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We will illustrate on how to find the inverse function.
First, recall that the inverse function is a function that given the output of a function, it will give you back the input out of which that output came from.
when athe function has a formula, we can follow some steps to find the inverse function. Suppose we are given the function
[tex]f(x)=3x+5[/tex]Now, we first change f(x) with the letter y. So we get
[tex]y=3x+5[/tex]now, we interchange variables x and y. So we get
[tex]x=3y+5[/tex]Finally we solve this equation for y. We will first subtract 5 on both sides and then divide both sides by 3. So we get
[tex]y=\frac{x\text{ -5}}{3}[/tex]and now we replace the y with the symbol of the inverse function. So we have that
[tex]f^{\text{ -1}}(x)=\frac{x\text{ -5}}{3}[/tex]Related Questions
A.Ghamarvion earned $8.00 an hour and was given a 75% wage ge increase. How much does Ghamarvion earn per hour after his ae raise? B. A population increased from 328 569 people to 400,232 people. What was the percent of change in the population?
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in point slope form: passes through (1, -3), slope = -1?
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Explanation
Step 1
Let
P1(1,-3)
slope=-1
Step 2
use the formula
[tex]y-y_1=m(x-x_1)[/tex]replacing
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-1(x-1) \\ y+3=-x+1 \\ \text{subtract 3 in both sides} \\ y+3-3=-x+1-3 \\ y=-x-2 \end{gathered}[/tex]I hope this helps you
WILL GIVE BRANLIEST Use the graph to write a linear function that relates y to x (for both please)
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Question:
Use the graph to write a linear function that relates y to x
Solution:
To find the linear function that relates y and x in the above graph, we have to know that a linear function is given by the following formula:
[tex]y\text{ = mx+b}[/tex]where m is the slope of the line and b is the y-coordinate of the y-intercept (when x = 0). Now, notice that in this case, when x = 0 then y= 2, thus we can conclude that b = 2 and:
[tex]y\text{ = mx+}2[/tex]On the other hand, by definition, the slope of the line is given by:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2, Y2) are any two points on the line. Take for example:
(X1,Y1) = (0,2)
(X2,Y2) = (6,10)
then, replacing this data in the equation of the slope, we obtain:
[tex]m\text{ = }\frac{10-2}{6-0}=\text{ }\frac{8}{6}[/tex]then, using the slope obtained above, we can conclude that the equation of the linear function is:
[tex]y\text{ = }\frac{8}{6}x\text{ + 2}[/tex]Zach bought a pair of jeans for $54.The next week he noticed that the price for the same pair of jeans was now $74. Find the percent of change.
Answers
Let's begin by listing out the information given to us:
Old Price = $54
New Price = $74
The percentage change is given by:
[tex]\begin{gathered} \text{\%}\Delta=\frac{|OldPrice-NewPrice|}{OldPrice}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|54-74|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{|-20|}{54}\cdot100\text{\%} \\ \text{\%}\Delta=\frac{20}{54}\cdot100\text{\%} \\ \text{\%}\Delta=37.04\text{\%} \\ \text{\%}\Delta\approx37\text{\%} \end{gathered}[/tex]The cost in dollars of making x items is given by the function C(x)=10x+700.The fixed cost is determined when zero items are produced. Find the fixed cost for this item.fixed cost=What is the cost of making 25 items?C(25)=Suppose the maximum cost allowed is $2700. What are the domain and range of the cost function, C(x)?When you enter a number in your answer, do not enter any commas in that number. In other words if you want to enter one thousand, then type in 1000 and not 1,000. It's not possible to understand what the interval (1,000,2,000) means, so you should write that as (1000,2000).domain=range=
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According to the situation, the domain of this function will contain all values that x can take. Since x is the number of items, it only can take values from 0 to a certain value.
To find this certain value, use the maximum cost allowed (2700) as C(x) and find x using the equation:
[tex]\begin{gathered} C(x)=10x+700 \\ 2700=10x+700 \\ 2700-700=10x \\ 2000=10x \\ x=\frac{2000}{10} \\ x=200 \end{gathered}[/tex]It means that the domain of the function is [0,200]
The range contains all the values that cost can take. We know that the fixed cost (which is the minimum cost) is 700 and the maximum cost is 2700.
