The inverse of the function is f ⁻¹(x) = 10ˣ
Given the function is y = log₁₀ x
In relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain. By replacing (x, y) with (y, x) with reference to the line y = x, one can obtain the graph of the inverse function.
steps to find the inverse of the function:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now replace y with x.
x = log₁₀ y
change the dependent variables.
f ⁻¹(x) = 10ˣ
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I need help with this.
20 people likes movies, such that 12 of these also like music, then the probability is just the quotient between:
Q = 12/20 = 0.6
The probability that a person likes music given that he/she lies movies is 0.6 or 60%
How to find the probability P(movies|music)?Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.
So the quotient between 12 and 20, that will gave us the probability we want to find.
The probability that a person likes music given that he/she lies movies is 0.6 or 60%
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WITHOUT GRAPHING identify the coordinates of A(-3, 7), B(4, 9), and C(0, -2) after the following transformations. 1. Translation 2 units up and 7 units right.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
What is transformation?Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.
Dilation is a transformation that affects the size of a figure.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
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Which angles are vertical to each other?
(Use the following statement to answer questions 10-16.)
“If a number is greater than -500, then the number is greater than 500.”
Determine the truth value of the conditional statement. Explain.
The truth value of the conditional statement is false
How to determine the truth value of the conditional statement?The conditional statement is given as
“If a number is greater than -500, then the number is greater than 500.”
The above conditional statement is false
This is so because
Not all numbers greater than -500 are greater than 500
Take for instance 499 is greater than -500, but less than 500
Hence, the truth value of the conditional statement is false
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Find the domain and range. Graph each relation.
1. {(0, 0), (1, -1),(2, -4).(3,-9),(4, -16)}
The domain of the relation: {0, 1, 2, 3, and 4}
The range of the relation: {0, -1, -4, -9, -16}
The graph for the relation is in the attachment.
What is the Domain is a Relation?A domain of a relation can be defined as the set of x-values or inputs of a relation.
What is the Range of a Relation?The set of all output or y-values that correspond to the x-values in a set of ordered pairs.
Given the relation, {(0, 0), (1, -1),(2, -4), (3,-9), (4, -16)}
The domain of the relation is: {0, 1, 2, 3, and 4} (these are all the input of the relation)
The range of the relation is: {0, -1, -4, -9, -16} (these are all the output of the relation)
The graph for the relation is in the attachment.
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Let g(x)=3 x+2 and f(x)=x-2 / 3 . Find each value.
(g⁰g)(1)
Value for (g⁰g)(1) = 17
What is the domain of the function (g⁰g)(1)?Now, (g⁰g)(x) = g[g(x)]
let g(x) = 3x + 2
(g⁰g)(x) = g(3x + 2)
(g⁰g)(1) = g(5)
(g⁰g)(1) = 3(5) + 2
(g⁰g)(1) = 17
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-46 decreased by the difference between -23 and -61
When -46 decreased by the difference between -23 and -61, the number becomes -18.
What is the value of the subtraction?
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
According to mathematical rules, when two negative signs are multiplied by each other, the number becomes positive.
The difference between -23 and -61: -61 - (-23)
-61 + 23 = -38
-46 - (-38)
-46 + 28 = -18
Here is the complete question:
-46 decreased by the difference between -23 and -61. What is the value of the number?
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Which operation would you do first in the following equation?
10-4÷1x 5
Simplify this please!
Answer:
Step-by-step explanation:
To get to work each morning, Emily takes a horse 10.9810.9810, point, 98 kilometers and a bike 4.064.064, point, 06 kilometers.
Answer: Emily's in total journey is 15.045 kilometers.
Step-by-step explanation:
Given data,
Emily traveled a certain distance on a horse = 10.98 kilometers
Emily traveled a certain distance on a bike = 4.06 kilometers
The overall distance traveled by Emily on her horse and bike needs to be determined.
For "Total Distance" , we will use addition operation:
So, Total distance covered by Emily's journey is given by equal to
Emily traveled a certain distance on a horse + Emily traveled a certain distance on a bike
Let us assume,
Total distance covered by Emily's journey is represented by 'x'
Then we can write,
x = 10.981 kilometers + 4.064 kilometers
x = 15.045 kilometers
Therefore, Emily's in total journey is 15.045 kilometers.
