Consider the graph shown. Which ordered pairs are on the inverse of the function? Check all that apply.
Answers
Notice that the graph of the function is a cubic polynomial. Also, the graph is moved one unit upwards, then, the function f(x) is:
[tex]f(x)=x^3+1[/tex]now, we can see from the y and x intercepts, that if we evaluate x= 0 and x = 1, we get:
[tex]\begin{gathered} f(0)=-1 \\ f(1)=0 \end{gathered}[/tex]then, applying the inverse function on both sides (we can do this since f(x) is a polynomial function and they always have inverse function), we get the following:
[tex]\begin{gathered} f^{-1}(f(0))=f^{-1}(-1) \\ \Rightarrow0=f^{-1}(-1) \end{gathered}[/tex]we can see that the first point that is on the graph of the inverse function is (-1,0). Doing the same on the second equation, we get:
[tex]\begin{gathered} f^{-1}(f(1))=f^{-1}(0) \\ \Rightarrow f^{-1}(0)=1 \end{gathered}[/tex]thus, the points that lie on the inverse function are (-1,0) and (0,1)
Related Questions
Y + 41 = 67 solve y using one step equation
Answers
Answer:
Y = 26
Step by step explanation:
[tex]y\text{ + 41 = 67}[/tex]
Then we pass the 41 to substract.
[tex]y\text{ = 67 - 41 = 26}[/tex]A tutoring service charges an initial consultation fee of $50 plus $25 for each tutoringsession.A. Write an equation that determines the total cost of tutoring services (y) based on thenumber of tutoring sessions (x).B. If a student decides to purchase 8 tutoring sessions, what will be his total cost?c. If a student had a total cost of $200, how many tutoring sessions did he attend?EditVioInsertFormatThols Table
Answers
A. y = 50 + 25x
B. number of session (x) = 8
Substitute x= 8 in the equation y= 50 + 25x
y = 50 + 25( 8 )= 50 + 200 = $250
The total cost for 8 tutoring sessions is $250
C. y = $200
x= ?
y = 50 + 25x
200 = 50 + 25x
200 - 50 = 25x
150 = 25x
Dividing through by 25
x = 150/25 =6
He attended 6 tutoring sessions
The area of Bryce is 71.5 sq units.what is the area of abcd?
Answers
Solution
Step 1:
Area of BXYC = 71.5 square units
Step 2:
The area of ABCD is twice the area of BXYC
Step 3:
[tex]\begin{gathered} \text{Area of ABCD = 2 }\times\text{ Area of BXYC} \\ Area\text{ of ABCD = 2 }\times\text{ 71.5} \\ Area\text{ of ABCD = 143 square units} \end{gathered}[/tex]Mike is shopping for new clothes. He has a coupon for 20% off of his total purchase. His purchase price before the discount is $68. Let T represent the total cost after the discount. Which equation can be written to model this scenario? Select all that apply.68-0.2(68) = T68 - .20 =T68-20 = T0.8(68) = T0.2(68) =T
Answers
ANSWER
68 - 0.2(68) = T
0.8(68) = T
EXPLANATION
The coupon allows for 20% off of his total purchase.
His purchase price before the discount is $68.
To find the price after the discount, we can use two methods:
=> Find 20% of $68 and then subtract from $68 to get T.
That is:
[tex]\begin{gathered} 68\text{ - (}\frac{20}{100}\cdot\text{ 68) = T} \\ \Rightarrow\text{ 68 - 0.2(68) = T} \end{gathered}[/tex]=> Subract 20% from a total of 100% and then multiply by $68 to get T.
That is:
[tex]\begin{gathered} (100\text{ - 20)\% }\cdot\text{ 68 = T} \\ \Rightarrow\text{ 80\% }\cdot\text{ 68 = T} \\ \Rightarrow\text{ 0.8(68) = T} \end{gathered}[/tex]Those are the two answers.
