Answers
Answer:
[tex]f^-^1(x)=\frac{x+1}{8}[/tex]
Step-by-step explanation:
f(x) = 8x - 1
==> replace "f(x)" with y
y = 8x - 1
==> inter exchange x and y
x = 8y - 1
==> solve for y now, first step would be to add 1 to both sides
x + 1 = 8y
==> divide both sides by 8
(x+1)/8 = y
==> replace y with f^-1(x)
f^-1(x)=(x+1)/8y
Related Questions
Part II: Graph the following inequalities on the coordinate grid provided. 5. y > 2x + 1 4. y
Answers
Given the inequality;
[tex]y\ge2x+1[/tex]to draw the inequality, first we need to graph the line y = 2x + 14
As the sign is > or equal , so the line will be solid line
So, the following image is the graph of the inequality
the shaded area represents the solution of the inequality
I need to see if I answer the problem Correctly
Answers
For every 2 green rattles, it sells 7 yellow rattles.
The ratio of green to yellow rattles sold is: 2:7
Total rattles sold: 108
Yellow rattles sold:
(total rattles/sum of ratio) x yellow ratio
(108/9)*7 = 12*7 = 84 rattles
84 yellow rattles
Which expressions are equivalent to the one below? Check all that apply.log71 •logg 25O A. 2• log77OB. 1O COO D. 5.7
Answers
Problem
[tex]\log ^1_7\text{ . }\log ^{25}_5[/tex][tex]\begin{gathered} =\text{ }\log ^{1\text{ }}_7\text{ x }\log ^{5^2}_5 \\ =\text{ }\log ^1_7\text{ x 2}\log ^5_5 \\ \log ^1_7\text{ = 0 and }\log ^5_5\text{ = 1} \\ =\text{ 0 }\times\text{ 2 }\times\text{ 1} \\ \text{= 0} \end{gathered}[/tex]Final answer
Option C is equivalent to the expression.
You survey 100 people in your school and ask them if they feel your school has adequate parking.
Only 30% of the sample feels the school has enough parking. If you have 728 students total in your school, how many would you expect out of all the student body that felt there was enough parking?
Answers
Answer:
218 students feel there is enough parking.
Step-by-step explanation:
First, we convert 30% into a decimal by moving the decimal point over twice to get 0.30. Then, we set up this equation:
0.30 x 728 = 218.4
Now, you can't have a fraction of a person, so we round to the nearest whole number to get 218 students.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The lines represented by the equations y + 3/2x = 7 and 9y - 6x = 27 are O parallel Submit Answer the same line O neither parallel nor perpendicular O perpendicular
Answers
y+3/2x=7 (a)
9y-6x=27 (b)
Express both lines in slope-intercept form:
y= mx+b
Where :
m= slope
b= y-intercept
a.
y= -3/2x+7
m= -3/2
b.
9y-6x=27
9y= 6x+27
y= (6x+27)/9
y= 2/3x+3
m= 2/3
Both slopes are negative reciprocals of each other.
If two lines have negative reciprocal slopes, they are perpendicular lines.
PERPENDICULAR.
Derive the following functionsa) (2x+1)⁴b) f(x) = [tex] \sqrt{6x + 3} [/tex]
Answers
Given:
18.
