Question 39.Find the inverse of the given function. Graph both functions on the some set of axes and show the line y=x as a dotted line in the graph.
Answers
First, to find the inverse of a function, call the original function "x" and call call "x" in the original function as the inverse function:
[tex]\begin{gathered} f(x)=5x+1 \\ x=5f^{-1}(x)+1 \end{gathered}[/tex]Now, we solve for the inverse function:
[tex]\begin{gathered} x=5f^{-1}(x)+1 \\ 5f^{-1}(x)+1=x \\ 5f^{-1}(x)=x-1 \\ f^{-1}(x)=\frac{x}{5}-\frac{1}{5} \end{gathered}[/tex]To graph lines, we can find two points in it and draw a line that passes through both.
Let's pick x = 0 and x = 1 for the first equation:
[tex]\begin{gathered} f(0)=5\cdot0+1=1 \\ f(1)=5\cdot1+1=6 \end{gathered}[/tex]So, we plot the points (0, 1) and (1, 6).
For the inverse, we can simply invet the coordinates, which is the same as picking x = 1 and x = 6:
[tex]\begin{gathered} f^{-1}(1)=\frac{1}{5}-\frac{1}{5}=0 \\ f^{-1}(6)=\frac{6}{5}-\frac{1}{5}=\frac{5}{5}=1 \end{gathered}[/tex]Thus, we have the points (1, 0) and (6, 1).
The line y = x is jus the diagonal that passes though point (0, 0) and (1, 1), for example.
Putting these points and drawing the lines, we get:
Related Questions
Solve for the Limit of Function by applying appropriate Limit Theorems
Answers
Answer:
Given to solve,
[tex]\lim _{x\to-1}(2x+2)(x+2)[/tex]From the rules for limits, we can see that for any polynomial, the limit of the polynomial when x approaches a point k is equal to the value of the polynomial at k.
The given function of the limit is a quadratic function, the limit of the quadratic equation when x approaches a point -1 is equal to the value of the quadratic equation at -1.
we get,
[tex]\lim _{x\to-1}(2x+2)(x+2)=(2(-1)+2)((-1)+2)[/tex][tex]=(-2+2)(1)=0[/tex][tex]\lim _{x\to-1}(2x+2)(x+2)=0[/tex]
Answer is : 0
Find the measure of x.26x = [?Round to the nearest hundredth.X78°
Answers
To answer this question we will use the trigonometric function cosine.
Recall that in a right triangle:
[tex]\cos\theta=\frac{AdjacentLeg}{Hypotenuse}.[/tex]Using the given diagram we get that:
[tex]\cos78^{\circ}=\frac{x}{26}.[/tex]Multiplying the above result by 26 we get:
[tex]\begin{gathered} 26\times\cos78^{\circ}=26\times\frac{x}{26}, \\ 26\cos78^{\circ}=x. \end{gathered}[/tex]Therefore:
[tex]x\approx5.41.[/tex]Answer:
[tex]x=5.41.[/tex]
At Bright Futures Middle School, 576 students ride their bike to school . If this number is 75% of the school enrollment, then how many students are enrolled
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
students on bike = 576
% students on bike = 75%
total students = ?
Step 02:
total students
[tex]\text{ \% students on bike = }\frac{students\text{ on bike }}{\text{total students }}\cdot100[/tex][tex]\begin{gathered} 75\text{ = }\frac{576}{\text{total students }}\cdot100 \\ \text{total students = }\frac{576}{75}\cdot100 \end{gathered}[/tex]total students = 768
The answer is:
The number of total students is 768.
The measure of the smallest angle in a right triangle is 45° 45 ° less than the measure of the next larger angle. Find the measures of all three angles.
Answers
Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.
How to measure the three angles?The smallest angle in a right triangle has a measure that is 45° smaller than the next largest angle.As a result, the other two angles' measurements must sum up to 90. The only solution to this would be for both of the remaining angles to be 45 degrees if the lowest angle is 45 degrees less than the next largest angle. The correct angle would be the next biggest angle.Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.To learn more about Right triangle refer to:
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(statistics) solve part A, B, and C in the question on the picture provide, in 1-3 complete sentences each.
Answers
(a.) First let's define the terms;
Population - it is the pool of individual in which a statistical sample is drawn.
