Answers
Answer:
\(g^-^1(x)=-8\)
\(h^-^1(x)=\frac{x-4}{3}\)
\((h^-^1 \ o\ h)(-3)=-3\)
Step-by-step explanation:
When given the following functions,
\(g=[(-2,-7),(4,6),(6,-8),(7,4)]\)
\(h(x)=3x+4\)
One is asked to find the following,
1. Question 1
\(g^-^1(4)\)
When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;
\(g^-^1(4)\)
\(g(4)=6\\g(6)=-8\\g^-^1(4)=-8\)
2. Question 2
\(h^-^1(x)\)
Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,
\(h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)\)
\(h^-^1(x)=\frac{x-4}{3}\)
3. Question 3
\((h^-^1 \ o\ h)(-3)\)
This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function (\(h^-^1\)) and simplify. Then substitute (-3) into the result.
\(h^-^1\ o\ h\)
\(\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x\)
Now substitute (-3) in place of (x),
\(=-3\)
Related Questions
Express the given trigonometric functions in terms of the same function of a positive acute angle.sec 948 degrees, cos(-948) degrees
Answers
Given the Trigonometric Functions:
\(\begin{gathered} sec(948\text{\degree}) \\ \\ cos(-948\text{\degree}) \end{gathered}\)Using your calculator you get:
\(sec(948\text{\degree})\approx-1.49\)By definition, Secant is negative in Quadrant III.
Finds its Reference Angle as follows:
\(948\text{\degree}-5\cdot180\text{\degree}=48\text{\degree}\)Because:
\(\frac{948}{180}\approx5\)Then, you get:
\(=-sec\left(48\text{\degree}\right)\)Notice that:
\(cos(-948\text{\degree})\approx-0.67\)Then, you can conclude that it is in Quadrant II.
Therefore its Reference Angle is:
\(5\cdot180\text{\degree}-948\text{\degree}=-48\)So you can set up:
\(=-cos\lparen-48)\)By definition:
\(cos(-\theta)=cos\theta\)Therefore, you can rewrite it in this form:
\(=-cos(48\text{\degree})\)Hence, the answer is:
\(\begin{gathered} sec(48\text{\degree}) \\ \\ -cos(48\text{\degree}) \end{gathered}\)23. (3 + d4)2 - (c + d), if c= -1 and d= 2
Answers
Answer:
here u go
Step-by-step explanation:
ur answer is 21
A truck with 30-in.-diameter wheels is traveling at 50 mi/h.
Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes:
_________rad/min
How many revolutions per minute do the wheels make?
___________rpm
Answers
Answer:
A. the angular speed is 3771.4 rad/min
b. 5921 rpms
Step-by-step explanation: I just got this same question right on a test.
Ryan sprinted 139 feet. How many yards did he sprint
Answers
Answer:
Ryan sprinted 46.33 yards.
Step-by-step explanation:
Ryan sprinted 139 feet.
1 feet = 0.33 Yard
Formula: Divide the length value by 3
Now,
139 ÷ 3 = 46.33
Thus, Ryan sprinted 46.33 yards.
-TheUnknownScientist
6x + y = 8
y= -6x + 8
Answers
Answer:
y = -6x + 8
Step-by-step explanation:
\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}
I don't know why it came out like this
I buy 4 5/8 blue fabric and 2 1/8 green fabric how much blue than green did i buy
Answers
Answer:
2.5
Step-by-step explanation:
We Know
You buy 4 5/8 blue fabric and 2 1/8 green fabric .
4 5/8 = 37/8 = 4.625 blue fabric
2 1/8 = 17/8 = 2.125 green fabric
How much blue than green did you buy?
We Take
4.625 - 2.125 = 2.5
So, you buy 2.5 blue more than green.
What is 5,421 rounded to the nearest hundred?