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Work out the following, giving your answers in their simplest form:
a) 4/7 / (1 3/4)
b) 5 3/5 / (2 2/3)
The simplest form of the following are -
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.
We have been given that
a) 4/7 / (1 3/4)
Rewrite as -
= (4/7) / (1× 3/4)
= (4/7) / (7/4)
= (4/7) × (4/7)
= 16/49
b) 5 3/5 / (2 2/3)
Rewrite as -
= (5× 3/5) / (2× 2/3)
= (5× 3/5) / (8/3)
= (28/5) / (8/3)
= (28/5) × (3/8)
= 7/5 × 3/2
= 21/10
= 2.1
Thus , the following are in order of simplicity:
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
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Kim has a part-time job assembling bicycles for a local store. each day, she earns $20 plus $15 for each bike assembled. kim's boss daily goal is to assemble no more than 6 bicycles a day. if x represents the number of bikes assembled, the total amount she earns can be represented by . what is the range for the function for this situation?
The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.
The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).
The total amount she earns can be represented by
y = 15x + 20
where y is her daily earnings and x is the number of bikes she assembles
If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).
domain : {x| 0 ≤ x ≤ 6}
where x is a whole number
Substituting the minimum and maximum value of x in the function.
y = 15(0) + 20 when x = 0
y = 20
y = 15(6) + 20 when x = 6
y = 110
range : $20 ≤ y ≤ $110
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Write each expression in simplest form. (x¹/₄ / y⁻³/₄)¹²
The given expression can be written in its simplest form by solving the exponents.
There are two types of exponent rules that will be applied to the expression. First, we will solve the negative exponent then we will multiply the exponents.
According to the negative exponent rule: x^-n=1/x^n.
Hence, applying the rule to the base term in the denominator, 1/y^⁻³/₄= y^³/₄
Therefore, x^¹/₄ / y^⁻³/₄= x^¹/₄ y^³/₄
According to the multiplication of exponent rule: (x^n)^m=x^nm
Hence, applying the rule to the expression,
(x^¹/₄ y^³/₄)^12=x^¹/₄*12 y^³/₄*12
Multiplying the powers and simplifying,
x^¹/₄*12 y^³/₄*12=x^3y^9
The simplest form of the expression (x^¹/₄/y^⁻³/₄)^12 is x^3y^9.
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Is the expression 33x33^7 equivalent to (33x33)^7? Explain.
Answer:
Step-by-step explanation:
no because perenthesis
Answer:
No it is not equivalent because the parenthesis
Step-by-step explanation: When it comes to parenthesis you have to do the problem in them, so you would do 33x33 rather than the whole problem at once. no idea if that makes sense bff it sounded right in my head
If a person walks
mile in 1 hour, how far does that person walk
in 1 3/4 hours at that rate?
7/4 miles distance does that person walk.
What is distance?
The length or width between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour. a distance; a space: The ship was encircled by a sizable body of water.We can use a ratio to solve
1 mile x miles
----------------= ---------------
1 hour 1 3/4 hours
Changing to improper fractions
1 mile x miles
----------------= ---------------
1 hour 7/4 hours
Using cross products
1 * 7/4 = 1 * x
7/4 = x
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If f(x)=3x+2 and g(x)=x(squared)−x, find the value.
f(-2)=______
Answer: f(-2) = - 4
Step-by-step explanation:
Which system of equations is represented by the matrix below?
[4 0 5
2 -117
47576777...................
Determine whether each logarithm is a common logarithm.
a. (log₂4)
the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.
In mathematics, the common logarithm is the logarithm with base 10.
It is also known as the decadic logarithm and as the decimal logarithm function.
Here, we have the logarithm function as:
( log ₂ 4 )
Now, we can see that:
It has a base of 2.
So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.
Therefore, we get that, the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.
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Solve each equation. Round to the nearest ten-thousandth. Check your answers.
25²x⁺¹=144
[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]25^{2x+1}=144[/tex]
Taking logarithm on both sides:
log ([tex]25^{2x+1}[/tex]) = log (144)
=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]
=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]
=> 2x + 1 = 1.544
=> 2x = 0.544
=> x = 0.272
Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.
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Phillis used the wrong metal in her experiment which had a very different density than the intended metal. As a result when calculating her results she found that the mass necessary was 612 grams instead of the theoretical 390 grams that was needed. What is her percent error?
The percent error is 56. 9%
What is percent error?Percent error is defined as the difference between the estimated value and the actual value in comparison to the actual value.