[tex]f(x)=\sqrt[]{6x-3}[/tex]To find the derivative of the given function, we apply chain rule first:
Therefore, the answer is :
[tex]\frac{3}{\sqrt[]{6x-3}}[/tex]The following sets of data show the high temperatures in four different cities for a week in December
Answers
the data that have the greatest spread are
(3, 12, 25, 34, 51)
Every time I type this in a calculator it’s shown 9.99999999999999999999
Answers
Given
[tex]\frac{2}{11}\times\frac{1}{2}[/tex]Answer
[tex]\begin{gathered} \frac{2}{11}\times\frac{1}{2} \\ =\frac{1}{11} \\ =0.909090\ldots \end{gathered}[/tex]Enter an equation in point-slope form for the line.Slope is -8 and (1,4) is on the line.The equation of the line in point slope form is:
Answers
y - 4 = -8 ( x - 1)
Explanations:The point slope form of the equation of a line is given as:
y - y₁ = m (x - x₁)
Where m represents the slope of the line
(x₁, y₁) are the coordinates of the point
Slope is -8 and (1,4) is on the line
m = -8
x₁ = 1
y₁ = 4
Substituting these into the equation:
y - y₁ = m (x - x₁)
y - 4 = -8 ( x - 1)
y=8x+3 ordered pairs
Answers
Answer: (1, 11) and (-1, -5), OPTION C
We are given the equation
y = 8x + 3
This implies that the value of y is a function of x
Firstly, we need to test the options
For (1, 11)
From the point given, let x = 1 and y = 11
Substitute the value of x and y in the above equation
Since, y = 8x + 3
11 = 8(1) + 3
11 = 8 + 3
11 = 11
This implies that (1, 11) satisfied the equation y = 8x + 3
For (-1, -5)
Let x = -1 and y = -5
-5 = 8(-1) + 3
-5 = -8 + 3
-5 = -5
The point (-1, -5) satisfies the equation y = 8x + 3
Hence, the answer is (1, 11) and (-1, -5)
use the function g=f+4 to find the value of g when f=1use the function u=10c to find the value of u when c=5how about this one use the function u=n-5 to find the value of u when n=7this one use the function h=g+13 to find the value of h when g =1use the function w=14f to find the value of w when f =4
Answers
Given function g=f+4
To find the value of g at f=1
substitute f=1 in the given equation
[tex]\begin{gathered} g=f+4 \\ g=1+4 \\ g=5 \end{gathered}[/tex]So, at f=1, the value of g will be 5.
(b).
At u=10c
to find the value of u at c=5
substitute the value c=5 in the given equation
[tex]\begin{gathered} u=10c \\ u=10\times5 \\ u=50 \end{gathered}[/tex]The value of u at c=5 is 50
(c).
Given function u=n-5
to find the value of u at n=7
substitute the value of n=7 in the given equation
[tex]\begin{gathered} u=n-5 \\ u=7-5 \\ u=2 \end{gathered}[/tex]So the value of u at n=7 is 2
(d).
Given function h=g+13
to find the value of h at g=1
substitute the value g=1 in the given equation
[tex]\begin{gathered} h=g+13 \\ h=1+13 \\ h=14 \end{gathered}[/tex]The value of h at g=1 is 14
(e).
Given function w=14f
to find the value of w at f=4
substitute the value f=4 in the given equation
[tex]\begin{gathered} w=14f \\ w=14\times4 \\ w=56 \end{gathered}[/tex]The value of w at f=4 is 56
GM no isiecrjreieief G k if f D F hi it
Answers
Solution
Proportion is represented by colon:
Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What is P(A and B)?
Answers
Given:
Events A and B are independent.
P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Required:
P(A and B).
Answer:
We have given that P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Then P(B)=
[tex]\begin{gathered} P(B)=1-P(not\text{ B}) \\ P(B)=1-\frac{2}{3}=\frac{1}{3} \end{gathered}[/tex]Hence, P(A and B)=
[tex]P(A)\cdot P(B)=\frac{3}{5}\times\frac{1}{3}=\frac{1}{5}[/tex]Final Answer:
P(A and B)=
[tex]\frac{1}{5}[/tex]suppose that R(x) is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros. Answer the following.Edit: if its ok please double-check the answers.
Answers
According to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
It is given to us that -
R(x) is a polynomial of degree 12 whose coefficients are real numbers.
The zeroes of R(x) are -
-6, -2+3i, -2-3i, 5+i
We have to find out -
(a) Another zero of R(x)
(b) The maximum number of real zeroes that R(x) can have
(c) The maximum number of non-real zeroes that R(x) can have
Since R(x) is a polynomial of degree 12, there are in total 12 roots.
(a) If a non-real, complex, root 5+i exists, then so it's conjugate 5-i exists which is another zero of R(x).
(b) Now, the total number of zeroes of R(x) can be stated as -
-6, -2+3i, -2-3i, 5+i, 5-i
From the above list of zeroes, we can see that there are at least 4 non-real zeroes. So, R(x) has a total of 12 zeroes and we know that there are at least 4 non-real zeroes.
Thus, we can say that the maximum number of real zeroes that R(x) can have is 12-4 = 8 real zeroes.
