Hi I’m looking to get a step by step solution in solving this problem in the red
Answers
Given:
[tex]\begin{gathered} f(x)=13x+2 \\ \\ g(x)=3x^2-13 \\ \\ h(x)=\frac{13}{x+13} \end{gathered}[/tex]Find-:
The inverse of a function.
Explanation-:
(a)
For the inverse of a function, x change as y and y change as x and solve for 'y'
[tex]\begin{gathered} f(x)=13x+2 \\ \\ f(y)=13y+2 \\ \\ x\rightarrow y \\ \\ y\rightarrow x \\ \\ \end{gathered}[/tex]Then solve,
[tex]\begin{gathered} y=13x+2 \\ \\ y-2=13x \\ \\ x=\frac{y-2}{13} \end{gathered}[/tex]So, value,
[tex]f^{-1}(y)=\frac{y-2}{13}[/tex](b)
[tex]g(x)=3x^2-13[/tex]So, the value is:
[tex]g(y)=3y^2-13[/tex]The inverse of a function is:
[tex]\begin{gathered} x=3y^2-13 \\ \\ x\rightarrow y \\ \\ y\rightarrow x \\ \\ y=3x^2-13 \\ \\ 3x^2=y+13 \\ \\ x^2=\frac{y+13}{3} \\ \\ x=\sqrt{\frac{y+13}{3}} \end{gathered}[/tex]So, the inverse value is:
[tex]g^{-1}(y)=\sqrt{\frac{y+13}{3}}[/tex](c)
[tex]h(x)=\frac{13}{x+13}[/tex]Value of h(y) is:
[tex]h(y)=\frac{13}{y+13}[/tex]Then solve for inverse function,
[tex]\begin{gathered} x=\frac{13}{y+13} \\ \\ x\rightarrow y \\ \\ y\rightarrow x \\ \\ y=\frac{13}{x+13} \\ \\ y(x+13)=13 \\ \\ x+13=\frac{13}{y} \\ \\ x=\frac{13}{y}-13 \end{gathered}[/tex]So, inverse value is:
[tex]h^{-1}(y)=\frac{13}{y}-13[/tex]
Related Questions
An unusual die has the numbers 2,2,3,3, 7 and 7 on its six faces. Two of these dice are rolled, and the numbers on the top faces are added. How many different sums are possible?
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To find the total numbers of sum, we just have to elevate the number of faces by the second power.
[tex]6^2=36[/tex]There are 36 total numbers of sums.
However, there are just 6 different sums.
[tex]\begin{gathered} 2+2=4 \\ 2+3=5 \\ 2+7=9 \\ 3+3=6 \\ 3+7=10 \\ 7+7=14 \end{gathered}[/tex]Therefore, there are 6 different sums.What is the value of x?
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Answer:
The two angles are congruent, so: 2x+2=3x-52
2x-3x=-2-52
-x=-54
x=54
What are the first and third quartiles of rainfall of this data? Q1 = 5. Q3 = 8 Q1 = 6, Q3 = 8 Q1 = 4, Q3 = 7 Q1 = 5, Q3 = 7.5
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Answer:
Q1 = 5, Q3 = 8
Explanation:
There are a total of 19 dots on the chart.
[tex]\begin{gathered} Item\; in\; Q_1=\frac{1}{4}\times19 \\ =4.75th\text{ item} \end{gathered}[/tex]The 5th item on the chart =5, therefore:
• Q1 = 5
Similarly:
[tex]\begin{gathered} Item\; in\; Q_3=\frac{3}{4}\times19 \\ =14.25th\text{ item} \end{gathered}[/tex]The 14th and 15th item on the chart =8, therefore:
• Q3 = 8
IF AN AUTO DRIVING AT 40MPH DRIVES 4 HOURS, ANDSTOPS, AND THEN DRIVE '2 HOURSMORE AT 10 Metly thoutte(MILES) DID IT GO?
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• We assume here that the auto drives at 40 mph for 4 hours.
,• Then, it stops and then drives for 2 hours at 10 mph.
,• We need to find the total miles the auto drove.
,• To answer this question, we need to know that we have a constant rate at each part of the driving of the auto: in the first part, it drove at a constant speed of 40 mph. In the second part, it drove at a constant speed of 10 mph.
,• We can say that the total distance for the first part is:
,• d1 = 40 miles/hour * 4 hours ---> ,d1 = 160 miles.