A.4,000
B.5,000
C.5,4000
D.5,200
Answers
Answer:
5,000
Step-by-step explanation:
it cant be 400 because the 4 in 5,421 is going to turn into a zero and everything behind that zero is a 0 as well and the thousand place is before the 0 so it stays the same
How many cartwheels can Suzy do? :)
Answers
Answer:
100 :)
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
If y varies inversely as X and y=16 when X=4,find y when X=32
Answers
\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)
Multiply the following using the vertical multiplication method:
Answers
Answer: A) 3x⁴ - x³ + 3x² + 18x + 4
Step-by-step explanation:
Vertical Multiplication is the same with polynomials as it is for numbers.
How would you multiply 1 2 3
x 4 5
You would multiply the top row by 5, shift everything one space to the left and multiply everything by 4, and then add those values.
We do the same for polynomials.
3x² + 5x + 1
x² - 2x + 4
4(3x² + 5x + 1) --> 12x² + 20x + 4
-2x(3x² + 5x + 1) --> -6x³ - 10x² - 2x
x²(3x² + 5x + 1) --> 3x⁴ + 5x³ + 1x²
Sum: 3x⁴ - 1x³ + 3x² + 18x + 4
For the rational function f(x)=x-2/3x^2+x-2, fill in the points on the graph at the function value f(x)=2.
Answers
Answer:
(-2/3, 2), (1/2, 2)
Step-by-step explanation:
A graphing calculator can show you those points: (-2/3, 2), (1/2, 2).
__
Put the given value in the equation and solve for x.
2 = f(x)
2 = (x -2)/(3x^2 +x -2)
2(3x^2 +x -2) -(x -2) = 0 . . . . . multiply by the denominator; put in standard form
6x^2 +x -2 = 0 . . . . . collect terms
(3x +2)(2x -1) = 0 . . . factor
Solutions are values of x that make the factors zero:
x = -2/3, x = 1/2
Then the points on the graph are (-2/3, 2) and (1/2, 2).
Ryan is saving for his college tuition. He has $2,550 in a savings account that pays 6.25% annual interest.
Answers
Which figures have point symmetry?
Answers
The figure has a line of symmetry and the point of symmetry is square. The correct answer would be an option (D).
What is the line of symmetry?A line of symmetry is a line that perfectly splits a shape in half. This indicates that if you divided the form along the line, both sides would precisely match. Similarly, if you placed a mirror along the line, the form would not alter.
According to the question
Line symmetry and point symmetry :
For
a) trapezoid
The trapezoid has no line of symmetry.
There is no point of symmetry in a trapezoid with only one set of parallel sides.
b) quadrilateral
There are no lines of symmetry or points of symmetry in the quadrilateral.
c) pentagon
A regular pentagon has 5 sides and 5 lines of symmetry.
There is no point of symmetry in a regular pentagon.
d) square
A square has four symmetry lines.
A square has four symmetry points.
Hence, the figure contains a line of symmetry with a square point of symmetry.
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The question is incomplete, the complete question would be as:
Which figure has line symmetry and point symmetry
a)trapezoid b)quadrilateral c)pentagon d)square
Mikey bikes 12 miles in 2 hours. How many miles does Mikey bike in an hour?
Answers
Answer:
6 miles
Step-by-step explanation:
2 hours can be made into 1 hour by dividing by 2. In order to keep the ratio, you also have to divide the miles by 2, giving you 6.
2:12
1:6
These tables represent a quadratic function with a vertex at (0,3). What is the
average rate of change for the interval from x = 7 to x = 8?
х
Interval
у
3
0
1
2
-1
-6
Average rate
of change
-1
1-2
-3
1-2
-5
1-2
-7
1-2
-9
1-2
-11
O to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
3
4
TTT
5
-13
-22
-33
6
Answers
Answer: -15
Step-by-step explanation:
The average rate of change for the interval from x = 7 to x = 8 is -15. The correct option is B.
What is quadratic function?A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.
