WILL MARK BRAINIEST!! 50 POINTS.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x).
Part B: Solve for k in each type of transformation.
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x).
Answers
Answer:
Part A: The two types of types of transformation are
1) Rotation of 11.3° about (1, 2)
2) By algebraic transformation
Part B:
Rotation by 11.3° and T(2 - y)×1/2 + x, 0)
Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
Step-by-step explanation:
The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)
The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)
The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(3 - 1) = 5
The equation in point and slope form is y - 3 = 5×(x -1)
y = 5·x - 5 + 3 = 5·x - 3
y = 5·x - 3
The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(1 - 1) = ∞
∴ The equation in point and slope form is x = 1
Therefore, the two equations meet at the point (1, 2)
The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows
Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°
Rotation of f(x) by 11.3° about (1, 2) gives g(x)
Hope this helped!
Related Questions
James is observing the population of the fish he put into a pond. He built a pond and
populated it with 700 fish. The population of the fish doubles every year.
Answers
The exponential equation is given by y = 700(2)ˣ
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of fish after x hours.
Given that he starts with 700 fishes, hence
a = 700
The population of the fish doubles every year, hence:
b = 2
The exponential equation becomes:
y = 700(2)ˣ
Find out more at: https://brainly.com/question/12490064
Which item produces the magnetic field in the electromagnet?
A-paperclips
B- a switch
C-paint brushes
D- a magnet
Answers
Answer:
Its ethier a switch or magnet
The Kicking Cacti and the Sprinting Stingrays met in their town's annual kickball championship this year. They were so evenly matched that the game lasted 11 innings! The Stingrays had 3 pitchers, and each of them pitched for the same number of innings.
How long did each of the pitchers for the Stingrays pitch?
Answers
Answer:
11/3 = 3 2/3 innings
Step-by-step explanation:
3 pitchers = 11 innings
1 pitcher = x innings
in the first equation, divide both sides by 3 to get 1 pitcher on one side
1 pitcher = 11/3 innings = 3 2/3 innings
What is the change in elevation for
(3)(4)(-3.5)
Answers
Hey there!
(3)(4)(-3.5)
= 12(-3.5)
= -42
Therefore, your answer SHOULD be: -42
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=−16x^2+160x+150
Answers
Answer:
Answer below
Step-by-step explanation:
Time can not be negative from any perspective. Hence, the correct answer is 10.16 seconds.
The equation of the path of a rocket is given that is y= x^2 + 153x + 98
We need to determine the time that the rocket will hit the ground.
Now, if the rocket hits the ground after the launching then the overall displacement at the time of hitting the ground will be zero.
Therefore, the value of y is 0.
Thus, -16x^2 +153x + 98 = 0
Now, the formula for finding the roots of the quadratic equation
ax^2 +bx +c = 0 is given as:
[tex]x^{1} =\frac{-b+\sqrt{b^2 -4ac} }{2a}[/tex]
[tex]x^2 = \frac{-b -\sqrt{b^2 -4ac} }{2a}[/tex]
Comparing the expression with the standard form of the equation.
a = -16b = 153 and c = 98
By applying the formula there are two values are come that is,
x^1 = -0.602555
x^2 = 10.1651
Time can not be negative from any perspective.
Hence, the correct answer is 10.16 seconds.
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(Hope this helps can I pls have brainlist (crown)☺️)
5(x-a)=3(x+b)
Solve for x
Answers
Answer:
[tex]x=\frac{3b}{2} +\frac{5a}{2}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
5(x - a) = 3(x + b)
5x - 5a = 3x + 3b
2x = 5a + 3b
x = 2.5a + 1.5b
Pls help me I’ll brainlest ASAP
Answers
A CD is on sale for $100.00. The sales tax rate is 6%. How much will the total cost be for the CD
Answers
Answer: $106.00
Step-by-step explanation:
If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answers
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
Learn more about rate of change here:
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88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86
Please answer this I really need help
Answers
Answer:
The answer is 90.
Step-by-step explanation:
90 is in the middle
Answer:
d
Step-by-step explanation:
cause i said so
Which equation below represents an equation in standard form?