,• In the second part:
,• d2 = 10 miles/hour * 2 hours ---> ,d2 = 20 miles.
,• Then, the total miles it went was:
,• ,d1 + d2 = 160 miles + 20 miles = 180 miles.
,• The auto drove for 180 miles.
,•
,•
What is the domain and range of y=-1/2x+3
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For the function
[tex]y=-\frac{1}{2}x+3,[/tex]the range is all the values y can have and the domain is all the possible values that x can take.
In our function there seems to be no restriction on what values x and y can take—our function is defined for all real values of x and y — therefore, the domain and the range of our function is all real numbers.
The rectangular floor of a classroom is 28 feet in length and 30 feet in width. A scale drawing of the floor has a length of 14 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
The Solution:
Given:
Required:
To find the perimeter (in inches) of the floor in the scale drawing.
Step 1:
Find the value of x.
By the similarity theorem:
[tex]\frac{14}{x}=\frac{28}{30}[/tex]Cross multiplying, we get:
[tex]\begin{gathered} 28x=14\times30 \\ \\ Dividing\text{ both sides by 28, we get} \\ \\ x=\frac{14\times30}{28}=\frac{30}{2}=15\text{ in.} \end{gathered}[/tex]Step 2:
Find the perimeter, in inches, of the floor in the scale drawing.
By formula, the perimeter is:
[tex]\begin{gathered} P=2(L+W) \\ \text{ Where:} \\ L=14\text{ inches} \\ W=x=15\text{ inches} \\ P=perimeter=? \end{gathered}[/tex]Substituting these values in the formula, we get:
[tex]P=2(14+15)=2\times29=58\text{ inches}[/tex]Therefore, the correct answer is 58 inches.
feet by You are preparing to tile the backsplash in a kitchen. The area you are tiling measures 8 1/2 feet. The tiles you plan to use are sold in boxes that have enough tiles to cover 10 square feet. What is the minimum number of boxes of tiles you should order to complete the job?A.1B. 2C. 12D. 13E. 20
Answers
hello
the area of the room is given by
[tex]8\frac{1}{2}by1\frac{1}{2}[/tex]let's convert the mixed fraction to improper fraction
[tex]\begin{gathered} 8\frac{1}{2}=\frac{17}{2} \\ 1\frac{1}{2}=\frac{3}{2} \end{gathered}[/tex]now, let's multiply the two dimensions given to find the area in squared feet.
[tex]\frac{17}{2}\times\frac{3}{2}=\frac{51}{4}[/tex]the area of the room is 51/4 ft^2
we can now find how many boxes of tiles will cover the room
1 box covers 10ft^2
let the number of boxes of tiles to cover 51/4ft^2 be represented by x
1 box = 10
x box = 51/4
[tex]\begin{gathered} 1=10 \\ x=\frac{51}{4} \\ \text{cross multiply both sides and solve for x} \\ 1\times\frac{51}{4}=10\times x \\ \frac{51}{4}=10x \\ \text{divide both sides by 10} \\ \frac{\frac{51}{4}}{10}=\frac{10x}{10} \\ x=\frac{51}{4}\times\frac{1}{10}=\frac{51}{40}=1.275 \end{gathered}[/tex]the number of boxes required to cover the room is 1.275 boxes and he'll need a minimum of 2 boxes to do so.
the answer is option B
Find the z-score for a test score of 86% if themean was 75% and the standard deviationwas 6 points.
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ANSWER
[tex]1.833[/tex]EXPLANATION
To find the z-score, we have to apply the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where x = Score
μ = Mean
σ = Standard deviation
Therefore, the z-score for the test score is:
[tex]\begin{gathered} Z=\frac{86-75}{6} \\ Z=\frac{11}{6} \\ Z=1.833 \end{gathered}[/tex]solve for y in the equation below
2 4y = 9
Answers
Answer:9/24
Step-by-step explanation
Which additional piece of information would you need to prove these two triangles are congruent using the side-side-side or SSS triangle congruence postulate?
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By using congruency of triangles, the result obtained is
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
Third option is correct
What is Congruency of triangles?
Two triangles are said to be congruent if the corrosponding sides and corrosponding angles are same.