Since the quadratic function has a vertex at (0,3), the equation for the function can be written in vertex form as:
y = a(x - 0)^2 + 3
Where "a" is a constant that determines the shape of the parabola. To find the value of "a", we can use one of the other points on the parabola. Let's use the point (1, 2):
2 = a(1 - 0)^2 + 3
Simplifying this equation, we get:
a = -1
So the equation for the quadratic function is:
y = -x^2 + 3
Now we can use this equation to find the average rate of change between x = 7 and x = 8. The value of the function at x = 7 is:
y = -7^2 + 3 = -46
The value of the function at x = 8 is:
y = -8^2 + 3 = -61
The average rate of change between x = 7 and x = 8 is:
(y2 - y1) / (x2 - x1) = (-61 - (-46)) / (8 - 7) = -15
Therefore, the average rate of change for the interval from x = 7 to x = 8 is -15.
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Please look at the photo. Thank you.
Answers
a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².
b) The side length that gives the maximum area that the playground can have is x = 30 m.
c) The maximum area that the playground can have is 900 m².
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths, we have:
120 = 2(x + W)
60 = x + W
W = 60 - x
Therefore, the area of the rectangular playground (in terms of x) is given by this function;
A = LW
A(x) = x(60 - x)
A(x) = 60x - x²
Part b.
For the side length, we would take the first derivative of the area:
A(x) = 60x - x²
A'(x) = dA/dx
A'(x) = 60 - 2x
60 - 2x = 0
x = 60/2
x = 30 m
Part c.
W = 60 - x
W = 60 - 30
W = 30 m.
Therefore, the maximum area is given by;
A = 30 × 30
A = 900 m².
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10 + 2x = 8 Can someone help me with this I forgot how to do this. Also please do a step by step please so i could use it to look off of for future problems.
Answers
Answer:
x = -1
Step-by-step explanation:
So you gotta work backwards a little bit here
Think about it as...
You have 10 of something, and you have to have 8 of them
Now typically you'd just subtract but in this problem it wants you to add a number
Soooo that means it has to be a negative number that you're adding
Ten plus what number would be 8? -2
So x must equal -1
2 x -1 = -2
And 10 + -2 = 8
Hope this makes sense! :)
The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (U.S. Department of Energy website, February 22, 2008). A portion of the data for 311 compact, midsize, and large cars follows. The column labeled Class identifies the size of the car; Compact, Midsize, or Large. The column labeled Displacement shows the engine's displacement in liters. The column labeled Fuel Type shows whether the car uses premium (P) or regular (R) fuel, and the column labeled HwyMPG shows the fuel efficiency rating for highway driving in terms of miles per gallon.
a) Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement.
Let x represent the engine's displacement.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x
b) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?: ____%
c) Consider the addition of the dummy variables ClassMidsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of ClassMidsize and the value of ClassLarge are both 0. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement and the dummy variables ClassMidsize and ClassLarge. Let x1 represent engine's displacement. Let x2 represent variable ClassMidsize. Let x3 represent variable ClassLarge.If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x1 + ___ x2 + ___ x3
d) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? : ___ %
e) Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement, the dummy variables ClassMidsize and ClassLarge, and the dummy variable FuelPremium. Let x1 represents engine's displacement. Let x2 represents variable ClassMidsize. Let x3 represents variable ClassLarge. Let x4 represents variable FuelPremium. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x1 + ___ x2 + ___ x3 + ___x4
f) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? : ___ %
Answers
a) Y=38.6594-5.4198x; b) 39.1% explained variation; c) Y=44.9379-5.9522x1-1.2758x2-2.0102x3; d) 49.9% explained variation; e) Y=45.2478-6.1081x1-0.9945x2-2.5692x3+0.9963x4; f) 53.1% .
a) The estimated regression equation for predicting fuel efficiency for highway driving is Y = 38.6594 - 5.4198x, where x represents the engine's displacement in liters.
b) The estimated regression equation explains 39.1% of the variation in the sample values of HwyMPG.
c) The estimated regression equation that includes the dummy variables ClassMidsize and ClassLarge is Y = 44.9379 - 5.9522x1 - 1.2758x2 - 2.0102x3, where x1 represents engine's displacement, x2 represents variable ClassMidsize, and x3 represents variable ClassLarge.
