How does the graph of g(x) = 1/x+4-6 compare to the graph of the parent function f(x)=1/x ?
Answers
f(x-c) is shifting to the right by c units
f(x+c) is shifting to the left by c units
f(x)+c is shifting up by c units
f(x)-c is shifting down by c units
given that f(x)=1/x
g(x)=f(x+4)-6 thus f(x) is shifted to the left 4 units and down 6 units
We are given a parent function f(x) as:
[tex]f(x)=\dfrac{1}{x}[/tex]
and the transformed function g(x) is given by:
[tex]g(x)=\dfrac{1}{x+4}-6[/tex]
We know that the transformation of the type:
f(x) → f(x+a)
is either a shift a units to the left or to the right depending whether a is positive or negative respectively.
Also, the transformation of the type:
f(x) → f(x)+a
is the shift of the function f(x) either upward or downward depending on whether x is positive or negative respectively.
Here the function g(x) is:
[tex]g(x)=f(x+4)-6[/tex]
This means that the function g(x) is a shift of the function f(x) 4 units to the left and then it is translated 6 units downward.
Also we may see by the graph.
Related Questions
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip? ANSWER ASAP
Answers
If Bryson purchased 40 raffle tickets. There were 500 raffle tickets sold. Then 2/25 is the theoretical probability of Bryson winning the trip
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Bryson hopes to win a three-day vacation in a drawing that is being held at his office.
Bryson purchased 40 raffle tickets
The number of raffle tickets sold were 500
We need to find the theoretical probability of Bryson winning the trip
P(win)=40/500
=4/50
=2/25
2/25 because he bought 40 out of the 500 tickets
Hence 2/25 is the theoretical probability of Bryson winning the trip
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ6
What property justifies this statement? If segment A B is congruent to segment D E and segment D E is congruent to segment F G, then segment A B is congruent to segment F G.
Answers
In the problem 17- 8= 9, the number 9 is the ____________
Answers
In the subtraction problem 17 - 8, the number 9 is the difference, which is the result obtained after subtracting 8 from 17.
In the problem 17 - 8 = 9, the number 9 is the difference. In subtraction, the difference is the result of subtracting one number from another. Here, when we subtract 8 from 17, we get the difference of 9. This is because 17 is the minuend (the number from which another number is subtracted), 8 is the subtrahend (the number that is to be subtracted), and 9 is the difference (the result of the subtraction).
The circle design a class which represents a circle in the (x,y) coordinate plane. a circle object is initialized with three input arguments. the center of the circle specified as the first two inputs (x,y) and the radius of the circle. by default the circle will be centered at (0, 0) with a radius of 1. c = circle(0, 0, 1) the circle class should provide proper getters/setters for the x and y coordinates of the center as well as the radius. the circle should also have a getarea() and getperimeter() method. finally, the circle should have a method called, ispointwithincircle(x, y) which takes as augments the x and y coordinate of a point and determines whether the point lies within the circle. it should return a boolean indicating whether the point is within the circle.
Answers
The circle design a class which represents a circle in the (x,y) coordinate plane.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
from math import dist # to calculate distance between two points
# defining class circle
class Circle:
# constructor of Circle
# with default parameters
def __init__(self, x_coord=0, y_coord=0, radius=1):
self.centre_x = x_coord
self.centre_y = y_coord
self.radius = radius
# getters
def getX(self):
return self.centre_x
def getY(self):
return self.centre_y
def getRadius(self):
return self.radius
# setters
def setX(self, x):
self.centre_x = x
def sety(self, y):
self.centre_y = y
def setRadius(self, r):
self.radius = r
# function to calculate and return area
def getArea(self):
return 3.141*(self.radius**2)
# function to calculate and return perimeter
def getPerimeter(self):
return 2*3.141*self.radius
# calculates the distance between circle centre and
# given coordinates
# returns true if distance is less than radius
def isPointWithinCircle(self, x, y):
return dist([self.centre_x, self.centre_y], [x, y]) < self.radius
c1 = Circle(3, 3, 7)
c2 = Circle()
print("First Circle perimeter: " + str(c1.getPerimeter()))
print("First Circle area: " + str(c1.getArea()))
c2.setX(3)
c2.sety(3)
c2.setRadius(2)
if c2.isPointWithinCircle(4, 3.7):
print("(4, 3.7) is within circle two")
else:
print("(4, 3.7) is not within circle two")
print("Moving second Circle")
c2.setX(3+c2.getX())
if c2.isPointWithinCircle(4, 3.7):
print("(4, 3.7) is within circle two")
else:
print("(4, 3.7) is not within circle two")
Thus, the circle design a class which represents a circle in the (x,y) coordinate plane.