Parameter - it is a measure of quantity that summarizes or describes a Population.
Sample - is a smaller and more managable version of a group or population.
Statistics - same with parameter but rather than the population, it summarizes or describes
the sample.
Now that we know the definitions we can now answe the letter a;
Population: Students
Parameter: the population portion of the new students that like the new healthy choices (p)
Sample: 150 students
Statistics: estimated propotion of the students that like the new healthy choices (p-hat)
(b) P-hat = 0.6267 simply means that 62.67% of the 150 sample students like the new healthy choices.
(c) The answer for that is NO, because the simulated propotion which is shown by the graph seems to be equally distributed below and above 0.7. To support the claim of the manager most of the dots should be below 0.7 to show support to his claim that 70% of the new students like the new healthy choices.
How many rays are in the next two terms in the sequence?
Answers
The sequnce is
2, 3, 5, 9, ....
this sequence follows the next formula:
[tex]a_n=2^{n-1}+1[/tex]where an is the nth term.
[tex]\begin{gathered} a_1=2^{1-1}+1=1 \\ a_2=2^{2-1}+1=3 \\ a_3=2^{3-1}+1=5 \\ a_4=2^{4-1}+1=9 \\ a_5=2^{5-1}+1=17 \\ a_6=2^{6-1}+1=33 \end{gathered}[/tex]The next two terms are 17 and 33
f(x) = x^2 g(x) = x^2 - 8 g(x)= x^2 - 8 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g, shift f [up/down/left/right] by [ ] units.
Answers
We have that the parent function (the original function is x^2). If we add a number after it as:
[tex]f(x)=x^2_{}+b[/tex]We affect the function in the y-axis, that is, we move the original function upward or downward.
Therefore, to get the function g, we need to shift the f function down by 8 units, that is
[tex]g(x)=f(x)-8=x^2-8[/tex]Forty percent of 90 is what number
Answers
90 represents the 100%
Let's call x to the number that represents the 40%
To find the 40%, we can use the next proportion:
[tex]\frac{90}{x}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 90\cdot40=100\cdot x \\ \frac{3600}{100}=x \\ 36=x \end{gathered}[/tex]36 is 40% of 90
Large Small
3
Blue 17
Red 8 12
Find: P(Red and Small)
Remember to reduce your answer.
Enter
Answers
Using mathematical operations, we know that P(Red and Small) is 4/3.
What exactly are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an expression.Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).So, simple form of P(Red and Small):
Red balls: 8 (large) + 12 (Small) = 20 red ballsSmall balls: 3 (Blue small balls) + 12 (Red small balls) = 15 small ballsThen, P(Red and Small):
20/154/3Therefore, using mathematical operations, we know that P(Red and Small) is 4/3.
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I survey found that 43 people like chocolate 39 people like peanut butter and 29 people like both draw an empty van diagram with intersections find how many people like only chocolate only peanut butter and both show your work fill in the V diagram according your numbers Calculate how many people are in the survey
Answers
Given:
There are 43 people who like chocolate 39 people like peanut butter and 29 people like both.
To draw: The ven diagram
Explanation:
Since 29 people like both chocolate and peanut butter.
Therefore,
The number of people who like chocolate only is,
[tex]43-29=14[/tex]The number of people who like peanut butter only is,
[tex]39-29=10[/tex]So, the total number of persons is,
[tex]14+29+10=53[/tex]The ven diagram is,
Where C represents the chocolate likers, B represents the peanut butter likers and U represents the total number of persons.
Final answer:
• The number of people who like chocolate only is 14.
,• The number of people who like peanut butter only is 10.
,• The total number of people is 53.