(c) The non-real complex zeroes always exist in conjugate pairs. And the total number of zeroes that R(x) can have is 12. And we already have determined that R(x) can have a maximum of 8 real zeroes.
Thus, the maximum number of non-real zeroes that R(x) can have is 12-8 = 4 non-real zeroes.
Therefore, according to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
To learn more about polynomial roots visit https://brainly.com/question/11906453
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The distance between two distinct points: ordered pair 1 (x , y) and ordered pair 2 (x, y) is given by the formula ____?____.(I need the formula)
Answers
Given an ordered pair 1:
[tex]\mleft(x,y\mright)[/tex]And a distinct ordered pair 2:
[tex](x,y)[/tex]You can rewrite them as:
[tex]\begin{gathered} (x_1,y_1) \\ \\ (x_2,y_2) \end{gathered}[/tex]According to the Pythagorean Theorem, for Right Triangles:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where "c" is the hypotenuse and "a" and "b" are the legs of the Right Triangle.
Then, you can set up that:
Then, to find the hypotenuse of the Right Triangle or the distance "d" between the points, you can apply the Pythagorean Theorem and set up that:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the answer is:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]COMPARING METHODS Consider the equation x+ 2 = 3x – 4.a. Solve the equation using algebra.
Answers
Answer: 2
We are given the equation
x + 2 = 3x - 4
To solve for x.
Firstly, we need to collect the like terms
x - 3x = -4 - 2
-2x = -6
Divide both sides by -2
-2x/-2 = -6/-2
x = -6/-2
Negative sign will cancel negative sign
x = 6/2
x = 2
The answer is 2
What is the area of parallelogram ABCD?This is a diagram of parallelogram ABCD. Point A is located at (2,1). Point B is located at (8,1). Point C is located at (11,5). Point D is located at (5,5).A. 30 units²B. 55 units²C. 24 units²D. 12 units²
Answers
If we draw the given points, we have the following:
The area of a parallelogram can be calculated as the height of it multiplied by its lenght of the base.
In this case, the height will be the distance of the coodinate y = 1 to the coordinate y = 5, which is equal to Δy = 5-1 = 4.
And the base is the distance from the point A to point B, which can be calculated as Δx = 8 - 2 = 6
Now, using the formula, we have:
[tex]\begin{gathered} A_{parallelogram}=b\times h \\ \\ A_{parallelogram}=6\times5 \\ \\ A_{parallelogram}=30\text{ }units² \end{gathered}[/tex]From the solution developed above, we are able to conclude that the correct answer for the present question is:
A. 30 units²Please ensure that you provide the important points (the x and y - intercepts, and the vertices),and please clearly label them on the Cartesian coordinate system. [15 points]
Answers
Given the piece-wise function
[tex]k(x)=\begin{cases}|x|,x\ge3 \\ \\ 2x^2-4x+3,x<3\end{cases}[/tex]The graph of
[tex]|x|\text{ for x }\ge3[/tex]Is shown below
The graph of
[tex]2x^2-4x+3\text{ for x < 3}[/tex]Is shown below
The graph of the piece-wise function is shown below
The blue curve represents the quadratic function and the red line represent the absolute function
the sum of z and 24 is equal to 116
Answers
Given that the sum of z and 24 equals 116, we can represent this statement as follows
We can then proceed to solve the equation by following the steps below:
[tex]z+24=116[/tex]Step 1: subtract 24 from both sides
[tex]z+24-24=116-24[/tex]Step 2: simplify the expression
[tex]z=92[/tex]Thus the value of Z = 92
Ab and CD are opposite sides so ab are congruent to CD 2a=34 a=17 find the value of each variable
Answers
Two segments of lines or two angles are congruent if the have the same length and the same measure, respectively. In a parallelogram, a geometric figure which opposite sides are parallel, opposite sides are congruent and opposite angles are also congruents.
In this case CD is opposite to AB, so they are congruent and have the same length. Since the segment AB measures 2a and the segment CD mesures 34, then we have the equation
[tex]\begin{gathered} 2a=34 \\ a=\frac{34}{2} \\ a=17. \end{gathered}[/tex]Similarly, the angles A and C are congruent since they are opposite, so their measurement is the same. Since the angle A measures 8b and the angle C measures 112, then we have the next equation
[tex]\begin{gathered} 8b=112 \\ b=\frac{112}{8} \\ b=14 \end{gathered}[/tex]
The slope of a graph is ratio of the change in the y - variable to the change in the x - variable True or false
Answers
ANSWER
True
EXPLANATION
We want to understand the meaning of slope.