Learn more about circle here:
brainly.com/question/11833983
#SPJ2
Which polynomial has a factor of 3x+2?
1.) 6x²+x-2
2.) 6x²-5x-9
3.) 3x²-x-4
4.) 3x²+8x-8
Answers
You can factor 6x+x-2 in many ways-
But the right answer from factoring should come out to be (3x+2)(2x-1) because when you multiply it back out using the FOIL method, you come back to the original problem. Hope this helps:)
If i flip a coin 4 times what is the probability of one tail
Answers
Probability means occurrence of chance.
You have two sides in a coin: heads and tails.
so when you flip the coin 4 times the probability on getting one tail is one. If you had to find the probability of 2 tails then the answer would be [tex]2/4[/tex].
P = (of one tail) = [tex]1/4[/tex]
It cannot be simplified further, as it is in its simplest form already.
Hope I helped (:
Have a great day!
recursive equation for 5,8,11,14,17
Answers
In traveling across flat land, you see a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 15 miles closer to the mountain, the angle of elevation is 9° (see figure). Approximate the height of the mountain. (Round your answer to one decimal place.)
Answers
[tex]\bf tan(3.5^o)=\cfrac{y}{15+x}\implies 15+x=\cfrac{y}{tan(3.5^o)}\\\\\\ \boxed{x=\cfrac{y}{tan(3.5^o)}-15} \\\\\\ tan(9^o)=\cfrac{y}{x}\implies x\cdot tan(9^o)=y\\\\\\ \left[ \cfrac{y}{tan(3.5^o)}-15 \right]tan(9^o)=y \\\\\\ \left[ \cfrac{y-15tan(3.5^o)}{tan(3.5^o)} \right]tan(9^o)=y \\\\\\[/tex]
[tex]\bf \cfrac{y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)}{tan(3.5^o)}=y \\\\\\ y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)=y\cdot tan(3.5^o) \\\\\\ ytan(9^o)-ytan(3.5^o)=15tan(3.5^o)tan(9^o) \\\\\\ \stackrel{common~factor}{y}[tan(9^o)-tan(3.5^o)]=15tan(3.5^o)tan(9^o) \\\\\\ y=\cfrac{15tan(3.5^o)tan(9^o)}{tan(9^o)-tan(3.5^o)}[/tex]
make sure your calculator is in Degree mode.
the amount is small, but bear in mind that is mile units.
To solve such problems we must know about Tangent (Tanθ).
What is Tangent (Tanθ) ?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the mountain is 1.495 miles.
Given to us
AB = 15 miles∠CAD = 3.5°∠CBD = 9°In ΔCAD,[tex]\rm{ tan(\angle A) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]
[tex]tan(3.5^o) = \dfrac{CD}{15+x}[/tex]
[tex]CD=tan(3.5^o) \times(x+15)[/tex]
In ΔCBD,[tex]\rm{ tan(\angle B) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle B) = \dfrac{CD}{BD}[/tex]
[tex]tan(9^o) = \dfrac{CD}{x}[/tex]
[tex]CD=tan(9^o) \times(x)[/tex]
Equating CD,
[tex]tan(3.5^o) \times (x+15) = tan(9^o) \times x\\\\(x+15)= \dfrac{tan(9^o) }{tan(3.5^o) }\times x\\\\x+15=2.59\ x\\15 = 2.59x-x\\15= 1.59x\\x = 9.44[/tex]
Substituting the value of x
[tex]CD=tan(9^o) \times(x)[/tex]
[tex]CD=tan(9^o) \times(9.44)\\CD= 1.495[/tex]
Hence, the height of the mountain is 1.495 miles.
Learn more about Tangent (Tanθ) function:
https://brainly.com/question/10623976
You are taking part in a charity walk, and you have walked 12.5 miles so far. Your girl is to walk 20 miles. How many more miles do you need to walk to meet your goal?
Answers
After walking 12.5 miles with a goal of 20 miles, you need to walk 7.5 more miles to meet your goal.
