Drag the tiles to the correct boxes. Not all tiles will be used. Consider the following function: f(x) = -3/4x+9. Place the steps for finding f^-1(x) in the correct order.
Answers
Answer:
The steps include:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Step-by-step explanation:
f(x) = –3/4x + 9
The inverse, f¯¹(x) of the above expression can be obtained as follow:
f(x) = –3/4x + 9
Let y = f(x)
y = –3/4x + 9
Interchange x and y
x = –3/4y + 9
Making y the subject of the expression, we have:
x = –3/4y + 9
Rearrange
x – 9 = –3/4y
Cross multiply
4(x – 9) = –3y
Divide both side by –3
–4/3(x – 9) = y
Clear bracket
y = –4/3x + 12
Replace y with f¯¹(x)
f¯¹(x) = –4/3x + 12
Therefore, the steps include:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Answer:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Step-by-step explanation:
f(x) = –3/4x + 9
The inverse, f¯¹(x) of the above expression can be obtained as follow:
f(x) = –3/4x + 9
Let y = f(x)
y = –3/4x + 9
Interchange x and y
x = –3/4y + 9
Making y the subject of the expression, we have:
x = –3/4y + 9
Rearrange
x – 9 = –3/4y
Cross multiply
4(x – 9) = –3y
Divide both side by –3
–4/3(x – 9) = y
Clear bracket
y = –4/3x + 12
Replace y with f¯¹(x)
f¯¹(x) = –4/3x + 12
Therefore, the steps include:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Step-by-step explanation:
Related Questions
Pawan is 10 years older than Arav. 5 years ago one seventh of pawan's age was equal to one fifth of Arav's age. Find their present ages.
Answers
Answer:
Arav is 30 and Pawan is 40
Step-by-step explanation:
We can call Arav's age x and Pawan's age x + 10, therefore we can write the following equation:
1/7((x + 10) - 5) = 1/5(x - 5)
1/7(x + 5) = 1/5(x - 5)
5(x + 5) = 7(x - 5)
5x + 25 = 7x - 35
-2x = -60
x = 30 so x + 10 = 40
If you have 2345 and you multiple it by 2 divide it by 6 and add on 22299 what will the answer be?
Answers
Answer:
69242/3 or 23080.666667
Step-by-step explanation:
2345 is multiplied by 2. Then the result is divided by 6. Then 22299 is added to the final result.
2345 × 2
= 4690
4690/6
= 2345/3
2345/3 + 22299
= 69242/3
solve systems by substitution method x + y = 20 3x + 4y = 72
Answers
Answer:
x = 8; y = 12.
Step-by-step explanation:
x + y = 20
x = -y + 20
3x + 4y = 72
3(-y + 20) + 4y = 72
-3y + 60 + 4y = 72
y = 12
x + 12 = 20
x = 8
Check your work!
3(8) + 4(12) = 72
24 + 48 = 72
72 = 72
Hope this helps!
Answer:
X=-12 and Y= 32
Step-by-step explanation:
x+y=20 -> 1
3x+4y=72 -> 2
Form 1,
[x+y=20]×4
4x+4y=60 ->3
Form 2,
3x+4y=72
4y= 72 -3x ->4
Sub (4) into (3)
4x+72-3x= 60
x = -12
Sub X=-12 into (1)
-12+y=20
y= 32
Hope this helps.
what is the slope of y =2x-1
Answers
Answer:
The slope m = 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the equation:
y = 2x - 1 → m = 2, b = -1
Answer:
The slope of this equation is 2.
Step-by-step explanation:
In a y=mx+b equation, the slope is 'm,' so whatever number is before x in an equation like this is the slope.
So y=mx+b -> y=2x+b -> 2=m, b=-1
n the kite, AC = 10 and BD = 6. What is the area of kite ABCD? 15 square units 30 square units 45 square units 60 square units
Answers
Answer:45
Step-by-step explanation:
Answer:
B. 30 square units
Step-by-step explanation:
Edge 2021
For which situations is it appropriate to use a sample? Select three options.
Answers
Answer:
when there are a lot of options
to experiment
to test
Step-by-step explanation:
Find the total surface area.
Answers
The pyramid consists of 4 congruent triangular faces, and 1 square base.