Answers
Answer:
C
Step-by-step explanation:
standard form is ax + by = c, which is true for the third option.
What is the total holiday debt (no less than $500) that you are trying to pay off and what did you purchase
to accrue (accumulate) that debt?
Answers
Ezra has $10 to spend on a taxi ride. The taxi company charges a flat rate of $4, plus $1.50 per mile. What is the maximum amount of miles Ezra can afford to travel in this taxi?
PLS ANSWER ASAP I WILL GIVE BRAINLIEST AND WILL GIVE 22 POINTS!!!!
Answers
The hypotenuse is NOT located across from the right angle
True or false
Answers
The statement, The hypotenuse is NOT located across from the right angle is false.
What is a right angled triangle?
A right-angled triangle is a type of triangle that has an angle that measures 90 degrees. The triangle has three sides. The hypotenuse is the longest side of a right-angled triangle. Other sides are the base and the length. The sum of sides in a a right-angled triangle is 180 degrees.
Please find attached an image of a right-angled triangle. To learn more about a triangle, please check: https://brainly.com/question/9329354
hi so my teacher gave me this and i am not sure if i did it right, this is what i put for the first Question
degree = 3
leading coefficient = 1
and the it is the arrows are going up/down so its a odd degree
and i put that the answer is d i did the rest like this please tell me where i went wrong/if i did
Answers
Answer:
First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients:❤
Help me with this question thanks so much
Answers
Since it’s times 6 each time and the base is 6 it can be written as an exponent 6*6*6...
Hope that helps :)
Helppppppppppppp helppppppppppppp
Answers
Answer: 2
Step-by-step explanation:
[tex]\frac{\sqrt{2x} }{\sqrt{} x-1}[/tex]
For which values of x does each expression make sense?
Answers
Answer:
The expression is unclear so:
If the denominator is [tex]\sqrt{x}-1[/tex] then your set of existence is given by
[tex]\left \{ {{x\ge0} \atop {x\ne1}} \right.[/tex]
since you want the quantity inside both square roots to be positive (and it happens for both to be simply [tex]x\ge0[/tex] and you don't want a zero at the denominator so you have to rule out 1.
If the square root includes the whole denominator [tex]\sqrt{x-1}[/tex] the condition becomes [tex]\left \{ {{x\ge0} \atop {x>1}} \right.[/tex]
where you don't include the extreme in the second condition since, again, you don't want to divide by 0. The answer in this case is simply [tex]x>1[/tex] since values between 0 and 1 will give a negative root which is not a real number.
Three segments are chosen at random from six segments having lengths of 2, 3, 5, 6, 7 and 10 units. What is the probability that the three segments chosen could form a triangle? Express your answer as a common fraction
Answers
Using the probability concept, it is found that there is a [tex]\frac{7}{20}[/tex] probability that the three segments chosen could form a triangle.
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order in which the sides of the segments are chosen is not important, hence, the combination formula is used to find the number of total outcomes.Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Total outcomes:
3 segments from a set of 6 lengths, hence:
[tex]C_{6,3} = \frac{6!}{3!3!} = 20[/tex]
Desired outcomes:
Segments can make a triangle if the sum of the lengths of the smaller segments is greater than the length of the larger segment.Hence, the possible options are: (2,5,6), (3,5,6), (3,5,7), (5,6,7), (5,6,10), (5,7,10), (6,7,10).There are 7 desired outcome, hence [tex]D = 7[/tex]Then:
[tex]p = \frac{D}{T} = \frac{7}{20}[/tex]
[tex]\frac{7}{20}[/tex] probability that the three segments chosen could form a triangle.
To learn more about the probability concept, you can take a look at https://brainly.com/question/24437717
Big Sam, an engineer of the Oval Express says: "We blew off a cylinder head an hour after leaving the station and had to continue the trip at three-fifths of the former speed, which brought us in two hours late. If the accident had occurred fifty miles father on, the train would have arrived forty minutes sooner". Based on Sam's description, how long was the run between the two train stations?