The different axioms of congruency are SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom
In [tex]\Delta STU[/tex] and [tex]\Delta SHU[/tex]
ST = HU [Given]
SU is common
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
To learn more about congruency, refer to the link-
https://brainly.com/question/2938476
#SPJ1
Complete Question
The diagram has been attached here
The point P. = (x,1/3) lies on the unit circle shown below. What is the value of x insimplest form?
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When a point (x,y) lies on a unit circle, the following equation holds true:
[tex]x^2+y^2=1[/tex]We are given
[tex]y=\frac{1}{3}[/tex]and need to find x.
Let's put it into the equation and figure out x. Shown below:
[tex]\begin{gathered} x^2+y^2=1 \\ x^2+(\frac{1}{3})^2=1 \\ x^2+\frac{1}{9}=1 \\ x^2=1-\frac{1}{9} \\ x^2=\frac{8}{9} \\ x=\sqrt[]{\frac{8}{9}} \\ x=\frac{\sqrt[]{8}}{\sqrt[]{9}} \\ x=\frac{\sqrt[]{8}}{3} \end{gathered}[/tex]We can simplify the square root of 8 by using the radical property:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\sqrt[]{b}[/tex]Thus, square root of 8 becomes:
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=\sqrt[]{4}\sqrt[]{2}=2\sqrt[]{2}[/tex]Thus, the simplest form of x is:
[tex]x=\frac{2\sqrt[]{2}}{3}[/tex]Mars is about 142 million miles from the sun. The earth is about 93,000,000 miles from the sun. How much farther from the sun is Mars than the earth? Express the answer in scientific notation State the letter of the correct answer. A.) 235x10 B.) 2.35x107 C) 4.9x10 D.) 49x107
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D)
1) Let's visualize it to better understand this
2) Let's pick the distance between Mars and the Sun, and subtract it by the distance (Earth-Sun):
[tex]142,000,000-93,000,000=49,000,000=49\cdot10^6\text{ or 4.9 }\cdot10^7[/tex]3) So Mars is 4.9 x 10^7 miles farther from the sun than the Earth.
What 4x 5 + 2?????? ????
Answers
Given:
[tex]4\times5+2[/tex]To find the value:
Using the BODMAS rule,
[tex]\begin{gathered} 4\times5+2=(4\times5)+2 \\ =20+2 \\ =22 \end{gathered}[/tex]Hence, the answer is 22.
what relationship between the number of extracurricular activists and gpa do the data suggest ?A)the more extracurricular activists a student participates in, the higher the students gpa.b) students who participate in exactly 2 extracurricular activities have the highest gpac) the fewer extracurricular activities a student participates in the higher the students gpad) there is no relationship between the number of extracurricular activities and gpa
Answers
Solution
For this case we can create the following table sorted by Extracurricular activities:
Name EAGPA
Overdown D03.1
Richards Z01.8
Garrison F12.8
Minton M13.5
House W23.9
Villanueva C23
Chapman V33.7
Solomon P43.3
West H 82.8
Lycan A 92.3
If we plot EA against GPA we have:
Then the best answer is:
d) there is no relationship between the number of extracurricular activities and gpa
Calculate Jayden's simple interest on a 5-year car loan for $33,486 at 2.38%.
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Answer:
$3984.83.
Explanation:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]In this particular case:
• The principal/loan amount = $33,486.
,• Rate = 2.38%.
,• Time = 5 years.
Substituting these into the formula above:
[tex]\begin{gathered} Simple\: Interest=\frac{33,486\times2.38\times5}{100} \\ =\$3984.83 \end{gathered}[/tex]Jayden's simple interest is $3984.83.
X-31The rational expression +5x X+2is equivalent to
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SOLUTION
Step 1 :
In this question, we are meant to simplify the rational fractions:
[tex]\frac{\text{x - 3 }}{5\text{ x }}\text{ + }\frac{1}{x\text{ + 2}}[/tex][tex]=\frac{(\text{ x - 3 ) ( x + 2 ) + 5 x }}{5\text{ x ( x + 2 )}}[/tex][tex]=\frac{x^2\text{ + 2 x - 3 x -6 + 5 x }}{5\text{ x ( x + 2 )}}[/tex][tex]=\text{ }\frac{x^2\text{ + 4x - 6 }}{5\text{ x ( x + 2 )}}\text{ --OPTION B}[/tex]Jen Butler has been pricing Speed-Pass train fares for a group trip to New York Three adults and tour children must pay $124. Two adults and three children must pay $88. Find the serice of the addit's ticket and the price of a child's ticketThe price of a child's ticket is $The price of an adult's ticket is $
Answers
It is given that two adults and three children pay $88.