The slope of a graph is known as the rate of change of the dependent variable with the independent variable.
It is the rate of change of the graph.
This means that it tells us how the y values of the graph vary with the x values.
Therefore, the slope of a graph is ratio of the change in the y - variable to the change in the x - variable.
Exercise #1: We would like to find the distance between points A and B if they have coordinates A(2,3) and B(14, 12). B (a) Sketch the right triangle below that could be used to calculate the length of AB and find its length using the Pythagorean Theorem. (b) How could we calculate the lengths of the legs of the right triangle in (a) from the coordinates of points A and B.
Answers
Answer
Check Explanation
Explanation
We've been asked to find the length of the distance between points A (2, 3) and B (14, 12).
a) First of, we've been asked to sketch the right angle triangle that coulb be used to calculate the distance AB
The sketch will be shown below
So, the figure above represents the right angle triangle that can be used to calculate the distance AB
Distance AB = hyp = ?
Distance between the x-coordinates of points A and B = x = 14 - 2 = 12
Distance between the y-coordinates of points A and B = y = 12 - 3 = 9
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are x and y respectively,
x² + y² = (hyp)²
For this question,
x = 12 units
y = 9 units
hyp = AB = ?
x² + y² = (hyp)²
12² + 9² = AB²
144 + 81 = AB²
225 = AB²
We can rewrite this as
AB² = 225
Take the square root of both sides
√(AB²) = √(225)
AB = 15 units
b) The second part of the question asks how we calculated the legs of the right angle triangle that we used to solve this distance between AB.
Since both points lie on given x and y axis levels in the coordinate system, the length of the legs of this right angle triangle is obtained simply by taking the difference between respective x and y coordinates.
For the base of the triangle,
Distance between the x-coordinates of points A and B
= x
= 14 - 2
= 12 units
For the height of the triangle,
Distance between the y-coordinates of points A and B
= y
= 12 - 3
= 9 units
Hope this Helps!!!
draw out the system on the bottom of the graph and chose what postulate proves the triangle is congruent hlsssaassasasa
Answers
The given postulates are:
hl: Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
sss: Two triangles have the corresponding three sides congruent (3 corresponding sides have the same measure)
aas: Two angles and a side not between those angles are congruent.
sas:Two sides and an angle between those sides are congruent.
asa: Two angles and a side between those angles are congruent.
---------------------
In the system you have two triangles that share side AC. Then one side is congrent in the triangles.
The line AC bisects angles BAD and BCD, it means taht the angle is equal up and down that line.
Then, the system has two angles and the side between those angles congruent. Triangles are congruent by asa18 in3.4.35 km5.6.15.6 amy7 mm7.8.58 yd10.2 m78-* 306.3: 243.47: 144:: 497: 8171 267*: 8417
Answers
We need to calculate the area of the circle
[tex]\begin{gathered} \text{Area of circle =}\pi r^2 \\ \text{radius of circle = 29ft,} \\ Area\text{ of circle = }\pi\text{ }\times(29ft)^2 \\ \text{Area of circle = }\pi\text{ }\times841ft^2 \\ \text{Area of circle = 84}1\pi ft^2 \end{gathered}[/tex]Therefore
The area of the circle is 841 square feet
Hello, I need some assistance with this homework question please for precalculusHW 23
Answers
ANSWER
slope = 1
EXPLANATION
Given:
Points (1, 2) and (8, 9).
Desired Outcome:
Slope of the line
Applying the slope formula
[tex]slope\text{ = }\frac{y_2\text{ - y}_1}{x_2\text{ - x}_1}[/tex]where:
y2 = 9,
y1 = 2
x2 = 8 and
x1 = 1
Substituting the values
[tex]\begin{gathered} slope\text{ = }\frac{9\text{ - 2}}{8\text{ - 1}} \\ slope\text{ = }\frac{7}{7} \\ slope\text{ = 1} \end{gathered}[/tex]Hence, the slope of the line containing the points (1, 2) and (8, 9) is 1.