To meet your goal in the charity walk, you need to calculate how many more miles are left to walk after having walked 12.5 miles with a goal of 20 miles. The calculation is simple subtraction: 20 miles (goal) - 12.5 miles (distance already walked) = 7.5 miles remaining to be walked. So, you need to walk 7.5 more miles to meet your goal.
A small train at an amusement park is carrying passengers. Half of the passengers are 4 years old, 1/10 are 5 years old, 3/10 are 6 years old, and 1/10 are 7 years old.
What is the expected age for one of the passengers on the train?
A. 5 years
B. 5.5 years
C. 6 years
D. 6.1 years
Answers
E(x) = 4(1/2) + 5(1/10) + 6(3/10) + 7(1/10)
E(x) = 5 years
By doing this we are giving each age group a percentage of the entire population.
Hope this helps!
A business owes $8000 on a loan. Every month, the business pays 12 of the amount remaining on the loan.
How much will the business pay in the sixth month?
Answers
Answer:
$125 on the 6th month
Two angles are supplementary. one angle is 4 degrees° less than three times the other. find the measures of the angles.
Answers
and we have the sum a+b=180.
in addition 3b-4=a
So we have 3b-4+b=180
or 4b=184 and at the end we have b=46, a= 134
Which angle is the included angle for MP¯¯¯¯¯¯ and MN¯¯¯¯¯¯¯ ?
∠M
∠N
∠P
Answers
Answer:
First one.
Step-by-step explanation:
M is in both angles.
we know that
An included angle is the angle between two sides of a triangle
so
in the triangle MNP
1) the included angle for MP and MN is the angle M
2) the included angle for PM and PN is the angle P
3) the included angle for NM and NP is the angle N
therefore
the answer is
the included angle for MP and MN is the angle M
There are 3 people who work full time and are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full time. if one of the people is budgeted for 1/2 of the time and the other person is budgeted for 1/3, what part od the third workers time should be budgeted to this project
Answers
5/6 + x = 1
x = 1/6
x being the amount of time for the third person. YOU'RE WELCOME :D
Please help thank you very much.
Answers
For the first picture, the correct answer is option B
They say that AB = BC = CD and they want us to find JM.
Well, since the right side are equal, the left side must equal to.
So, all we have to do is add them.
JK = KL = LM
7 + 7 + 7 = 21
------------------------------
The answer is 720
Sum = (6-2) * 180
Sum= 4 * 180
Sum = 720
For the last one, the correct answer is 99
This is too complicated to explain :)
I hope this helps!
Solve the system of equations by graphing [tex] \left \{ {{y=- \frac{3}{2}x+2 } \atop {y=3x-7}} \right.[/tex] *Show all work
Answers
That is a straightline with slope -3/2 and y-intercept 2
If you do not know how to graph it, you can make a table like this:
x y = (-3/2)x + 2
-1 3/2 + 2 = 7/2
0 0 + 2 = 2
2 - 3 + 2 = -1
4 - 6 + 2 = - 4
2) Graph of y = 3x - 7
That is a straight line with slope 3 and y intercept -7
If you do not know how to graph it you can make a table like this:
x y = 3x - 7
-1 - 3 - 7 = - 10
0 0 - 7 = - 7
1 3 - 7 = - 4
2 6 - 7 = - 1
3 9 - 7 = 2
3) When you draw the two lines you will see that the intersect at x = 2, with the correspondant y = - 1.
That point of intercection is the solutions of the system (2, -1)
Write 1.42 as a fraction or mixed number in simplest form.
Answers
Mr.Williams' physical education class lasts 7/8 hour.How many minutes are not spent on instructions . playing game:1/2 , instructions: 1/5 ,warm up and cool down:3/10
Answers
1/5 spent on instruction - 20%
Just find 80 percent of 52.5 and you will get 42 minutes not spent on instruction
A company can manufacture x x hundred items for a total cost of c = 500 + 1100 x − 100 x 2 c=500+1100x-100x2. find x x if the total cost is $ 2 , 300 $2,300.
Answers
We are given the equation:
c = 500 + 1100 x – 100 x^2
Solve for x given the value of c = 2300
Rearrange and substitute:
- 100 x^2 + 1100 x + 500 = 2300
Divide everything by -100:
x^2 – 11 x – 5 = - 23
x^2 – 11 x = - 18
Completing the square:
(x – 11/2)^2 = - 18 + (11/2)^2
x – 11/2 = ±3.5
x = 2, 9
So x is 2 or 9
Can you pease help me find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic devision?
thank you!