It means that the range of the function is [700,2700]
Answer:
it is not clear
Step-by-step explanation:
Solve each inequality. Then graph the solution.1. -6t-3-2t - 192. - 3(m - 4) <63. 4(1 - x) < 164. 2y <-35. 3(v - 4) 5V - 246. -X – 1 > 3x + 1Solve each inequality.7. 2(k + 4) – 3k < 148. 3(4c – 5) – 2c> 09. 15(j – 3) + 3j < 4510. 22 > 5(2y + 3) – 3y11. -53 > -3(3z + 3) + 3z12. 20(d – 4) + 4d < 813. -2(6 + s)< -16 + 2s14. 9 - 2x < 7 + 2(x – 3)Solve each inequality.If all real-number values of x are solutions of the inequality, write TRUE.If no real-number values of x are solutions of the inequality, write FALSE.15. 2(n − 3) < -13 + 2n16. -3(w + 3) < 9 - 3w17. The unit cost for a piece of fabric is $4.99 per yard including tax. You havto spend on material. How many whole feet of material can you buy?
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7. The unit cost for a piece of fabric is $4.99 per yard including tax. You have $30 to spend on material. How many whole feet of material can you buy?
we know that
1 yard --------> cost $4.99
so
x yards ------> $30
Applying proportion or rule of three
x=30/4,99
x=6.01 yd
answer 6 yards
what is the value of x in this equation ?
Answers
Solution
We have the following equation given:
4(2x+1)= 27 + 3(2x-5)
And we can solve for x on this case:
8x +4 = 27 + 6x -15
8x -6x = 27-15 -4
2x = 8
x= 8/2= 4
A company discovers that to produce x=700 new electronic parts, it will cost y=$61100. To produce 620 new electronic parts, it will cost $54460
Answers
Answer:
The cost increases at a rate of $83 per item.
Step-by-step explanation:
Given two points, use the following to determine the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given the points (700,61100) and (620, 54460), substitute and compute for the slope:
[tex]\begin{gathered} m=\frac{61100-54460}{700-620} \\ m=\frac{}{}83 \end{gathered}[/tex]The cost increases at a rate of $83 per item.
Evaluate the integral of the product if x and quantity x squared plus 1 and x, dx.
Answers
The integral is given
[tex]\int x(x^2+1)dx[/tex]ExplanationTo determine the solution to the integral.
[tex]\int x(x^2+1)dx=\int x^3+x\text{ dx}[/tex][tex]\int(x^3+x)dx=\frac{x^4}{4}+\frac{x^2}{2}+C[/tex]AnswerHence the correct option is C.
[tex]\frac{x^4}{4}+\frac{x^2}{2}+C[/tex]How to Graph 2x-3y=6 in a coordinate plane.
Answers
Explanation:
To graph the equation 2x - 3y = 6, we need to find two points in the line.
So, first let's make y = 0 and solve for x
2x - 3y = 6
2x - 3(0) = 6
2x = 6
2x/2 = 6/2
x = 3
Then, if x = 0, we get:
2x - 3y = 6
2(0) - 3y = 6
-3y = 6
-3y/(-3) = 6/(-3)
y = -2
Therefore, the points that we will use to graph the equation are (3, 0) and (0, -2).
Answer:
So, the graph of 2x - 3y = 6 is
if G(t)=(3t-5)^2 + 4t - 1 find each of the following g of a and g of a plus 2
Answers
For point A, you just have to replace t by a in the given function, like this
[tex]\begin{gathered} G\mleft(t\mright)=\mleft(3t-5\mright)^2+4t-1 \\ \text{ Replacing} \\ G\mleft(a\mright)=\mleft(3a-5\mright)^2+4a-1 \\ \text{ Solving you have} \\ G(a)=(3a-5)(3a-5)+4a-1 \\ G(a)=9a^2-30a+25+4a-1 \\ \text{ Add similar terms} \\ G(a)=9a^2-26a+24 \end{gathered}[/tex]For point B, you just have to replace t by a+2 in the given function, like this