Illustrate the ratio 7:3 using 'X' for 7 and 'y for 3
Answers
Given the ratio:
7:3
To illustrate the ratio above using x for 7 and y for 3, we have:
All you need to do is to replace 7 with x and replace 3 with y
7 : 3 ==> x : y
ANSWER:
x : y
4y - 6 = 2y + 8how to solve this equation
Answers
To solve this equation, we need to collect like terms
To collect like terms, we bring the terms similar to each other to the same side
In this case, the value having y will be brought to same side of the equation
Kindly note that if we are bringing a particular value over the equality sign, then the sign of the value has to change
This means if negative, it becomes positive and if positive, it becomes negative
Proceeding, we have
4y - 2y = 8 + 6
2y = 14
divide both sides by 2
2y/2 = 14/2
y = 7
The value of y in this equation is 7
A study determined that 9% of children under 18 years of age live with their father only. Find the probability that at most 2 persons selected at random from 12 children under18 years of age lived with their father onlyThe probability that at most 2 children live with their father only is(Do not round until the final answer. Then round to the nearest thousandth as needed)
Answers
Step 1: Write out the formula for binomial distribution
[tex]P(x)=^nC_x\times p^x\times q^{n-x}[/tex]Where
[tex]\begin{gathered} p\Rightarrow\text{probability of success} \\ q\Rightarrow\text{probability of failure} \\ n\Rightarrow\text{ number of trails } \\ x\Rightarrow\text{ number of success required} \end{gathered}[/tex]Step 2: State out the parameters needed in the formula to find the probabilty
[tex]\begin{gathered} p=9\text{ \%=}\frac{9}{100}=0.09 \\ q=1-p=1-0.09=0.91 \\ n=12 \\ x\Rightarrow\le2\Rightarrow0,1,2 \end{gathered}[/tex]Step 3: The probability that at most 2 children live with their father only can be described as;
[tex]P(x\le2)=P(0)+P(1)+P(2)[/tex]Step 4: Find the probability of each number of successes required
[tex]\begin{gathered} P(0)=^{12}C_0\times(0.09)^0\times(0.91)^{12-0} \\ P(0)=1\times1\times0.322475487=0.322475487 \end{gathered}[/tex][tex]\begin{gathered} P(1)=^{12}C_1\times(0.09)^1\times(0.91)^{12-1} \\ =^{12}C_1\times(0.09)^1\times(0.91)^{11} \\ =12\times0.09\times0.354368667=0.38271816 \end{gathered}[/tex][tex]\begin{gathered} P(2)=^{12}C_2\times(0.09)^2\times(0.91)^{12-2} \\ =^{12}C_2\times(0.09)^2\times(0.91)^{10} \\ =66\times0.0081\times0.389416118=0.208181856 \end{gathered}[/tex]Step 5: Add all the number of successess required
[tex]\begin{gathered} P(x\le2)=0.322475487+0.38271816+0.208181856 \\ =0.913375503 \\ \approx0.913 \end{gathered}[/tex]Hence, the probability that at most 2 children live with their father only is 0.913
at Kelly's school, 2/3 of the play ground is covered by grass, and 3/5 of the grassy area is a baseball field. how much of the school playground is baseball feild?
Answers
At Kelly's school, 2/3 of the playground is covered by grass, and 3/5 of the grassy area is a baseball field.
How much of the school playground is the baseball field?
SOLUTION
2/3 of the playground is covered by grass and 3/5 of the grassy area is a baseball field.
The area of the school playground which is baseball field =
[tex]\frac{2}{3}\text{ x }\frac{3}{5}\text{ = }\frac{6}{15\text{ }}\text{ = }\frac{2}{5}[/tex]CONCLUSION :
[tex]\frac{2}{5}\text{ of the school field = Area of the Basket Ball Field.}[/tex]
1) A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours. a) What does the 65 tell us in this situation? b) How many miles does the car travel in 1.5 hours? Show your work. c) How long does it take the car to travel 26 miles at this speed? Show you
Answers
The equation d = 65t
represents the distance (d) the car travels at a 65 mile speed in t hours
a. 65 tells us the speed at which the car travels
b. If the car travels in 1.5 hrs, then
d = 65(1.5)
= 97.5 milestone.
c. To travel 26 miles, we have d = 26
26 = 65t
t = 26/65
= 0.35 (approximately)
x^2 = 16, therefore x = 4.
Is this a valid conclusion? If not, give a counterexample.
Answers
Is x5 + x2 + x a polynomial? Explain why or why not.
Answers
A polynomial is a mathematical expression formed by variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponentiation of variables.
The expression:
[tex]x^5+x^2+x[/tex]Is formed by the addition of three terms, each consisting of the variable x raised to a positive integer quantity. Therefore, the given expression is a polynomial.
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Answers
Answer:
3d - 15.70 = 2.30
Step-by-step explanation:
We don't know the cost of one DVD, so let's use d to represent this unknown variable. Eddie sold 3 DVDs, so 3 multiplied by d equals his total earnings.