Area of 1 triangular face:
1/2 * (5 in)/2 * (5.6 in) = 7 in^2
Area of base:
(5 in)^2 = 25 in^2
Then the total surface area is
4 * (7 in^2) + 25 in^2 = (28 + 25) in^2 = 53 in^2
PLEASE HELP!!!
What is the interquartile range of this data set?
1,5, 27, 29, 34, 46, 48, 61, 64, 84, 96
Answers
Answer:
37
Step-by-step explanation:
Answer:
D. 37
Step-by-step explanation:
Your choice is correct!
The diagonals of a quadrilateral are of lengths 6cm and 8cm. If the diagonals bisect each other at the right angles. Find the length of each side of quadrilateral ?
Answers
Answer:
Each side is 5 cm
Step-by-step explanation:
What you are being told is that the figure is a rhombus. The two sides of a right triangle are 1/2 the size of the diagonals.
a = 3
b = 4
c = the side length of the rhombus.
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
Take the square root of 25
sqrt(c)^2 = sqrt(25)
c = 5
Evaluate 4 - 0.25g + 0.5h when g = 10 and h = 5
Answers
Answer:
4
Step-by-step explanation:
Well first we need to plug in 10 for g and h for 5.
4 - .25(10) + .5(5)
4 - 2.5. + 2.5
1.5 + 2.5
= 4
Thus,
the answer is 4
Hope this helps :)
Answer:
4
Step-by-step explanation:
We are given the expression:
4 - 0.25g + 0.5h
We know that g= 10 and h=5. Therefore, we can substitute 10 and 5 into the expression.
4-0.25(10)+0.5(5)
Now, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
First, multiply 0.25 and 10
4-2.5+0.5(5)
Next, multiply 0.5 and 5
4-2.5+2.5
Next, subtract 2.5 from 4
1.5+2.5
Finally, add 1.5 and 2.5
4
4 - 0.25g + 0.5h when g=10 and h=5 is 4.
What is the sine value of pi over 6? negative 1 over 2 1 over 2 negative square root 3 over 2 square root 3 over 2
Answers
Answer:
1/2
Step-by-step explanation:
[tex]sin(\frac{\pi }{6} )=\frac{1}{2}[/tex]
sin(pi) = 0
sin(7pi/6) = -1/2
sin(pi/6) = 1/2
sin 3pi/2 = -1
sin pi/2 = 1
sin pi/3 = √3/2
sin 4pi/3 = -√3/2
Answer:
1/2
Step-by-step explanation:
I got it right on the exam.
A King wanted to replace his Prime-Minister but didn't want to upset him too much. So he called the Prime-Minister to his chamber and put two pieces of paper in his briefcase. He told the Prime-Minister that "On one piece of paper it says 'leave' and on the second piece of paper it says 'stay'". The piece of paper that you pull out of the briefcase will decide your fate." The Prime-Minister realized that both pieces of paper say 'leave'. What should the Prime-Minister do to be able to keep his position?
Answers
Answer: Ask the king to draw first and read it. Explain that if the king selects "leave" the PM's choice could only be "stay". It is then unnecessary for the PM to draw. It avoids embarrassing the king in his lie, demonstrates the PM's intelligence, and keeps his job.
Step-by-step explanation:
Please help ASAP! I’ll give brainliest:))
Answers
Answer with explanation:
After dilation about the origin(0,0) with the scale factor of 'k" , the image of the original point (x,y) becomes (kx,ky)
From the given graph, the coordinates of point C = (0,6) [Since it lies on y-axis , the x-coordinate is zero]
After a dilation about the origin(0,0) with the scale factor of [tex]\dfrac{1}{2}[/tex], the new point will be [tex](\dfrac{1}{2}\times0,\dfrac{1}{2}\times6)=(0,3)[/tex]
Now plot this point on y-axis at y=3 as given in the attachment.
Daniel is a very good television salesperson. His annual sales average at $187,400. His commission on sales is 30% and his annual base salary is $40,000. On average what is his annual gross income?
Answers
Answer: $96,220
Step-by-step explanation:
From the questionwe are we informed that Daniel is a very good television salesperson and that his annual sales average at $187,400 and his commission on sales is 30% while his annual base salary is $40,000.
His annual gross income will be his annual base salary plus commission annually. This will be:
= $40,000 + (30% × $187,400)
= $40,000 + (0.3 × $187,400)
= $40,000 + $56,220
= $96,220
A paintball court charges an initial entrance fee plus a fixed price per ball. P represents the total price (in dollars) as a function of the number of balls used n P=0.80n+5.50 What is the price for 10 balls, not including the entrance fee?