[tex]\begin{gathered} G(t)=(3t-5)^2+4t-1 \\ \text{ Replacing} \\ G(a+2)=(3(a+2)-5)^2+4(a+2)-1 \\ \text{ Solving you have} \\ G(a+2)=(3a+6-5)^2+4(a+2)-1 \\ G(a+2)=(3a+1)^2+4a+8-1 \\ G(a+2)=(3a+1)(3a+1)+4a+8-1 \\ G(a+2)=9a^2+6a+1+4a+8-1 \\ \text{ Add similar terms} \\ G(a+2)=9a^2+10a+8 \end{gathered}[/tex]Find the missing value in theequivalent ratio 12:18 = 16:ChooseA.20B.24C.28
Answers
we have that
12:18 is the same that 12/18
simplify
12/18=6/9=2/3
Multiply by 8/8
(2/3)*(8/8)=16/24 ------> 16:24
therefore
the answer is the option BProblem N 2
we have that
each earbud costs 0.94
so
Multiply by 22
0.94*22=$20.68
the answer is $20.68Jamal's deck is in the shape of a polygon and is shown on the grid below.(-8,6)(6,6)o[(-8, -4),(6,-4)What is the area of Jamal's deck?square units
Answers
Let;
A(-8,6) B(6,6) C(6, -4) D(-8, -4)
Let's find the length AB
x₁= -8 y₁=6 x₂=6 y₂=6
We will use the distance formula;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]=\sqrt[]{(6+8)^2+(6-6)^2}[/tex][tex]=\sqrt[]{14^2+0}[/tex][tex]=14[/tex]Next, we will find the width BC
B(6,6) C(6, -4)
x₁= 6 y₁=6 x₂=6 y₂=-4
substitute into the distance formula;
[tex]d=\sqrt[]{(6-6)^2+(-4-6)^2}[/tex][tex]=\sqrt[]{(-10)^2}[/tex][tex]=\sqrt[]{100}[/tex][tex]=10[/tex]Area = l x w
= 14 x 10
= 140 square units
A new auditorium is being built for a college. The balcony has 60 seats. Thefloor has 15 rows with x seats in each row. The number of people in theauditorium must be under 315 to meet safety regulations.What is the solution of this inequality, and what is its meaning?
Answers
x < 17
This means the new auditorium must have less than 17 seats 1n each row on the floor to meet the safety regulations.
Explanation:Number seats in the balcony = 60
Number of seats on the floor = number of rows × number of seats on each row
Number of seats on the floor = 15× x = 15x
The number of people in the auditorium must be under 315:
This means the number of people can be less than 315 but not above it.
We represent less than 315 as < 315
The inequality equation:
Number seats in the balcony + Number of seats on the floor < 315
60 + 15x < 315
Rewritting the inequality equation:
15x + 60 < 315
Solving the inequality:
15x + 60 < 315
collect like terms by subtracting 60 from both sides:
15x + 60 - 60 < 315 -60
15x < 255
Divide both sides by 15:
15x/15 < 255/15
x < 17
This means the new auditorium must have less than 17 seats in each row on the floor to meet the safety regulations.
Please use photo for better understanding Please also know this is 6th grade level math.
Answers
ANSWER
1/3
EXPLANATION
We know that 2/3 of all the students in the orchestra play stringed instruments and that of that fraction, 1/2 play violins. To find how many students in the orchestra play violins, we have to multiply the two fractions. In other words, we have to find what fraction is half of the two thrids who play stringed instruments,
[tex]\frac{2}{3}\times\frac{1}{2}[/tex]We have a number 2 in the numerator of the first fraction and the same number is in the denominator of the second fraction, thus these two numbers are canceled, and we have,
[tex]\frac{1}{3}\times\frac{1}{1}=\frac{1}{3}[/tex]Hence, 1/3 of the students in the orchestra play violins.