Eddie then used $15.70 of his earnings to buy a pair of headphones. We can represent this by subtracting 15.70 from the total earnings (3d).
After buying/subtracting the price of the headphones from his total earnings, Eddie had $2.30 left over, which can be represented by making 3d - 15.70 equal 2.30.
So, the final equation turns out to be: 3d - 25.70 = 2.30
:)
4 boxes of crayons cost $12.50 How much would 16 boxes cost? (Show work) Thank you!
Answers
Answer:
$50.08
Step-by-step explanation:
Find the unit rate.
[tex]\frac{12.50}{4}[/tex] Each box cost $3.125. We cannot have .125 cents, so round up to 3.13
3.13 x 16 = $50.08
f(x) = square root of x - 5. find f^-1 (x) and it’s domain
Answers
Given:
f(x) = root x - 5
Rewrite the function using y,
[tex]y=\sqrt[]{x}-5[/tex]Now, interchange the position of x and y in the function,
[tex]x=\sqrt[]{y}-5[/tex]Isolate the dependent variable
[tex]\begin{gathered} \sqrt[]{y}=x+5 \\ y=(x+5)^2 \end{gathered}[/tex]Therefore,
[tex]f^{-1}(x)=(x+5)^2[/tex]And the domain is minus infinity to infinity
[tex]\begin{gathered} f^{-1}(x)=(x+5)^2 \\ \text{Domain}=(-\infty,\infty) \end{gathered}[/tex]Give me a rhombus ABCD with BC =25 and BD= 30 find AC and the area of ABCD
Answers
300 u²
1) Let's start by sketching out this:
2) Since a Rhombus have 4 congruent sides, then we can state that 4 sides are 25 units, and we need to find out the other Diagonal (AC)
Applying the Pythagorean Theorem, to Triangle COD
a² =b² +c²
25² = 15² +c²
625 = 225 + c² subtract 225 from both sides
625-225 = c²
400 = c²
√c² =√400
c =20
2.2) Now, we can calculate the area, applying the formula for the area of a rhombus (the product of its diagonals).
[tex]\begin{gathered} A=\frac{D\cdot d}{2} \\ A=\frac{40\cdot30}{2} \\ A=\frac{1200}{2} \\ A\text{ = 600} \end{gathered}[/tex]3) Hence, the answer is 300 u²
5. Graph the function f (x) = 3sin (2x) + 1 Be sure to identify the midline, period, and amplitude.
Answers
Given that f(x) = 3 sin (2x) + 1
Given that : a sin (bx + c ) + d
let a = amplitude,
Midline is the that runs between the maximum and minimum value
[tex]\begin{gathered} \text{ Since, amplitude = 3} \\ \text{the graph is shifted 1 unit in positive y - coordinate} \\ \text{Maximum value = 3 - 1 = 2} \\ \text{ minimum value = -3 - 1 = -4} \\ \text{Midline is the center of (2, - 4)} \\ \text{Midline = }\frac{\text{2 - 4}}{2} \\ \text{midline = -1} \end{gathered}[/tex]Period is calculated as
[tex]\begin{gathered} \text{period = }\frac{2\pi}{|b|} \\ \\ \text{b = 2} \\ \text{Period = }\frac{2\pi}{2} \\ \text{Period = }\pi\text{second} \end{gathered}[/tex]Frequency = 1 / period
[tex]\text{frequency = }\frac{1}{\pi}\text{ Hz}[/tex]Perform the following matrix row operation and write the new one.
Answers
Given: A matrix
[tex]\begin{bmatrix}{1} & {-3} & {2} \\ {3} & {9} & {5} \\ {} & & {}\end{bmatrix}[/tex]Required: To perform the following matrix row operation
[tex]-3R_1+R_2[/tex]Explanation: The operation is to be applied on the first row of the given matrix. Hence the second row will be same as that of the initial matrix.
The elements of the first row are first multiplied by 3 and then added with second row to give the required matrix.
Hence,
[tex]\begin{bmatrix}{-3+3} & {9+9} & {-6+5} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]which gives
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Final Answer: The required matrix is
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Which of the following tables shows a uniform probability model?