d) The estimated regression equation with the added dummy variables explains 49.9% of the variation in the sample values of HwyMPG.
e) The estimated regression equation that includes the dummy variable FuelPremium is Y = 45.2478 - 6.1081x1 - 0.9945x2 - 2.5692x3 + 0.9963x4, where x1 represents engine's displacement, x2 represents variable ClassMidsize, x3 represents variable ClassLarge, and x4 represents variable FuelPremium.
f) The estimated regression equation with all three dummy variables explains 53.1% of the variation in the sample values of HwyMPG.
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m varies directly as n, and m = 14 when n = 7. Write a direct proportion equation using the above information.
Answers
With constant of proportionality=2, the direct proportion equation for the given information is m = 2n.
What is a constant of proportionality?
A constant of proportionality is a value that relates two variables that are directly proportional to each other. In a direct proportion, if one variable (say, x) increases by a certain factor, then the other variable (say, y) also increases by the same factor. The constant of proportionality is the ratio of the two variables.
For example, if y varies directly with x, we can write:
y = kx
where k is the constant of proportionality.
Now,
If m varies directly as n, then we can write:
m = k * n
where k is a constant of proportionality. To find the value of k, we can use the given information that m = 14 when n = 7:
14 = k * 7
Solving for k:
k = 14/7
k = 2
Substituting this value of k in the direct proportion equation:
m = 2n
Therefore,
the direct proportion equation for the given information is m = 2n.
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1) The perimeter of a rectangular garden is 344M. If the width of the garden is 76M, what is its length?
Equation:
Solution:
(I need the equation and solution)
2) The area of a rectangular window is 7315CM^2 (^2 is squared). If the length of the window is 95CM, what is its width?
Equation:
Solution:
(Once again, I need the equation and solution)
3) The perimeter of a rectangular garden is 5/8 mile. If the width of the garden is 3/16 mile, what is its length?
4) The area of a rectangular window is 8256M^2 (^2 is squared). If the length of the window is 86M, what is its width?
5) The length of a rectangle is six times its width. The perimeter of the rectangle is 98M, find its length and width.
6) The perimeter of the pentagon below is 58 units. Find VW. Write your answer without variables.
Answers
The length of the rectangle is 96 m, the width of the rectangle is 77 cm , the length of the rectangle is 1/8 mile, the length and width of the rectangle is 7 m and 42 m respectively, VW is 11 units.
According to the question,
1) Perimeter of rectangle = 344 M
Width = 76 M
Perimeter of rectangle = 2(length + width)
2(length+76) = 344
length+76 = 172
length = 172-76
Length of the rectangle = 96 M
2) Area of a rectangular window = 7315 \(cm^{2}\)
Length of the window is 95 cm.
Area of rectangle = length*width
95*width = 7315
width = 7315/95
Width of the rectangle = 77 cm
3) The perimeter of a rectangular garden is 5/8 mile.
The width of the garden is 3/16 mile.
Perimeter of rectangle = 2(length+width)
2(length+3/16) = 5/8
length+3/16 = 5/(2*8)
length = 5/16-3/16
Length of the rectangle = 2/16 or 1/8 mile
4) The area of a rectangular window is 8256 \(m^{2}\).
The length of the window is 86 m.
Area of rectangle = length*width
86*width = 8256
width = 8256/86
Width of the rectangle = 96 m
5) The length of a rectangle is six times its width. The perimeter of the rectangle is 98 m.
Let's take width of the rectangle to be x m.
Length of rectangle = 6x m
2(length+width) = 98
2(6x+x) = 98
2*7x = 98
14x = 98
x = 98/14
x = 7 m
Width = 7 m
Length = 7*6 m or 42 m
6) The perimeter of the pentagon is 58 units.