Answers
Answer:
$8
Step-by-step explanation:
It says P = per ball (which will be a number, n, for balls times the fixed price) plus a set entrance fee. So we find that the price per ball is $0.80, so 10 balls cost $8.
Answer:
$8
Step-by-step explanation:
A total of 46 percent of the voters in a certain city classify themselves as Indepen-dents, whereas 30 percent classify themselves as Liberals and 24 percent say thatthey are Conservatives. In a recent local election, 35 percent of the Independents,62 percent of the Liberals, and 58 percent of the Conservatives voted. A voter ischosen at random. Given that this person voted in the local election what is theprobability that he or she is
Answers
Complete question :
A total of 46 percent of the voters in a certain city classify themselves as Indepen-dents, whereas 30 percent classify themselves as Liberals and 24 percent say thatthey are Conservatives. In a recent local election, 35 percent of the Independents,62 percent of the Liberals, and 58 percent of the Conservatives voted. A voter ischosen at random. Given that this person voted in the local election what is theprobability that he or she is Given that this person voted in the local election, what is the probability that he or she is (a) an Independent? (b) a Liberal? (c) a Conservative? (d) What fraction of voters participated in the local election?
Answer:
A) 0.331 ; B) 0.383 ; C) 0.286 ; D) 0.4862
Step-by-step explanation:
Given the following :
P(Independent(I)) = 46/100 = 0.46
P(Liberal(L)) = 30/ 100 = 0.3
P(Conservative(C)) = 24 / 100 = 0.24
Election participation (EP) :
P(EP | I) = 35 / 100 = 0.35
P(EP | L) = 62/100 = 0.62
P(EP | C) = 58/100 = 0.58
P(EP) = P(EP | L)*P(L) + P(EP | I)*P(I) + P(EP | C)*P(C)
P(EP) = (0.62*0.3) + (0.35*0.46) + (0.58*0.24)
P(EP) = 0.186 + 0.161 + 0.1392 = 0.4862
A) probability of Independent given that the person participated in election:
P(I Given EP) = [P(EP | I) * P(I)] / P(EP)
= (0.35 * 0.46) / 0.4862
= 0.161 / 0.4862
= 0.331
B) probability of Liberals given that the person participated in election:
P(L Given EP) = [P(EP | L) * P(L)] / P(EP)
= (0.62 * 0.3) / 0.4862
= 0.186 / 0.4862
= 0.383
C.) P(C Given EP) = [P(EP | C) * P(C)] / P(EP)
= (0.58 * 0.24) / 0.4862
= 0.1392 / 0.4862
= 0.286
A quarterback throws a football to a teammate. The football is 6.5ft above the ground when it leaves the quarterback's hand. His teammate catches it 3.5s later, at a height above the ground of 5 ft. Which quadratic model
Answers
Answer:
y = - 16t² + 55.6t + 6
Step-by-step explanation:
Using y - y₀ = vt - 1/2gt² where g = 32 ft/s², and v the velocity of the football
So y = y₀ + vt - 1/2 × (32 ft/s²)t²
y = y₀ + vt - 16t² where y₀ = 6.5 ft
y = 6 + vt - 16t²
Now, when t = 3.5 s, that is the time the teammate catches the ball after the quarterback throws it, y = 5 ft. Substituting these into the equation, we have
5 = 6.5 + v(3.5 s) - 16(3.5 s)²
5 = 6.5 + 3.5v - 196
collecting like terms, we have
5 - 6.5 + 196 = 3.5v
194.5 = 3.5v
v = 194.5/3.5 = 55.57 ft/s ≅ 55.6 ft/s
So, substituting v into y, our quadratic model is
y = 6 + 55.6t - 16t²
re-arranging, we have
y = - 16t² + 55.6t + 6
please help :) What is 96,989,200 written in scientific notation? A. 96.9892 × 10 to the 5 power B. 9.69892 × 10 to the 7 power C. 9.69892 × 10 to the 6 power D. 9.69892 × 10 to the 8 power
Answers
Answer: B. 9.69892 × 10^7
You'd have to move the imaginary decimal at the end of the number 96,989,200 seven times in order to get only one number that isn't zero before the decimal point.