The formula for percent error is expressed as;
Percent error = [tex]\frac{|VA - VE|}{VE}[/tex] × 100/1
Where;
VA is the actual value = 612 gramsVE is the expected value = 390 gramsSubstitute the values
Percent error = | 612 - 390| / 390 × 100/ 1
Percent error = 222/ 390 × 100/ 1
Percent error = 0. 56 × 100
Percent error = 56. 9%
Thus, the percent error is 56. 9%
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Solve each equation. Check for extraneous solutions. √x+4=√3 x
The solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).
Quadratic equationAny equation of the form [tex]\rm ax^2+bx+c=0[/tex] is called a quadratic equation.
The formula for the roots of the quadratic equation is found by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
The equation is:
√x + 4 = √3 x
√x = √3 x - 4
Squaring both sides:
x = (√3 x - 4)²
x = 3x² - 8√3 x + 16
2x² - 8√3 x + 16 = 0
x² - 4√3 x + 8 = 0
After solving with the quadratic formula:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\rm x = \dfrac{-(-4\sqrt3) \pm\sqrt{(-4\sqrt3)^2-4(1)(8)}}{2(1)}[/tex]
x = 2(1 + √3) or x = 2(1 - √3)
Thus, the solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).
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Devon has 4 3/4 bags of soil to put in hs flower bed each bag will cover 15 ft2 how many squares will he be able to cover
Devon will be able to cover 71.25 ft² of flower bed.
The number of bags of soil Devon has = [tex]4\frac{3}{4}[/tex]
Converting mixed fraction to fraction
Number of bags of soil = (4×4+3)/4
Performing multiplication and addition in numerator to find the number of bags of soil with Devon
Number of bags of soil = 19/4
Now, it is stated that area covered by 1 bag = 15 ft²
So, 19/4 bags will cover area = 15×(19/4)
Performing multiplication and division to find the area covered by the bags of soil
Area covered by bags of soil Devon has = 71.25 ft²
Hence, the area covered by bags of soil Devon has is 71.25 ft²
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The complete question is -
Devon has 4 3/4 bags of soil to put in his flower bed. Each bag will cover 15 ft2. How many square feet will he be able to cover?
Confused on this entire problem i apoligize
The linear function f(x) with a slope of -8 and that f(1) = 2 is f(x) = 10 -8x
Equation of a lineFrom the question, we are find a linear function with slope of -8 and that f(1) = 2
If f(1) = 2, then the line passes through the point (1, 2)
Using the point-slope form of the equation of a straight line
y - y₁ = m(x - x₁)
Where m is the slope
Then,
y - 2 = -8(x - 1)
Simplify
y - 2 = -8x + 8
y = -8x + 8 + 2
y = -8x + 10
∴ f(x) = -8x + 10
f(x) = 10 - 8x
Hence, the linear function is f(x) = 10 -8x
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The grid shows Figure Q and its image Figure Q′ after a transformation.
Figure Q is a pentagon drawn on a coordinate grid with vertices in clockwise order at point 2 comma 4, point 3 comma 7, point 7 comma 5, point 5 comma 4, and point 4 comma 2. Figure Q’ is a pentagon drawn with vertices in clockwise order at point negative 2 comma negative 4, point negative 3 comma negative 7, point negative 7 comma negative 5, point negative 5 comma negative 4, and point negative 4 comma negative 2.
Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent?
Counterclockwise rotation of 90° about the origin
Counterclockwise rotation of 270° about the origin
Clockwise rotation of 90° about the origin
Clockwise rotation of 180° about the origin
The transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape or position of a point, a line, or a geometric figure.
We have,
Coordinates of a pentagon Q.
(2, 4), (3, 7), (7, 5), (5,4), and (4,2).
Coordinates of pentagon Q'.
(-2, -4), (-3, -7), (-7, -5), (-5,-4), and (-4,-2).
We see that the coordinates of each point of the pentagon Q have changed their position as negative coordinates in pentagon Q'
The coordinates of pentagon Q are in (x, y) which can be assumed to be in the first quadrant of the coordinate plane.
The coordinates of pentagon Q' are in (-x, -y) which is in the 3rd quadrant.
From the first quadrant to 3rd quadrant there is a rotation of 180°.
Thus the transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.