Represent it as equation
2x+3y=88
Then three adults and four children pay $124.
It is written is equation form as follows.
3x+4y=124
Here x is adults' price and y is children's price.
Solve the system of equation as follows.
[tex]\begin{gathered} 3x+4y=124 \\ 2x+3y=88 \\ 6x+8y=248 \\ 6x+9y=264 \end{gathered}[/tex]Now subtract each of the last two equations to get -y=-16
Hence y = 16
Substitute in equation 1, we get
[tex]\begin{gathered} 2x+48=88 \\ 2x=40 \\ x=20 \end{gathered}[/tex]Therefore, adult price is $20 and children price is $16
-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)simply please
Answers
-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)
We must open the parenthesis first by multiplying the elements in it be the elements outside
Bearing in mind that
- * - = +
- * + = -
-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)
= -b - 8 -7 + b + 6b - 1
Now we rearrange so all like terms are together noting the signs before each term
= -b + b + 6b - 8 - 7 - 1
= 6b - 16
You may leave the answer in this form or go further to factorize
= 2 (3b - 8)
Find the area of the shaded region.3112Note: Use either the pi button on your calculator or 3.14 for pi. Round to the nearest tenth.
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The area of a sector of a circle can be calculated by using the formula:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ where }\theta\text{ is the angle in degrees and r is the radius}[/tex]The total area of a circle can be calculated as:
[tex]A_{total}=\pi\cdot r^2\text{ where r is the radius}[/tex]To find the area of the shaded region, you need to calculate the total area of the circle and then subtract the area of the non-shaded region, as follows:
[tex]\begin{gathered} A_{total}=\pi\cdot r^2\text{ The given value for r is 3} \\ A_{total}=\pi\cdot3^2\text{ } \\ A_{total}=\pi\cdot9 \\ A_{total}=3.14\cdot9 \\ A_{total}=28.3 \end{gathered}[/tex]Now let's calculate the area of the non-shaded region:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ the given values for }\theta=112\text{ and r=3} \\ A=\frac{112}{360}\cdot\pi\cdot3^2\text{ } \\ A=0.31\cdot3.14\cdot9 \\ A=8.8 \end{gathered}[/tex]The area of the shaded region will be:
[tex]\begin{gathered} A_{SR}=A_{total}-A \\ A_{SR}=28.3_{}-8.8 \\ A_{SR}=19.5 \end{gathered}[/tex]6. Use common denominators for these fractions. Arrange them from smallest to largest.
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Given the fractions:
[tex]\frac{9}{16},\frac{3}{8},\frac{1}{4},\frac{5}{8}[/tex]We will arrange them from the smallest to the greatest using the common denominators
So, the common denominator for the fractions will be = 16
[tex]\begin{gathered} \frac{9}{16}=\frac{9}{16} \\ \\ \frac{3}{8}=\frac{2\cdot3}{2\cdot8}=\frac{6}{16} \\ \\ \frac{1}{4}=\frac{4\cdot1}{4\cdot4}=\frac{4}{16} \\ \\ \frac{5}{8}=\frac{2\cdot5}{2\cdot8}=\frac{10}{16} \end{gathered}[/tex]So, the answer will be the arrange will be:
[tex]\begin{gathered} \frac{4}{16},\frac{6}{16},\frac{9}{16},\frac{10}{16} \\ \\ \frac{1}{4},\frac{3}{8},\frac{9}{16},\frac{5}{8} \end{gathered}[/tex]
Find the missing length indicated. Leave your answer in the simplest radical form.92112-1620649
Answers
Apply teh altitude theorem:
9/12 = 12/x
Solve for x:
9x = 12 (12)
9x = 144
x = 144/9
x = 16
A piece of wire 32 cm long is cut into two pieces, each to be bent to make a square. The length of a side of one square is to be 4 cm longer than the length of a side of the other How should the wire be cut?The length of the shorter piece of wire is :
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Let P1 represent the perimeter of the larger square and let P2 represent the perimeter of the smaller square. Since the piece of wire is 32 cm long and both squares are made of this wire, we have the following:
[tex]P_1+P_2=32[/tex]Now let x be the length of the side of the smaller square. Since the larger square has sides 4cm longer than the length of the side of the other square, we have the following:
[tex]\begin{gathered} P_1=4(x+4) \\ P_2=4x \end{gathered}[/tex]using these expressions on the first equation and solving for x, we get:
[tex]\begin{gathered} 4(x+4)+4x=32 \\ \Rightarrow4x+16+4x=32 \\ \Rightarrow8x=32-16=16 \\ \Rightarrow x=\frac{16}{8}=2 \\ x=2 \end{gathered}[/tex]we have that x = 2. Then, the length of the shorter piece of wire will be the perimeter of the smaller square, therefore, the length of the shorter piece of wire is P2 = 4(2) = 8 cm
Find the area of the given geometric figure. If the figure is a circle, give an exact area and then use 22/7 as an approximation for pie to approximate the area. r=2in
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the area of a circle is given by:
[tex]\text{Area}=\pi\cdot radius^2[/tex]Step 1
replace
[tex]\begin{gathered} \text{Area}=\frac{22}{7}\cdot(2inches)^2 \\ \text{Area}=\frac{22}{7}\cdot4in^2 \\ \text{Area}=\frac{22\cdot4}{7} \\ \text{Area}=12.57 \end{gathered}[/tex]so, the answer is 12.57 square inches
Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for 2005 through 2014 can be approximated by 7.1x-y=-254. The number of network and data analyst jobs for the same years can be approximated by 12.2x-y=-231. For both equations, x is the number of years since 2005 and y is the number of jobs in thousands.Solution to the ordered pairs:(5, 286)Use your result from part (a) to estimate the year in which the number of both jobs is equal.
Answers
Given the system of equations:
7.1x - y = -254
12.2x - y = -231
Where x is the number of years since 2005
y is the number of Jobs in thousands.
After solving the system, we have the solution:
(x, y) ==> (5, 286)
Let's determine the year in which the number of both jobs is equal.
The graph of both lines will meet at the solution point.
Given that x represents the number of years since 2005, the year which the number of both jobs is equal will be 5 years after 2005.
Hence, we have:
Year in which number of both jobs are equal = 2005 + 5 = 2010
Therefore, in 2010, the number of both jobs will be equal.
ANSWER:
2010
A school track team member ran for a total of 149.5 miles in practice over 57.5 days. About how many miles did he average per day?
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Data
• Total: 149.5 miles
,• Days: 57.5
,•
Solve the quadratic equation by factoring.2x^2+24x+22=0
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Solution
[tex]\begin{gathered} 2x^2+24x+22=0 \\ Divide\text{ through by 2} \\ x^2+12x+11=0 \\ x^2+11x+x+11=0 \\ x(x+11)+1(x_+11)=0 \\ (x+11)(x+1)=0 \\ x+11=0\text{ or x+1=0} \\ x=-11\text{ or x = -1} \end{gathered}[/tex]Question 7 of 10Estimate the sum of the decimals below by rounding to the nearest wholenumber. Enter your answer in the space provided.8.9995.496+ 1.199
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given decimals
[tex]8.999+5.496+1.199[/tex]STEP 2: Round the given decimals
[tex]\begin{gathered} 8.999\approx9 \\ 5.496\approx5 \\ 1.199\approx1 \end{gathered}[/tex]STEP 3: Find the sum
[tex]9+5+1=15[/tex]Hence, the sum is estimatedly 15
Lola has 8 bear figurines. These bear figurines make up 40% of her collection of animal figurines. Find the total number
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Hence, the total number of bear figurines are 20
Sam read 6 books in the time it took his little sister, faith, to read 1/2 of a book
Sam's sister read how many times as many books as sam read?
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Answer:
3
Step-by-step explanation:
6 x 1/2 = 3
Use to reflect over the x-axis. Identify the transformed vector.
Answers
To reflect the given matrix over the x-axis, you have to multiply both matrices:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}[/tex]Multiply each term of the first row of the first matrix with the corresponding terms of the column of the second matrix and add the results:
Repeat the process for the second row of the first matrix
The resulting matrix is:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}=\begin{bmatrix}{(1\cdot7)+(0\cdot-12)} \\ {\square}(0\cdot7)+(-1\cdot-12)\end{bmatrix}=\begin{bmatrix}{7} \\ {12}\end{bmatrix}[/tex]The correct option is option D.