Which graph shows the solution to the system of linear inequalities? x + 3y > 6 y ≥ 2x + 4 PLEASE HELP
Answers
A system of inequalities can be solved graphically.
See attachment for the required graph
The inequalities are given as:
[tex]\mathbf{x +3y > 6}[/tex]
[tex]\mathbf{y \ge 2x + 4}[/tex]
The options are not given.
So, I have attached the graph that illustrates the solution to the system of inequalities
From the graph, we have the solutions as:
[tex]\mathbf{x >-0.857}[/tex][tex]\mathbf{y \ge 2.286}[/tex]Read more about graphs of inequalities at:
https://brainly.com/question/15748955
Currently 350bales of hay are stored in a barn. Each day, a farmer stacks 30 more bales of hay in the barn. Let H be the number of bales of hay in the barn after t days have passed. Which of the following best explains the relationship between t and H?
Answers
Answer:
Hey there!
We have H=30t+350.
350 is the original value, and for every day t, 30 more bales are added.
Hope this helps :)
Answer:
H = 350 + 30t
Step-by-step explanation:
350 bales plus 30 bales per day
350 + 30t
H = 350 + 30t
Consider a standard deck of 52 playing cards with 4 suits. If A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck, what is the intersection of A and B? (Remember that the black cards are spades and clubs.)
Answers
Answer: Intersection of A and B = 2
Step-by-step explanation:
Total cards = 52
Let A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck.
Total cards having 6 on them = 4
[There are 4 suits of two different colors red and black.]
Total black playing card =26
Intersection of A and B = Black cards having 6 = 2
hence, Intersection of A and B = 2
evaluate f(x)=-2x-5forx=3 -6 1 11 -11
Answers
Answer:
-11
Step-by-step explanation:
f(x)=-2x-5
Let x = 3
f(3) = -2 *3 -5
= -6 -5
= -11
please help :) Choose the expression that is equivalent to the expression: 2 x 2 x 2 x 2 A. 2 x 4 B. 4 to the 2 power C. 2 to the 4 power D. 2 x 2 x 2 x 2 x 4
Answers
Answer:
C. 2 to the 4'th power
Step-by-step explanation:
2x2x2x2 is 4 2's, the number of 2's indicates the power, so the answer would be 2 to the power of 4 because there are 4 2's
Hope this helps, If you have any questions, feel free to ask.
Have a good day! :)
Answer:
C 2 to the power of 4
Step-by-step explanation:
There are 2*2*2*2* 4 of the 2 so 2 to the power of 4
A survey asks "would you like to see more or less government spending on natural disasters?" Of the 1496 respondents, 723 responded "more" or "much more". The population of interest consists of
A) the proportion of American adults who would respond "more" or "much more"
B) the 723 respondents who responded "more" or "much more"
C) the 1496 respondents
D) all American adults
E) the proportion of respondents who responded "more" or "much more"
Answers
Answer:
D) all American adults
Step-by-step explanation:
The 1496 respondents are the sample of the survey that was used to represent the population of interest, which is the total population from which the sample was drawn and the population from which the researchers want to find conclusions.
Looking at the alternatives, the only one that fits the description is alternative D) all American adults .
Please help urgently ❤️❤️❤️
Answers
Greetings from Brasil...
Here we have application of Trigonometry
COS β = adjacent side ÷ hypotenuse (H)
bringing to our problem....
COS A = AC ÷ H
But we dont have AC.... We have to use Pitagoras:
AB² = AC² + BC²
AC² = AB² - BC²
AC = √(AB² - BC²)
AC = √(10² - 8²)
AC = √(100 - 64)
AC = √36
AC = 6So
COS A = AC ÷ H ⇔ COS A = AC ÷ AB
COS A = 6/10
COS A = 3/5Answer: B) 3/5
Step-by-step explanation:
Cos = adjacent/hypotenuse
Thus, the cos is AC/AB.
Because of Pythagorean Theorem, AC^2=AB^2-BC^2. Let AC be x.
[tex]x^2=10^2-8^2\\x^2=100-64\\x^2=36\\x=6[/tex]
Thus, the cos is 6/10, or 3/5
can someone help....