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If f(x) is given as an equation and g(x) is given as a table, how i can tell they are inverses
Answer: f(x) and g(x) both represent y of the equations
Step-by-step explanation: f(x) and g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.
I need some help with these it's hard for me can some help asap
Answer:
C and B
Step-by-step explanation:
Evaluate g(5) then substitute the value obtained into f(x)
g(5) = [tex]\sqrt{5-1}[/tex] = [tex]\sqrt{4}[/tex] = 2 , then
f(2) = 3(2) + 1 = 6 + 1 = 7
-----------------------------------------------------------------------------
f(x) = [tex]\frac{x^2+3}{(x-4)(x+8)}[/tex]
the denominator of f(x) cannot be zero as this would make f(x) undefined.
equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
(x - 4)(x + 8) = 0
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 8 = 0 ⇒ x = - 8
the vertical asymptotes are x = 4 and x = - 8
Elena has $225 in her bank account. She takes out $20 each week for w weeks. After w weeks she has d dollars left in her bank account.
Write an equation that represents the amount of money left in her bank account after w weeks.
Answer:
y20=225x or y225+x20 ir can be
Solve. Check for extraneous solutions. (x+5)¹/₂-(5-2 x)¹/₄=0
No extraneous solution to the equation.
The equation is
[tex](x + 5)^{1/2}[/tex] - [tex](5 - 2x)^{1/4}[/tex] = 0
To know whether the equation is an extraneous solution we first need to find the value of x.
So we have,
[tex](x + 5)^{1/2} = (5 - 2x)^{1/4}[/tex]
Multiply both sides with the power of 4, then we have
[tex]((x+ 5)^{1/2})^{4}[/tex] = [tex]((5 - 2x)^{1/4} )^{4}[/tex]
[tex](x+ 5)^{2}[/tex] = 5 - 2x
[tex]x^{2}[/tex] + 10x + 25 = 5-2x
[tex]x^{2}[/tex] + 12x + 20= 0
[tex]x^{2}[/tex] + 10x + 2x + 20 = 0
x(x + 10 ) + 2(x + 10) = 0
(x + 10)(x+2) = 0
x = -10, -2
Now we have to put the value of x in the equation
x = -10
[tex](-10 + 5 )^{1/2}[/tex]-[tex](5 - 2 * -10)^{1/4}[/tex] = 0
[tex](-5)^{1/2}[/tex] - [tex]25^{1/4}[/tex]= 0
[tex](-5)^{1/2}[/tex] - [tex]5^{1/2}[/tex] = 0
Which has not possible as we don't have negative number in the square root.
x = -2
[tex](-2 + 5)^{1/2}[/tex] -[tex](5-2*-2)^{1/4}[/tex]=0
[tex]3^{1/2}[/tex]- [tex]9^{1/4}[/tex]=0
[tex]3^{1/2}[/tex]- [tex]3^{1/2}[/tex]=0
0 = 0
Therefore there is no extraneous solution to the equation
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1.49 round to a whole number
Answer:
the answer is 1
Step-by-step explanation:
trust mehhhh
The data show the traveler spending in billions of dollars for a recent year for a sample of the states. find the range, variance, standard deviation for the data. 20.1, 33.5,21.7,58.4,23.2,110.8,30.9,24.0,74.8,60.0
We know that the measures of dispersion tend to see how numbers are scattered around the mean. In this case, we are asked to find three of the measures of dispersion which are; range, variance and standard deviation.
We first have to arrange the data in the proper order as follows;
20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8
It is now easier for us to find the range of the data set as the difference between the largest and the smallest value; 110.8 – 20.1 = 90.7
The mean of the dataset is = 20.1 + 21.7+ 23.2 + 24.0 + 30.9 + 33.5 + 58.4 + 60.0 + 74.8 + 110.8/10
= 45.74
Now;
Variance = (20.1 - 45.74)^2 + (21.7 - 45.74)^2 + (23.2 - 45.74)^2 + (24.0 - 45.74)^2 + (30.9 - 45.74)^2 + (33.5 - 45.74)^2 + (58.4 - 45.74)^2 + (60.0 - 45.74)^2 + (74.8 - 45.74)^2 + (110.8 - 45.74)^2/10
= 657.4 + 577.9 + 508.1 + 472.6 + 220.2 +149.8 + 160.3 + 203.3 + 844.5 + 4233/10
= 802.71
Standard deviation = √variance = √802.71
= 8.96
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