3z+10+z+3+2z-1+10 = 58
6z+10+3-1+10 = 58
6z+22 = 58
6z = 58-22
6z = 36
z = 36/6
z = 6 units
VW = 2z-1
VW = 2*6-1
VW = 12-1
VW = 11 units
Hence, the answer to 1 is 96 m , 2 is 77 cm, 3 is 1/8 mile , 4 is 96 m , 5 is 7 m and 42 m and 6 is 11 units.
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i need help i will crown brainiest
Answers
Answer:25 if your looking for the number of ways to order 5 objects
Step-by-step explanation:
If your looking for the probability of 1 number the ways for it to be arranged l believe It is 5x5 hope this helps
Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Answers
Explanation
The square root of a number is “what number times itself”
2 x 2 = 4
3 x 3 = 9
7 is between 4 and 9 so C is the correct answer
Please help thank you
Answers
I can't see the whole paper the sentences is cut
what is the answer I need help
Answers
Answer:
Step-by-step explanation:
The vertex is at (-3, -1) and the leading coefficient is negative ( because the curve is inverted)
y = -a(x + 3)^2 - 1
One point on the curve is (-2, -3) so
-3 = -a(-2+3)^2 - 1
-3 = -a - 1
-a = -2
So we have
y = -2(x + 3)^2 - 1
y = -2(x^2 + 6x + 9) - 1
y = -2x^2 - 12x - 19.
how does h (x) =-0.1x-5 change over the interval from x=2 to x=4
Answers
The given expression is,
\(h(x)==0.1x-5\)Let us first consider, x = 2. We have,
\(h(2)=0.1\times2-5=-4.98\)Now, let us take x = 4, we have,
\(h(4)=0.1\times4-5=-4.6\)So the range is, -4.98 to -4.6. So, h (x) decreases by 0.3
In two or more complete sentences, explain how to use ordered pairs of points in and to determine if and are inverses of each other.
Answers
For any point (x, y), that DOESN'T appear in one function, the point (y, x) must NOT appear in the other function.
So if you find any point that DOESN'T meet the above rules, you can prove that the functions are NOT inverses of each other.
But if you want to prove that they ARE inverses of each other, you have to check ALL points in the functions, and there are infinity of them, so that's not practical. Instead, you can write f(x) like this:
y = 3x - 5
Now solve for x:
y + 5 = 3x
x = (y + 5) / 3
Now swap x and y:
y = (x + 5) / 3
This is the same as g(x). Therefore the functions are inverses of each other. oh
What is the range of y = 7x^2 + 14x – 9?
Answers
Answer:
-1,-16
Step-by-step explanation:
y=ax^2+box+c
what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
help with this question please i need help
Answers
Answer:
⇒ X = (-2/7, 48/7)
Step-by-step explanation:
Use this formula to find the point X.
([mx₂ + nx₁] / [m+n], [my₂ + ny₁] / [m+n])
Where m:n is the ratio, and the points are x₁, y₁ and x₂, y₂.
The formula can be thought like this:
When the midpoint of a line is taken, we take the average of the x coordinates and the average of the y coordinates. This is in the ratio 1:1.
If we were to take the point on a line in a ratio [m:n], we take the weighted average.
X = ([3*2 + 4*-2] / [3 + 4], [3*4 + 4*9] / [3 + 4])
∴ X = (-2/7, 48/7)
Answer:
So I did the work, but it won't let me upload a picture of it, so when I solved it my answer that I had gotten foe this solution was x(-2/7,48/7).
I hope it was correct for you.
A flower bed is 2 meters wide and 3 meters long.What is the area of the flower bed i square feet? Round your converted dimensions and your final answer to the nearest hundredth show your work.
Answers
Answer:
64.58
Step-by-step explanation:
1 meter is 3.28084 so 3 meters is 9.84252 because you multiply it by 3 or add them to each other 3 times. 2 meters is 6.56168 because you multiply it by 2 or add them to each other. now that you have 6.56168 and 9.84252 multiply them with each other and you get 64.5834666336 but it was said to round to nearest hundredth so since the 3 in front of the 8 is not a 5 and above the answer is 64.58 and not 64.89