A. 150 miles
B. 200 miles
C. 250 miles
D. 300 miles
Answers
{(y/50)+2} hour=y/30 hour gives y=150 miles. Since, the train already had covered 50 miles at full-speed before the cylinder blew, so the run between the stations was 50+150=200 miles.
Answer:
Ig 200 miles
Step-by-step explanation:
I am guessing
I was absentee and i dont know how to solve it help plz
Answers
Answer:
-1/3 or 1/-3 (it doesn't matter which one you pick because its still the same)
Step-by-step explanation:
You find slope by doing rise over run. Its left to right so you start on the left dot and go down one. This makes it -1 because you're going down, not up. You move 3 to the right which makes it positive. Once you do this itll lead you right the the 2nd point. 1 down= -1
3 right= 3
-1/3
Find x given the prism has a surface area of 286 in². Explain your thoughts
Answers
Answer:
h
=
3
r
=
4
h
=
2
r
=
6
h
=
4
l
=
4
w
=
4
Step-by-step explanation:
22
23
The Krishna family of 5 spent $12 per person at the golf
range plus an additional $40 for equipment. How much
did they spend?
24
i
Answers
Answer:
$100
Step-by-step explanation:
12x5=60
+40= $100
Answer:
$100
Step-by-step explanation:
This is easy
12x5=60
+40=$100
Someone help?
Find the problem:
-5x - 16 = 8x - 1
Fix the problem:
?
Answers
[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]
A shed has dimensions of 12m in length and 5 m in width. Both the length and width are increased by the same amount in order to increase the floor area by more than double the original area?
Answers
The amount by which the length and width of a shed can be increased to
more than double the area, depends on the initial dimensions.
The amount that can be added to both the length and the width to increase the floor area by more than double the original area is more than 3 meters.Reasons:
The given parameters of the shed are;
The length of the shed = 12 m
Width of the shed = 5 m
The amount by which the length and the width are increased = The same amount
The new area after the increase in the length and width of the shed = More than double the initial area
Required:
The amount of increase in the length.
Solution:
Let the amount by which the length and width are increased = x
We have;
Initial area of the shed = 12 m × 5 m = 60 m²
The new area = (12 + x) × (5 + x) > 2 × 60
By multiplication, we get;
(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120
x² + 17·x + 60 - 120 > 120 - 120 = 0
x² + 17·x - 60 > 0
By factorization, we get;
(x + 20)·(x - 3) > 0
x > -20, or x > 3
The increase (positive) amount of the solution is x > 3
Therefore, the amount by which both the length and the width can be increased to more than double the area is x > 3 meters
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What is the mass of an object that has 50 newtons of force and is accelerating at the rate of 2 m/s/s
HELP PLEASE!! Do not explain need full answer
Answers
Answer:
F= ma
m = F/a
m = 50/2
m = 25
Answer equal 25
Work out the area of the shaded shape.
Answers
Answer:
61 m²
Step-by-step explanation:
Find the area of the whole rectangle and subtract the part that is cut off
Area = [tex]11 *8 - 9 *(8-5)[/tex]
= [tex]88 - 9*3[/tex]
= [tex]88 - 27[/tex]
= [tex]61[/tex]
Units = m * m or m²
61 m²
-Chetan K
HELP PLSSS
Use the commutative
property to make an
equivalent
expression.
4+m=?
A. 4-m
B. m+4
Answers
Answer:
B. m+4
Step-by-step explanation:
You are just writing the same equation but backwards so that the numbers still stay the same as well as the answer.
Answer: A
Step-by-step explanation:
2 times the difference of 5 and 3
Answers
Answer:
4
Step-by-step explanation:
Equation:-
2(5-3)
=> 2(2)
=> 4
A-B equals, if A =5x^2-4x-11 and B=-x^2+3x-5
Answers
Answer:
A-B = 6x^2-7x-6
Step-by-step explanation:
A = 5x^2-4x-11
B = x^2+3x-5
A-B = (5x^2-4x-11) - (-x^2+3x-5) = 5x^2-4x-11+x^2-3x+5 = 6x^2-7x-6