Let MF = 3x - 4 and BM = 5x - 5
Answers
Answer:
Explanation:
a)Here, we want to get the value of x
Mathematically, we know that for a triangle with median M, the length of one of the sides is two times the length of the other side of the median
We have this as:
[tex]BM\text{ }=\text{ 2MF}[/tex]Using the side lengths given, we have it that:
[tex]\begin{gathered} 5x-5\text{ = 2(3x-4)} \\ 5x-5\text{ = 6x-8} \\ 6x-5x=8-5 \\ x\text{ = 3} \end{gathered}[/tex]b) We want to find the length of MF. We just have to substitute the value of x in the expression for MP
Mathematically, we have this as:
[tex]MF\text{ = 3(3)-4 = 9-4 = 5}[/tex]c) We want to find the length of BM
[tex]5x-5\text{ = 5(3)-5 = 15-}5\text{ = 10}[/tex]d) Here, we want to find the length of BF
[tex]\begin{gathered} BF\text{ = BM + MF} \\ BF\text{ = 10 + 5 = 15} \end{gathered}[/tex]O DESCRIPTIVE STATISTICInterpreting relative frequency-histogramsStudents at a major university in Southern California are complaining about a serious housing crunch. Many of the university's students, they complain, have tocommute too far to school because there is not enough housing near campus. The university officials' response is to perform a study. The study, reported in theschool newspaper, contains the following histogram summarizing the commute distances for a sample of 100 students at the university:Relative frequencyCommute distance (in miles)Based on the histogram, find the proportion of commute distances in the sample that are at least 16 miles. Write your answer as a decimal, and do not roundyour answer
Answers
Since the graph gives us the relative frequency we just have to add those who are more or equal to 16; in this case we have to add 0.11 and 0.06, therefore the proportion in this case is 0.17
Explain if the triangles are similar using SAS-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)
Answers
We have two triangles GBL and XYL.
From the picture we notice that the GL=39 and BL=34. We also notice that XL=30 and YL=27.
The SAS theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
This means that we need that:
[tex]\frac{GL}{XL}=\frac{BL}{YL}[/tex]and that the angle between them is the same.
It is clear that the angle L is the same for both triangles, hence we only need to proof tha the sides are congruent, but in this case:
[tex]\frac{39}{30}\ne\frac{34}{27}[/tex]since the sides are not proportional, we conclude that triangles are not congruent.
Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:
Answers
Given:
Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.
The total number of sample space is, N = 10.
Head for female kitten
T for male kitten.
The objective is to find the probability that at least three of the kittens will be male.
Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4
Now, the probability of at least three of the kittens will be male can be calculated by,
[tex]undefined[/tex]Evaluate the expression when a=3 and b=6. b2-4a
Answers
b² - 4a
evaluated when a = 3 and b = 6 is:
6² - 4(3) =
= 36 - 12=
= 24
Two Way Tables, URGENT
Answers
Step-by-step explanation:
a) modal number is 3
b) mean is x = ∑fx/n
= ((5•1)+ (2•10)+(3•15)+(7•4)+(3•5))/(5+10+15+7+3)
= 113/40
= (Decimal: 2.825)
Hello I I am confused because their are two different letters.
Answers
Let's begin by listing out the information given to us:
Line AB is parallel to Line CD; this implies that the angle formed by the two lines are right angles (90 degrees)
E is the intersecting point of both lines AB & CD (figure attached)
Let us put this into its mathematical form:
[tex]\begin{gathered} m\angle AED=(6x-24)=90^{\circ} \\ 6x-24=90\Rightarrow6x=90+24 \\ 6x=114\Rightarrow x=19 \\ x=19 \\ m\angle CEB=(4y+32)=90^{\circ} \\ 4y+32=90\Rightarrow4y=90-32 \\ 4y=58\Rightarrow y=17 \\ y=17 \end{gathered}[/tex]If the correlation coefficient r is equal to 0.755, find the coefficient of determination and the coefficient of nondetermination.Question 10 options: The coefficient of determination is 0.430 and the coefficient of nondetermination is 0.570 The coefficient of determination is 0.869 and the coefficient of nondetermination is 0.131 The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430 The coefficient of determination is 0.131 and the coefficient of nondetermination is 0.869
Answers
Given the word problem, we can deduce the following information:
The correlation coefficient r is equal to 0.755.
To determine the coefficient of determination and the coefficient of nondetermination, we use the formulas below:
[tex]Coefficient\text{ }of\text{ }Determination=r^2[/tex][tex]Coefficient\text{ }of\text{ N}ondetermination=1-r^2[/tex]Now, we first plug in r=0.755 to get the coefficient of determination:
[tex]Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ D}eterm\imaginaryI nat\imaginaryI on=r^2=(0.755)^2=0.57[/tex]Next, we get the coefficient of nondetermination:
[tex]\begin{gathered} Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ N}ondeterm\imaginaryI nat\imaginaryI on=1-r^2=1-0.57=0.43 \\ \end{gathered}[/tex]Therefore, the answer is:
The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430
Write an exponential function in the form y = ab that goes through points (0,18) and (3,6174).