Answers
| 1 - 5 6 - 30
|
|
5 | 5 0 30
----------------------------------------------
| 1 0 6 0 <------ the resiude is 0.
Resiude 0 means that the polynomial is divisible by x - 5, and that means the root is x = 5.
That is the only rooto because the quotient is x^2 + 6, which does not have real roots.
Answer: x = 5
Which shows the image of ΔRST after the rotation (x, y) → (y, –x)?
Answers
examples?
Step-by-step explanation:
which number is halfway between 1/2 and 5/6
Answers
The fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
What is a fraction ?
A fraction is used to represent a portion or component of a whole. The numerator and denominator are its two parts.
The two fractions are given which are [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex].
We know that numerator is the top value of the fraction whereas the denominator is the bottom value of the fraction. We need to add the given fractions and then divide it by 2 to find the halfway between the two given functions.
To add the fractions we need to equal denominator firstly. The common denominator of 2 and 6 will be 6 because 6 is a multiple of both 2 and 6.
So ,
Halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is :
= ( [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{6}[/tex] ) / 2
= [tex]\frac{3 + 5}{6}[/tex] / 2
= [tex]\frac{8}{6}[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{6}[/tex]
or
[tex]\frac{2}{3}[/tex]
Therefore , the fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
Learn more about fractions here :
https://brainly.com/question/17220365
#SPJ2
what is the curconfrrince
Answers
Plz mark me brainliest!
Hope this helps!
The distance around a circle is called the circumference,while, the distance through the circle through the center is called the diameter. π is the ratio of the circumference to the diameter. Meaning, for any circle, if you divide the circumference by the diameter, you will always get π. This is expressed in the formula: C/d=π
Find the percent change from 60 to 63. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent.
Answers
[tex] \frac{3}{60}[/tex] = 0.05 ≈ 5%
5% increase
what is 10 1/2 divided by 2 1/4
Answers
The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The mathematical expression is;
'' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] ''
Now, Solve the mathematical expression by using division method as;
The mathematical expression is,
[tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] = [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
Change the mixed fraction into improper fraction as;
⇒ [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
⇒ [tex]\frac{21}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]
It can be solve as;
⇒ 21/2 ÷ 9/4
⇒ 21/2 × 4/9
⇒ 14/3
Change into mixed fraction as;
⇒ [tex]\frac{14}{3} = 4 \frac{2}{3}[/tex]
So, [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex] = [tex]4 \frac{2}{3}[/tex].
Therefore,
The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].
Learn more about the divide method visit:
https://brainly.com/question/28119824
#SPJ2
1/2 of 6 is what percentage of 1/4 of 60 options: A 16 2/3 B 8 1/3 C 37 1/2 D 8 E 12 1/2 Show work
Answers
CAN someone please check this i will give out brainliest !
its proofs and theorems in geometry
check the ones in red
Answers
Reason 3 should be "angle congruence postulate" leading us from the congruent notation shown in statement 2 to the equality notation in statement 3.
In short, you have reason 2 and reason 3 swapped. Reason 5 is in the proper place.
How do you think business owners determine how much of each of their products to make?
Answers
Answer: First - Add your costs to your mark-up. (Costs + Mark-up Amount = Baseline Price), Next - If you want to find the price percentage, (Costs x Mark-up Percentage = Mark-up Amount) (Mark-up Amount + Costs = Baseline Price) Next - Multiply your baseline price by your overhead percentage and figure out what is the amount that you must add to the baseline prices so that the overhead expenses can be covered. (Price x Overhead Percentage = Overhead Contribution)Now you must finally add your overhead contribution to your baseline price: (Overhead Contribution + Baseline Price = Final Price)
If Log 4 (x) = 12, then log 2 (x / 4) is equal to
A. 11
B. 48
C. -12
D. 22
Answers
The answer to your problem is D. 22. Hope this helps and have a wonderful day!
The easiest way:
a) log₄ (x) = 12, re write it in exponential way : x = 4¹² = 16,777,216
b) Plug the value of x in log₂ (x / 4)
log₂ (16,777,216 / 4) → log₂(4,194,304)
and log₂(4,194,304) = 22
A gasoline pump delivers 4 2/5 gallons of gas per minute. How many minutes will it take to fill a gas tank that holds 17 1/4 gallons?
Please show all steps and equation.