1 1/6cdx (-6/7c raised to the 9 power d raised to the 7 power.I'll upload a picture
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ANSWER:
[tex]-c^{10}d^8[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]1\frac{1}{6}cd\cdot\mleft(-\frac{6}{7}c^9d^7\mright)[/tex]We simplify as follows:
[tex]\begin{gathered} 1\frac{1}{6}=\frac{6+1}{6}=\frac{7}{6} \\ \frac{7}{6}cd\cdot(-\frac{6}{7}c^9d^7) \\ \frac{7}{6}\cdot-\frac{6}{7}\cdot cd\cdot(c^9d^7)=-1\cdot c^{10}d^8=-c^{10}d^8 \end{gathered}[/tex]3.2 radians=________degrees
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SOLUTION
To convert from radians to degrees, we have the conversion rate
[tex]\begin{gathered} \pi radians=180^0 \\ 2\pi radians=360^0=180\times2 \end{gathered}[/tex]Then 3.2 radians will be
[tex]3.2\pi radians=180\times3.2=576^0[/tex]Therefore 3.2 radians =576°
• Which ratios have a unit rate of 37 Choose ALL that apply. 15 1 1 1 cup : cup cups: 25 cups 3 ) 3 3- cups : 2 cups 4 2 2 () 2 cups : cup 3 21 / 1 5 cups : cup 6 cup : 1 cup 3
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Explanation:
The ratios are like fractions, they can be simplified. And since fractions are divisions in some occasions we can do the division in order to get a simpler number:
• 1 cup: 1/4 cup _ we can do the division with the KCF method: keep the first fraction, change division sign into multiplication sign and flip the second fraction:
[tex]1\colon\frac{1}{4}=1\times4=4[/tex]• 2 cups : 2/3 cup
[tex]2\colon\frac{2}{3}=2\times\frac{3}{2}=3_{}[/tex]• 15/2 cups : 2 1/2 cups
[tex]\frac{15}{2}\colon2\frac{1}{2}=\frac{15}{2}\colon\frac{5}{2}=\frac{15}{2}\times\frac{2}{5}=3[/tex]• 2 1/2 cups : 5/6 cup
[tex]2\frac{1}{2}\colon\frac{5}{6}=\frac{5}{2}\colon\frac{5}{6}=\frac{5}{2}\times\frac{6}{5}=\frac{6}{2}=3[/tex]• 3 3/4 cups : 2 cups
[tex]3\frac{3}{4}\colon2=\frac{15}{4}\colon2=\frac{15}{4}\times\frac{1}{2}=\frac{15}{8}[/tex]• 2/3 cup : 1 cup
[tex]\frac{2}{3}\colon1=\frac{2}{3}\times1=\frac{2}{3}[/tex]Answers:
The answers are the ones in a red rectangle:
Thor was selling candy at a softball game and recorded the number of candy he sold each day in the line graph above. Which histogram below represents the data shown in the line graph?.
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Day 1 = 70, Day 2 = 74, Day 3 = 78, Day 4 = 80
Use the function y = 200tan x on the interval 0 deg <= x <= 141 deg Complete the ordered pair (x, 0). Round your answer to the nearest whole number.
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The value of x for the ordered pair (x,0) is 0. B is the correct option.
What is ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Given function is
y = 200 tan x.
Given ordered pair is (x,0).
The value of y for the given ordered pair is 0.
The value of tangent function is increasing with increase the value of degree.
The value of tangent at 0 degree is 0 that is tan 0 = 0.
If we multiply a number with zero it returns 0.
The possible value of x is 0.
Hence option B is the correct option.
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Question 9 of 22Which number produces a rational number when added to5?O A. 5.38516480...B. 10C.O D. 0.22SUBMIT
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A rational number can be said to be a number that is expressed as a quotient of s fraction. The denominator of a rational number must be a non-zero number.
You can simply say a rational number is any number that can be written as a fraction.
To find the number when added to 5 produces a rational number, we have:
A. 5.38516480...
This number has infinite decimal so it is an irrational number
B. 10
10 + 5 = 15
This is not a rational number
C. 0
0 + 5 = 5
This is not a rational number
D. 0.22
0.22 + 5 = 5.22
This is a rational number because it can be written as a fraction
[tex]5.22=\frac{522}{100}[/tex]Therefore, the number that produces a rational number when added to 5 is 0.22
ANSWER:
D. 0.22
Find the length of RS to the nearest tenth of a meter
Answers
We were given a right triangle, with a known angle and a known hypothenuse, we want to find the nearest side to the known angle, so we must use the cosine relation, as shown below:
[tex]\begin{gathered} \cos (28)=\frac{RS}{QS} \\ 0.88=\frac{RS}{9.6} \\ RS=9.6\cdot0.88=8.45\text{ m} \end{gathered}[/tex]The length of the side RS is approximately 8.5 meters.
The graph shows a relationship between temperature and time.504030Temperature (°F)2010h246810Number of HoursWhich best represents the equation that shows the temperature, t, after h hours?tu-n +45t = -45ht = -5h + 45t= -3h + 45
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as we can see in the graph we know that the equation that represents a line is the equation of the line
in this case
y=t
x=h
we need two points in order to calculate the slope
(0,45)=(x1,y1)
(5,30)=(x2,y2)
[tex]m=\frac{y2-y1}{x2-x1}=\frac{30-45}{5-0}=\frac{-15}{5}=-3[/tex]the y-intercept is 45
the form of the equation of the line is
[tex]y=mx+b[/tex]where
m=slope
b=y-intercept
in this case
m=-3
b=45
[tex]y=-3x+45[/tex]using the variables of the problem the equation that represents the problem is
[tex]t=-3h+45[/tex]the correct answer is the last one
Divide. Reduce your answer to lowest terms.- 2/3 divide 7/9
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For the division, the fraction is reciprocated with change in sign from divison to multiplictaion.