Answers
Using the first point given in the statement you can find a, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 0 and y = 18} \\ 18=ab^0 \\ 18=a\cdot1 \\ 18=a \end{gathered}[/tex]Now, since you already have the value of a, you can find the value of b using the second point, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 3 and y = 6174} \\ 6174=18\cdot b^3 \\ \text{ Divide by 18 into both sides of the equation} \\ \frac{6174}{18}=\frac{18\cdot b^3}{18} \\ 343=b^3 \\ \text{ Apply cube root to both sides of the equation} \\ \sqrt[3]{343}=\sqrt[3]{b^3} \\ 7=b \end{gathered}[/tex]Therefore, the exponential function that passes through the points (0,18) and (3,6174) is
[tex]y=18\cdot7^x[/tex]For the compound inequalities below (5-7), determine whether the inequality results in an overlapping region or a combined region. Then determine whether the circles are open are closed. Finally, graph the compound inequality. Simplify if needed. x-1>_5 and 2x<14
Answers
The inequalities are:
[tex]x-1\ge5\text{ and }2x<14[/tex]So, we need to solve for x on both inequalities as:
[tex]\begin{gathered} x-1\ge5 \\ x-1+1\ge5+1 \\ x\ge6 \end{gathered}[/tex][tex]\begin{gathered} 2x<14 \\ \frac{2x}{2}<\frac{14}{2} \\ x<7 \end{gathered}[/tex]Now, we can model the inequalities as:
So, the region that results is an overlapping region and it is written as:
6 ≤ x < 7
So, the lower limit 6 is closed and the upper limit 7 is open.
Answer: The region is overlaping and it is 6 ≤ x < 7
Hello! I need some help with this homework question, please? The question is posted in the image below. Q6
Answers
Step 1
Given;
[tex]g(x)=3x^2-5x-2[/tex]Required; To find the zeroes by factoring
Step 2
Find two factors that when added gives -5x and when multiplied give -6x
[tex]\begin{gathered} \text{These factors are;} \\ -6x\text{ and x} \end{gathered}[/tex][tex]\begin{gathered} -6x\times x=-6x^2 \\ -6x+x=-5x \end{gathered}[/tex]Factoring we have and replacing -5x with -6x and x we have
[tex]\begin{gathered} 3x^2-6x+x-2=0 \\ (3x^2-6x)+(x-2)_{}=0 \\ 3x(x-2)+1(x-2)=0 \\ (3x+1)(x-2)=0 \\ 3x+1=0\text{ or x-2=0} \\ x=-\frac{1}{3},2 \\ \text{The z}eroes\text{ are, x=-}\frac{1}{3},2 \end{gathered}[/tex]Graphically the x-intercepts are;
The x-intercepts are;-1/3,2
Hence, the answer is the zeroes and x-intercepts are the same, they are;
[tex]-\frac{1}{3},2[/tex]Triangle DEF is rotated 60⁰ clockwise about the vertex to obtain triangle LMN. if the m
Answers
EXPLANATION
The measure of the angle LMN is equal to 40 degrees, then the measure of the angle LMN is the same because the rotation does not modify the angle.
Identify the leading coefficient, degree and end behavior. write the number of the LC and degree
Answers
Given
[tex]P(x)=-4x^4-3x^3+x^2+4[/tex]Solution
The LC is -4
End behavior is determined by the degree of the polynomial and the leading coefficient (LC).
TThe degree of this polynomial is the greatest exponent is
[tex]\begin{gathered} x\rightarrow\infty\text{ then P\lparen x\rparen} \\ p(\infty)=-4(\infty)^4-3(\infty)^3+\infty^2+4 \\ p(\infty)=-4\infty^4-3\infty^3+\infty^2+4 \\ P(\infty)=-\infty \\ \end{gathered}[/tex][tex]\begin{gathered} x\rightarrow-\infty \\ p(-\infty)=-4(-\infty)^4-3(-\infty)^3+(-\infty)^2+4 \\ P(-\infty)=-4\infty^4+3\infty^3+\infty^2+4 \\ P(-\infty)=-\infty \end{gathered}[/tex]The degree is even and the leading coefficient is negative.