Answers
The answer is the third choice
Where all probability are equal
Find the slope, if it exists, of the line containing the pair of points. (−2,−6) and (−15,−7)
Answers
The linear regression for a given data set has the form
[tex]y=a+bx[/tex]where the values a and b can be solved using the equation
[tex]\begin{gathered} a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2} \\ b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2} \end{gathered}[/tex]Based on the given data set, we have n equals 5. We will solve for the values of the summation first. We have the following
[tex]\begin{gathered} \sum y=4+4+6+6+8=28 \\ \sum x=1+3+5+7+9=25 \\ \sum xy=(1\cdot4)+(3\cdot4)+(5\cdot6)+(7\cdot6)+(8\cdot9)=160 \\ \sum x^2=1^2+3^2+5^2+7^2+9^2=165^{} \\ (\sum x)^2=25^2=625 \end{gathered}[/tex]Using these values to compute for the values of a and b, we get
[tex]\begin{gathered} a=\frac{(28\cdot165)-(25\cdot160)}{5(165)-625}=\frac{31}{10}=3.1 \\ b=\frac{5(160)-(28\cdot25)}{5(165)-625}=\frac{1}{2}=0.5 \end{gathered}[/tex]Take note that the problem wants us to reduce the numbers to the nearest tenth. Hence, the linear regression for the given data set is written as
[tex]y=3.1+0.5x[/tex]clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. before treatment 19 subjects had a mean wake time of 100.0 min after treatment the 19 subjects had a mean wake time of 71.6 min and a standard deviation of 20.4 min assume that the 19 sample value appears to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatment what does the result suggest about the wake time of 100.0 min before the treatment does the drug appears to be effective
Answers
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=71.6.
The sample size is N=19.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{20.4}{\sqrt{19}}=\dfrac{20.4}{4.359}=4.68[/tex]The degrees of freedom for this sample size are:
[tex]df=n-1=19-1=18[/tex]The t-value for a 99% confidence interval and 18 degrees of freedom is t=2.878.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.878\cdot4.68=13.471[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=M-t\cdot s_M=71.6-13.471=58.129 \\ UL=M+t\cdot s_M=71.6+13.471=85.071 \end{gathered}[/tex]The 99% confidence interval for the mean is (58.129, 85.071). This interval does not include the value 100, so we can conclude that there is statistical evidence that the treatment reduces the mean wake time.
Find the links of the sides of these special triangles
Answers
From the triangle, we express the tangent of 60° as:
[tex]\tan 60\degree=\frac{Z}{7}[/tex]But tan(60°) = √(3), then:
[tex]\begin{gathered} \frac{Z}{7}=\sqrt[]{3} \\ \Rightarrow Z=7\sqrt[]{3}\text{ ft} \end{gathered}[/tex]A loan is paid off in 15 years with a total of $192,000. It had a 4% interest rate that compounded monthly.
What was the principal?
Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.
Answers
The principal amount with the given parameters if $165.
Given that, Amount = $192,000, Time period = 15 years and Rate of interest = 4%.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100} )^{nt}[/tex]
Now, [tex]192,000=P(1+\frac{4}{100} )^{15\times 12}[/tex]
⇒ [tex]P=\frac{192,000}{(1.04)^{180}}[/tex]
⇒ P = $164.93
≈ $165
Therefore, the principal amount with the given parameters if $165.
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Answer:
Step-by-step explanation:
Use the compound interest formula and substitute the values given: $192,000=P(1+.0412)12(15). Simplify using order of operations: $192,000=P(1+.0412)180
P=192,000(1+.0412)180
P≈$105477.02
At 3:00 PM a man 138 cm tall casts a shadow 145 cm long. At the same time, a tall building nearby casts a shadow 188 m long. How tall is the building? Give your answer in meters. (You may need the fact that 100 cm = 1 m.)
Answers
A tall man(138cm) casts a shadow of 145cm
A building nearby casts a shadow of 188m
Using the information you have to determine the height of the building.
First step is to convert the units of the height of the man and the length of his shadow from cm to meters:
100cm=1m
So 145cm=1.45m
And 138co=1.38m
Now that the measurements are expressed in the same units you can determine the height shadow ratio of the man and use it to calculate the height of the bulding.
[tex]\frac{\text{height}}{\text{shadow}}=\frac{1.38}{1.45}[/tex]Compare this ratio with the ratio between the heigth/shadow ratio of the building to determine the heigth of the building.