Divide the expression.
[tex]\begin{gathered} -\frac{2}{3}\times\frac{9}{7}=-\frac{2\cdot3}{1\cdot7} \\ =-\frac{6}{7} \end{gathered}[/tex]So answer is -6/7.
A six-sided number cube is rolled. Event A consists of rolling an even number. Event B consists of rolling a number greater than four. Match the correct sample space to each event.
Answers
EXPLANATION :
From the problem, we have two events :
Event A : rolling an even number {2, 4, 6}
Event B : rolling a number greater than four {5, 6}
1. Union of A and B is the combination of Event A and B
Since there's a common element, 6, we will take this as one only.
That will be {2, 4, 5, 6}
2. Intersection of A and B is the common element between the two events.
So that is {6}
3. Complement of A is the set of elements that is NOT present in Event A.
Since a cube has 6 sides, the elements are {1, 2, 3, 4, 5, 6}
The complement of A will be {1, 3, 5}
4. Event B, from the data we have from above, B will have {5, 6}
solve the system using any method
-x^2-10x-y=30
3x^2+30x-y=-66
Answers
Answer:
(-4,-6) (-6,-6)
Step-by-step explanation:
-y = x^2 + 10x + 30
y = -x^2 - 10x - 30
3x^2 + 30x -(-x^2-10x-30) = -66
3x^2 + 30x + x^2 + 10x + 30 = -66
4x^2 + 40x +30 + 66 = 0
4x^2 + 40x + 96 = 0
x^2 + 10x + 24 = 0
(x+6)(x+4) = 0
x = -6
x = -4
y = -x^2 - 10x - 30
y = -(-6)^2 - 10(-6) - 30
Y = -36+60 - 30
y= -6
y= -(-4)^2 - 10(-4) - 30
y = -16 + 40 - 30
y = -6
Solve for the values of x and y for the regular hexagon.a. x = 120, y = 60b. x = 110, y = 70c. x = 105, y = 75d. x = 60, y = 120e. X = 115, y = 65
Answers
Remember that the sum of the interior angles of an hexagon is equal to 720°
Because this is a regular hexagon,
[tex]\begin{gathered} 6x=720\rightarrow x=\frac{720}{6} \\ \rightarrow x=120 \end{gathered}[/tex]Notice angles x and y lay in the same straight line.
Thereby,
[tex]\begin{gathered} x+y=180 \\ \rightarrow120+y=180 \\ \rightarrow y=180-120 \\ y=60 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=120 \\ y=60 \end{gathered}[/tex](The correct answer is option A)
all you need is in the photo please answer fast only give the answer don't put step by step pleaseeeeeeeeeeeeeeeeeeeeee
Answers
The value of x1 = 7 and x2 = -2
From the question, we have
a=1
b=-5
c=-14
x= [-b ± √(b2 – 4ac)]/2a
substituting the value, we get
x= [5 ± √(-5² – 4*1*-14)]/2*1
=[5 ± √(25+56)]/2
=[5 ± √81]/2
=[5 ± 9]/2
x1 =[5 +9]/2=7
x2 =[5 -9]/2=-2
Quadratic Equation:
The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).It is a given that the quadratic equation has two roots. Roots might have either a true or made-up nature.
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If 6 garbage trucks can collect the trash of 36 homes in a day. How many trucks are needed to collect in 180 houses?
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In the question, we are given that 6 garbage trucks can collect the trash of 36 homes in a day. We can find how many trucks are needed to collect in 180 houses below.
Explanation
[tex]\begin{gathered} \text{If 6 trucks collect for 36 houses} \\ x\text{ truck will collect for }180\text{ houses} \\ \text{Therefore using direct proportion} \\ \frac{6}{x}=\frac{36}{180} \\ \frac{6}{x}=\frac{1}{5} \\ \text{cross multiply} \\ x=30 \end{gathered}[/tex]Answer: 30 trucks
a cone has a height of 8 cm and a slant height of 10cm. Calculate the radius of the cone.
HALP PLEASE
Answers
The radius of the cone is= 3.14*160 cm^2.
What is equations?There are many different ways to define an equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1.This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.According to our question-
Total SA of a cone = πr^2+πrl = πr(r+l)
Here r = 8 cm , slant height l=12 cm.
SA of cone =3.14 * 8 * ( 8+12) cm^2
=> 3.14*160 cm^2
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