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A pentagon has vertices at (-1,-1), (-5,-2), (-6,-4), (-4,-7), and (-2,-3). If the pentagon is rotated 180* coordinates of the vertices of the image?
Answer:
(1, 1) , (5, 2), (6, 4), (4, 7) and (2, 3)
Step-by-step explanation:
When a point is rotated 180° about the origin(either clockwise or anticlockwise), the transformed coordinates are the negatives of the original coordinates.
Thus when a point (x, y) is rotated about the origin, its new coordinates become (-x, -y)
Given the original 5 vertices of the pentagon, the vertices of the rotated pentagon are transformed as follows
Original Vertex ==> Transformed Vertex
(-1, -1) ==> (1, 1)
(-5, -2) ==> (5, 2)
(-6, -4) ==> (6, 4)
(-4, -7) ==> (4, 7)
(-2, -3) ==> (2, 3)
5(x+8)-7 < 23 help me
Answer:
5x+40-7<23
5x+33<23
5x<-10
x<-2
Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. What is the angle of inclination from Lily's location to the top of the waterfall?
I think its 87. 6 ¯\_(ツ)_/¯
If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.
Angle of inclinationGiven data or information:
Feet away=40 feet away
Feet high=1,000 feet high
Now let find or determine the angle of inclination rom Lily's location to the top of the waterfall
Hence,
tanФ=1,000/40
Ф=tan^-1 (1,000/40)
Ф=87.70°
Therefore If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.
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Write an expression for 88 added to v
Answer:
[tex]\mathrm{88 + v}[/tex]
how did the graph change from y = x2 to y = (x+3)2
The function y = (x + 3)² is the result of translating the function y = x² 3 units in the -x direction.
How to modify a function by using transformation rules
In this question we have a function of the form y = f(x), which is modified by transformation rules. The statement defines the original function as y = x² and we see that the resulting expression is y = (x + 3)². By direct observation, we that the latter function is the consequence of using an horizontal translation of the form:
g(x) = f(x - k), where k < 0.
This transformation rule indicates a horizontal translation in the - x direction. To be specific, a horizontal translation 3 units in the -x direction. Graphically specific, the graph of f(x) is moved 3 units in the - x direction.
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Christopher bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it decreased by 11%. During the second year the value of the stock decreased by 27%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.
The value of the stock after 2 years was 0.6497xx.
What is Mathematical expression?
The combination of number and variable by using addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
Christopher bought stock in a company two years ago that was worth xx dollars.
In the first year that he owned the stock, then it decreased by 11%.
In the second year the value of the stock decreased by 27%.
Now,
The multiplier of value for the first year was (1 - 11%) = 0.89
The multiplier of value for the second year was (1 - 27%) = 0.73
Then the multiplier of value for the two years was = 0.89 * 0.73
= 0.6497
Hence, The value of the stock after 2 years was 0.6497xx.
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6.32455532034 in simplest radical form
Answer:
2√10
Step-by-step explanation:
You want the simplest radical form of 6.32455532034.
ApproximationIn order for the given decimal value to have a "simplest radical form," we must assume it is an approximation of an irrational root. The given rational number is approximately equal to √40, differing in the 12th decimal place and beyond.
6.32455532034 ≈ √40 = 2√10
__
Additional comment
The radical is simplified by removing all of the perfect squares from under the radical.
40 = 2^3 × 5 = (2^2)(2×5) = (2^2)(10)
√40 = 2√10
What combination of items on the list could Darla buy to spend as close to $15 as possible with tax without going over? Justify your solution.
Darla can spend the greatest total cost of groceries in order to spend as close to $15 as possible is approximately $14.20.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Let the cost of the groceries be represented as "c", then we have;
Cost price + VAT = c + (5% of c)
In order to get the cost, c, that make him spend as close to $15. Since the tax is 5% of the cost price, then the cost price will be close to $15.
Let c = $14.20, then;
So that,
c + (5% of c) = 14.20 + (5% of 14.20)
= 14.20 + 0.71
= $14.91
Therefore, the greatest total cost of groceries she can spend in order to spend as close to $15 as possible is approximately $14.20.
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Solve for x and graph the solution on the number line. If possible, resolve your answer to a single inequality. In case of no solution leave the number line blank.
22>=-3x+7 and -3x + 7 >-17
The solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x < 8
What is a number line?A number line is a vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval
How to plot the number line?The expression is given as
22 >= -3x + 7 and -3x + 7 >-17
The above expression is an inequality expression
As a general rule:
Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
So, we have
22 >= -3x + 7 and -3x + 7 >-17
Evaluate the like terms
15 >= -3x and -3x >-24
Divide through by -3
So, we have
-5 <= x and x < 8
Combine the expressions
-5 <= x < 8
Hence, the solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x < 8
See attachment for the number line
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Can you guys pls help me
Hi
Step-by-step explanation:
Y should have a negative side in front of it.
[tex]2x - y = 5 \\ - y = - 2x + 5 \\ y = 2x - 5[/tex]
What is the equation of the line that passes through the point (-5,-6) and has a slope of 1/5
the equation of the line that has a slope of 1/5 and passes through (-5, -6) is: y = 1/5x - 5.
How to Find the Equation of a Line?Given that the line passes through (-5, -6), and has a slope (m) = 1/5, to find the equation of the line, do the following:
Substitute (x, y) = (-5, -6) and m = 1/5 into y = mx + b to find the value of b:
-6 = 1/5(-5) + b
-6 = -1 + b
Add 1 to both sides
-6 + 1 = -1 + b + 1
-5 = b
b = -5
Substitute m = 1/5 and b = -5 into y = mx + b
y = 1/5x + (-5)
y = 1/5x - 5
Thus, the equation of the line that has a slope of 1/5 and passes through (-5, -6) is: y = 1/5x - 5.
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100pts When you are getting dressed, you put your socks on first and then your shoes on second. But to undo this, you take your shoes off first and your socks off second. Why do you have to reverse the order? Use this scenario to help you explain why it is helpful to work backward when solving equations.
5. A shark is swimming 60 feet below the surface of
the ocean. There is a fish that is 25 feet deeper
in the water. Use the expression (-60) + (-25) to
describe the fish's location relative to the surface
of the ocean.
Answer:
-85
Step-by-step explanation:
(-60) + (-25) = (-85)
Answer:
Step-by-step explanation:
the fish is 85 feet bellow the surface
explanation 60+25 is 85 so therefor -60-25 would be -85
Write inequalities to represent each situation:
A) Matt either spends less than 20 or more than 150 on his shoes.
B) Sarah has at least $25 in the bank.
C) The speed limit on a road is 35. Jena got a ticket.
D) Rusty will pay no more than $4 for a haircut.
Answer:
A. x < $20 or x > $150
B. x [tex]\geq[/tex] $25
C. x [tex]\leq[/tex] 35mph
D. x [tex]\leq[/tex] $4
Step-by-step explanation:
Not sure of the format desired for item A but this is what I came up with.