The final answer
u(x) = 4x - 2 w(x) = - 5x + 3The functions u and w are defined as follows.Find the value of u(w(- 3)) .
Answers
Solution
- We are given the two functions below:
[tex]\begin{gathered} u(x)=4x-2 \\ \\ w(x)=-5x+3 \end{gathered}[/tex]- We are asked to find u(w(-3)).
- In order to find u(w(-3)), we need to first find u(w(x)) and then we can substitute x = -3.
- Since we have been given u(x), then, it means that we can find u(w) as follows:
[tex]\begin{gathered} u(x)=4x-2 \\ u(w),\text{ can be gotten by substituting w for x} \\ \\ u(w)=4w-2 \end{gathered}[/tex]- But we have an expression for w in terms of x. This means that we can say:
[tex]\begin{gathered} u(w)=4w-2 \\ \\ w(x)=-5x+3 \\ \\ \therefore u(w(x))=4(-5x+3)-2 \\ \\ u(w(x))=-20x+12-2 \\ \\ \therefore u(w(x))=-20x+10 \end{gathered}[/tex]- Now that we have an expression for u(w(x)), we can proceed to find u(w(-3)) as follows:
[tex]\begin{gathered} u(w(x))=-20x+10 \\ put\text{ }x=-3 \\ \\ u(w(-3))=-20(-3)+10 \\ \\ u(w(-3))=60+10=70 \end{gathered}[/tex]Final Answer
The answer is
[tex]u(w(-3))=70[/tex]the score on the right is a scaled copy of the square on the left identify the scale factor express your answer in the simplest form
Answers
Answer
Scale factor = 3.5
Explanation
Scale factor expresses how much the copy/image of the original figure is bigger or smaller than the original figure.
If the scale factor is more than 1, then the image is an enlargement of the original figure.
But if the scale factor is less than 1, then the image is a reduction of the original figure.
Mathematically,
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Length of a side of the image or scaled copy = 56
Corresponding length of that side on the original figure = 16
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Scale factor = (56/16) = (7/2) = 3.5
Hope this Helps!!!
Answer
Scale factor = 3.5
Explanation
Scale factor expresses how much the copy/image of the original figure is bigger or smaller than the original figure.
If the scale factor is more than 1, then the image is an enlargement of the original figure.
But if the scale factor is less than 1, then the image is a reduction of the original figure.
Mathematically,
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Length of a side of the image or scaled copy = 56
Corresponding length of that side on the original figure = 16
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Scale factor = (56/16) = (7/2) = 3.5
Hope this Helps!!!
Collinear points are two or more points that lie on the sameA. planeB. angleC. lineD. space
Answers
Collinear points are two or more points that lie on the same line.
For Example:
Point A, B and C
Select all statements that are true about equilateral triangle ABC.
Answers
To determine statements that are correct, we proceed as follows:
Step 1: We recall the definition of an "equilateral" triangle
An equilateral triangle is one which"
- has all its sides equal to each other
- has all its internal angles equal to 60 degrees each
From the above definition, it can be concluded that
(A) Angles B and C are 60 degrees is a true statement
Step 2: We solve the triangle for x, as follows:
Now, consider the left right-triangle:
Now, we apply the sine trigonometric ratio to obtain the value of x,
[tex]undefined[/tex]the perimeter of the rectangle belowis 112 units. Find the value of y
Answers
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]SSS
L
J
++
A) LJ=HF
LK=LG
C)
K
H
G
F
B) LJ LF or
D) ZL=LH
Answers
Answer:
A. LJ≅HF
Step-by-step explanation:
Same as last time
Given the sequence 4, -16, 64, -256..a) Write the explicit rule for the sequence. b) Find a7 c) Write the recursive rule for the sequence.
Answers
the given series is 4 -16 64 -256
that is
4 x -4 = -16 = -4^2
-16 x -4 = 64 = 4^3
64 x -4 = -256 = -4^4
so we can say that is every time the number is multiplied with -4,
for a7, as 7 is an odd number so the negative sign will be there from the above observations
-4^7 = -16384
the recursive rule will be'
[tex]a_n=a_{n-1}\times-4[/tex]