Said height will be symbolized as "x"
[tex]\begin{gathered} \frac{1.38}{1.45}=\frac{x}{188} \\ x=(\frac{1.38}{1.45})188 \\ x=178.92m \end{gathered}[/tex]The building is 178.92m
HELP!! My question isUsing the formula below, solve when s is 3The formula is A = 6s² and I need to know the steps on how to solve it please help! I really dont understand and my teacher is not at school to help me
Answers
The given expression : A = 6s²
Substitute s = 3 in the given expression
A = 6s²
A = 6(3)²
as : 3² = 3 x 3
3² = 9
A = 6 x 9
A = 54
Answer : A = 54
White the inequality shows by the shaded region in the graph with the boundary line y=x/3-5
Answers
From the given figure
Since the line is a dashed line, then
The sign of inequality does not have equal (< OR > )
Since the shading area is down the line, then
The sign of inequality should be smaller than (<)
Then the inequality is
[tex]y<\frac{x}{3}-5[/tex]A retail clothing store offers customers an opportunity to open up a credit card during checkout. One location of the retail clothing store states that the number of credit cards, A, that are opened t months since January can be modeled by the function A(t) = 15 + 3t. The number of credit cards opened at another location, B, is defined by the function B(t) = 25 − t. What is an expression that can be used to determine the total amount of credit cards opened at the two locations?
(A + B)(t) = 40 + 4t
(A + B)(t) = 40 + 2t
(A − B)(t) = −10 + 2t
(A − B)(t) = −10 + 4t
Answers
The expression that is useful to determine the total amount of credit cards opened at the two locations is (A + B)(t) = 40 + 2t so option (B) is correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
The amount in location A is given as
A(t) = 15 + 3t
The amount in location B is given as
B(t) = 25 − t
The total amount combined between A and B is given as,
(A + B)(t) = 15 + 3t + 25 - t
(A + B)(t) = 15 + 25 + 3t - t
(A + B)(t) = 40 + 2t
Hence "The expression that is useful to determine the total amount of credit cards opened at the two locations is (A + B)(t) = 40 + 2t".
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Write and solve the equation that has been modeled below.
Answers
Solution
[tex]\begin{gathered} x+x+1+1+1+1+1+1+1=1+1+1+1+1+1+1+1+1 \\ 2x+7=9 \\ \text{Separate similar terms} \\ 2x=9-7 \\ 2x=2 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{2}{2} \\ \\ x=1 \end{gathered}[/tex]The final answer
[tex]x=1[/tex]Line AB and line DA are?
Answers
Answer:
perpendicular
Step-by-step explanation:
Square
Rectangle
Right triangle
Cube
Rectangular prism
are all examples of perpendicular shapes
i hope this helped
have a good day ^^
Which equation has at least one solution? Mark all that app A. 2x-1= 2 B. 3 y + 1) = 3y 1 C. 5p - (3 + p) = 6p + 1 D. 4/5m=1-1/5m E. 10 +0.5w =1/2w - 10 F. 4a + 3(a - 2) = 8a - (6 + a) Answer Choices:
Answers
Let's check the options
A.
2x - 1 = 2
2x= 3
x= 3/2=1.5
option A has atleast one solution
B
3y+ 1 = 3y
option B has no solution
C.
5p - (3 + p) = 6p + 1
5p - 3 - p = 6p + 1
4p - 6p = 1 + 3
-2p = 4
p =-2
option C has atleast one solution
D.
4/5 m = 1- 1/5 m
4/5 m + 1/5m = 1
1m = 1
m = 1
Option D has atleast one solution
E.
10 + 0.5w = 1/2w - 10
0.5 w - 1/2 w = -10 - 10
option E has no solution
F.
4a + 3(a-2) = 8a - (6+a)
4a +3a - 6 = 8a -6 - a
7a -6 = 7a - 6
option F has many solution. Hence it also has atleast one solution
Therefore;
option A, C, D and F has atleast one solution
Fowler has a collection of marbles of different sizes and colors. Big Small Red 9 9 Green 14 9 Purple 9 6 Blue 0 10 What is the probability that a randomly selected marble is not red or is not small? Simplify any fractions.
Answers
From the given table, the following are observed:
No. of marbles that are not red and not small = No. of Big Green and Big Purple
= 14 + 9
= 23 Marbles
Total number of marbles = 9 + 14 + 9 + 9 + 9 + 6 + 10 = 66 Marbles
We get,
[tex]\text{ Probability of getting a marble that is not red or not small = }\frac{\text{ 23 Marbles}}{66\text{ Marbles}}[/tex][tex]\text{ = }\frac{23}{66}[/tex]We can no longer simplify 23/66. Therefore, 23/66 is the answer.