Simplify the expression:9m + 6( m + 7 )
Answers
ANSWER
15m + 42
EXPLANATION
We want to simplify:
9m + 6(m + 7)
To do this, first expand the bracket:
9m + 6m + 42
Now, collect like terms and simplify:
15m + 42
That is the simplified expression.
Graph the following relation. Use the graph to find the domain and range (in interval form) and indicate whetherthe graph is the graph of a function.y = -4 Domain: Range { }
Answers
Given:
[tex]y=-4[/tex]Required:
To draw the graph and find the domain and range.
Explanation:
The graph of the function will be,
We know that,
The domain is the set of all input values for the function and the range is the set of all output values for the function.
Therefore, we get,
[tex]\begin{gathered} Domain:(-\infty,\infty) \\ Range:\lbrace-4\rbrace \end{gathered}[/tex]Yes, it is a function.
Because each input value has exactly one output value.
Final answer:
[tex]\begin{gathered} Domain:(-\infty,\infty) \\ Range:\lbrace-4\rbrace \end{gathered}[/tex]
And it is a function.
If A= { 1,2,4,5,7,9} and B= {2,3,4} and U = {1,2,3,4,5,6,7,8,9} Find A’
Answers
SOLUTION
Given the sets in the question tab, the following are the solution steps to get the answer
Step 1: Write the given sets
[tex]\begin{gathered} A=\mleft\lbrace1,2,4,5,7,9\mright\rbrace \\ B=(2,3,4\} \\ U=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace \end{gathered}[/tex]Step 2: Find A'
A' denotes the complement of set A. The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. The Universal set is denoted by capital letter U.
Hence, the elements in set A' will be the elements present in the set U but not set A
[tex]A^{\prime}=\mleft\lbrace3,6,8\mright\rbrace[/tex]a)Kat's equation b) Carter's equation c) After how many car washes will they both have the same amount of money? d) How much money will they each have
Answers
Answer:
a) Kat's equation is 10 + 12x = Amount
b) Carter's equation is 85 + 7x = Amount
c)
Explanation:
Kat has $10 saved up in her account and charges $12 for each car she washes, the equation representing this is:
10 + 12x
Where x is the number of cars she washes.
Carter's equation is:
85 + 7x
I
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is y=-0.2x + 1. Graph the equation and use it to answer questions 1 and 2. a. What is the x-intercept? What does it represent? b. What is the y-intercept? What does it represent?c. After how many hours is the battery power at 75%d. what is the percentage of battery power remaining at 3 hours?
Answers
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is given by
[tex]y=-0.2x+1[/tex]Let us graph the above equation
a. What is the x-intercept? What does it represent?
The x-intercept is the point where the line intersects the x-axis.
From the graph, we can see that the x-intercept is (5, 0)
The x-intercept represents that it takes 5 hours for the battery power to go to 0%
You can manually find out the x-intercept by substituting y = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ 0=-0.2x+1 \\ 0.2x=1 \\ x=\frac{1}{0.2} \\ x=5 \end{gathered}[/tex]Therefore, the x-intercept is (5, 0)
b. What is the y-intercept? What does it represent?
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the y-intercept is (0, 1)
The y-intercept represents that the battery power is 1 (100%) when x = 0 hours.
You can manually find out the y-intercept by substituting x = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(0)+1 \\ y=1 \end{gathered}[/tex]Therefore, the y-intercept is (0, 1)
c. After how many hours is the battery power at 75%
We need to substitute y = 0.75 (that means 75%) into the equation to find out x (number of hours)
[tex]\begin{gathered} y=-0.2x+1 \\ 0.75=-0.2x+1 \\ 0.75+0.2x=1 \\ 0.2x=1-0.75 \\ 0.2x=0.25 \\ x=\frac{0.25}{0.2} \\ x=1.25\: \text{hours} \end{gathered}[/tex]Therefore, after 1.25 hours, the battery power is at 75%
d. what is the percentage of battery power remaining at 3 hours?
We need to substitute x = 3 hours into the equation to find out y (remaining battery power)
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(3)+1 \\ y=-0.6+1 \\ y=0.4 \end{gathered}[/tex]Therefore, the remaining battery power is 40% after 3 hours.