Answers
Answer:
-7 is no, -2 is no, 7 is no, and 10 is yes
Step-by-step explanation:
-5+9*(-7)>58
-5+-63>58
-68>58
-5+9*(-2)>58
-5+-18>58
-23>58
-5+9*(7)>58
-5+63>58
58>58
-5+9*(10)>58
-5+90>58
85>58
so the only one that is a solution is v=10, hope this helps
Answer: No, No, No, Yes
Step-by-step explanation:
Solve the equation for "v":
-5 + 9v > 58
9v > 63
v > 7
Check the options to see if they make a true statement:
-7 > 7 False
-2 > 7 False
7 > 7 False
10 > 7 TRUE!
Help please ty ty Appreciate it
Answers
Answer:
a. 113.1 cm^3.
b. 339.29 cm^3.
c. 18 cm.
d. 508.94 cm^3.
e. 169.65 cm^3.
Step-by-step explanation:
a. (4/3) * pi * (3^3) = (4/3) * pi * 27 = 36 * pi = 113.0973355, which is about 113.1 [tex]cm^{3}[/tex].
b. 113.0973355 * 3 = 339.2920066, which is about 339.29 cm^3.
c. Since the radius of a tennis ball is 3 cm, the diameter is 6 cm. There are three tennis balls, and the diameters added up become the height of the cylinder. 6 + 6 + 6 = 18 cm.
d. pi * (3^2) * 18 = pi * 9 * 18 = pi * 162 = 508.9380099, which is about 508.94 cm^3.
e. 508.9380099 - 339.2920066 = 169.6460033, which is about 169.65 cm^3.
Hope this helps!!
Two angles form a linear pair. The measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘ . Find the measure of each angle.
Answers
Answer:
70° and 110°
Step-by-step explanation:
If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘
Let A be the first angle = x°
Let B be the second angle = (1.4x+12)°
Since they form a linear pair, then
A+B = 180°
x + 1.4x+12 = 180°
2.4x = 180-12
2.4x = 168
x = 168/2.4
x = 70°
The measure of angle A = 70°
The measure if angle B = 1.4x+12
B = 1.4(70)+12
B = 98+12
B = 110°
The measure of both angles are 70° and 110°
In an experiment, three people toss a fair coin one at a time until one of them tosses a head. Determine, for each person, the probability that he or she tosses the first head. Verify that the sum of the three probabilities is 1.
Answers
Answer:
Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.
Step-by-step explanation:
The coin theoretically could give a very large number of tails first so each person's probability is made up of an infinite series.
P(1st person wins) = P(H) + P(TTTH) + P(TTTTTTH) + . . . etc
= 1/2 + (1/2)^4 + (1/2)^7 + (1/2)^10 + . . .
This is a geometric series with first term a = 1/2 and common ratio r = 1/8
Using formula a/(1 - r) this is (1/2)/(7/8) = 4/7
P(2nd person wins) = P(TH) + P(TTTTH) + P(TTTTTTTH)
= (1/2)^2 + (1/2)^5 + (1/2)^8 + . . .
Geometric series with sum (1/4)/(7/8) = 2/7
P(3rd person wins) = P(TTH) + P(TTTTTH) + P(TTTTTTTTH) + . . .
= (1/2)^3 + (1/2)^6 + (1/2)^9 + . . .
Geometric series with sum (1/8)/(7/8) = 1/7
Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.
Hope this helped!
Charlie used a regression calculator to generate the equation f(x) = –0.15x + 20.1 for the ordered pairs (2, 15), (4, 21), (6, 26), (8, 20), and (10, 14).
Is a linear representation the best way to represent the data? If it is, explain why. If not, explain why and suggest a better alternative.
Answers
Answer and Step-by-step explanation:
According to the given situation, The r-value associated with the ordered pairs for the linear function is very nearest to zero which does not results in adequate presentation of the outcome.
A quadratic model could properly comprise of a combination of data, as the set of data has a turning point.
This result in data rises and falls which represents the graph of quadratic's graph
A linear representation is not the best way to show the data from the equation as derived from the regression calculator.
What is the linear representation about?Note that when plotted on a graph, it will show an upside down u kind of shape, and it as such look linear is not a good choice.
Note also that the r-value is linked with the ordered pairs for the linear function as it is said to be closer to zero and thus, it does not show an adequate depiction of the outcome.
Therefore, A linear representation is not the best way to show the data from the equation as derived from the regression calculator.
Learn more about from
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