Answers
Answer:
Third option.
Step-by-step explanation:
The coordinates are (1, 3)
x = 1
y = 3
Put x as 1, the output should be 3.
g(1) = 3(1)²
g(1) = 3(1)
g(1) = 3
The transformation of a function may involve any change. The function of the g(x) can be written as 3x². The correct option is C.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f(\dfrac{x}{k})Given that f(x)=x², since the function g(x) is also similar to f(x), therefore, both the function are quadratic functions.
Since f(x) is streched vertically to form g(x), therefore, the function g(x) in terms of f(x) can be written as,
g(x) = k × f(x)
y = k × x²
Also, it is passing through the point (1,3), therefore, we can write,
3 = k × (1)²
3 = k
Thus, the function of the g(x) can be written as 3x².
Hence, the correct option is C.
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Related Questions
Stats question two way tables
Answers
Answer:
Step-by-step explanation:
Not liking rock mostly doesn't effect not liking just rap, since half like both rock and rap.
Though, there are 2 more people that like just rock compared to just rap, so you are more likely to like just rock.
Additionally, if you don't like rock, there is a 31.4 % that you don't like rap as well, since 17 people like neither.
There are two consecutive even numbers such
that twice the first is 46 more than the second.
Form an equation and solve to find the two
numbers.
Answers
Step-by-step explanation:
Let the numbers be x and y
2 consecutive even nos.
therefore y = x+2
twice of the first (2x) is 46 more than y
2x = y+46
Solving both the equations
x - y + 2 = 0
(-)2x - y - 46 = 0
____________
-x + 0 + 48 = 0
____________
x = 48
y = x+2
= 48 +2
= 50
Therefore the 2 nos. are 48 and 50
Hope this answers helps you
Which of the following have 3 significant figures? Check all that apply
Answers
Answer:
B.
D.
Step-by-step explanation:
Which two values of x are roots of the polynomial below?
x²-11x+17
Answers
Answer:
It is E and F
Step-by-step explanation:
A quadratic equation is written in the form of ax²+bx+c. The two values of x that are the roots of the polynomial are E and F.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The roots of the quadratic equation are found as shown below,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
If the given equation x²-11x+17 is compared with the general quadratic equation ax²+bx+c, then the value of a, b, and c is 1, -11, and 17, respectively.
The roots of the given polynomial x²-11x+17=0 can be found as shown below. Therefore, The roots of the polynomial are,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\x = \dfrac{-(-11) \pm \sqrt{(-11)^2 - 4(1)(17)}}{2(1)}\\\\x = \dfrac{11 \pm \sqrt{121 - 68}}{2}\\\\x = \dfrac{11 \pm \sqrt{53}}{2}[/tex]
x= (11 + √53)/2 , (11 - √53)/2
Hence, the two values of x that are the roots of the polynomial are E and F.
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Find the sum 3/5+1/9
Answers
hope it helps you tell me in the comment box
(•‿•)
evaluate 0.53n + 5 when n= 3 and when n= -3
Answers
Answer:
6.59 and 3.41
Step-by-step explanation:
To evaluate, substitute n for each of the given values.
So when n= 3:
0.53n + 5 = 1.59 + 5 = 6.59
And when n = -3
0.53 n + 5 = -1.59+5=3.41
Hope this helps
I REALLY NEED HELP MY DAD YELLED AT ME
Answers
Answer:
2/3
Step-by-step explanation:
f(x)=g(x)
-3x+4=2
Add 3x
3x+2=4
subtract 2
3x=2
divide by 3
x=2/3
Answer:
x= 2/3
Step-by-step explanation:
The value where f(x) = g(x) is where the two functions intersect
That would be at
f(x) = g(x)
-3x +4 = 2
Subtract 2 from each side
-3x = -2
x = 2/3
We know the y value. Substitute x into the equation
g(2/3) = 2
y = 2
The point is (2/3,2)
The first two terms in a sequence are 8 and 11. What is the next value if this sequence is arithmetic?
Answers
Answer:
14
Step-by-step explanation:
From the question we are given the first term 8,second term 11 and we are to find the third term.
Using the formula:Tn=a+(n-1)d
Where a=first term=8
n=number of terms =3
d= difference between terms( second term -first term)=11-8=3
T3=8+(3-1)3
=8+2(3)
=8+6
The next term =14
a parking garage charges $2.50 base free plus an hourly rate of $4.00. If you hve most $12.50 how many parking you can
Answers
Answer: 2.5 hours or 2 hr and 30 min
Step-by-step explanation:
We can set up an equation to find how many hours you can park.
2.5+4x=12.5
The 2.5 comes from the base fee. The 4x is the hourly rate, where x is hours. The 12.5 is the total amount of money you have.
Since we have our equation, we can solve for x.
4x=10
x=2.5
You can park for 2.5 hours, or 2 hours and 30 min.
if x4x2/3=x^awhat is the value of a?
(Number 7)
Answers
Answer:
4 2/3
Step-by-step explanation:
[tex]x^4x^{2/3}= \\\\x^{4+2/3}= \\\\x^{4 \ 2/3}[/tex]
Therefore, a= 4 2/3.
Hope this helps!
3×-y=5,2×+y=5 pleaseplease
Answers
Answer:
x = 2
y = 1
Step-by-step explanation:
3x - y = 5..............(1)× 1
2x + y = 5...….......(2)× 1
3x - y = 5..............(3)
2x + y = 5.............(4)
Cancel y
3x + 2x = 5 + 5
5x = 10
Divide both sides by 5
x = 2
Substitute for the value of y
3x - y = 5
3(2) - y = 5
6 - y = 5
6 - 5 = y
1 = y
y = 1
30 points A repeating decimal + A fraction...
Answers
Answer:
rational
Step-by-step explanation:
Answer:
Rational Number
Step-by-step explanation:
A repeating decimal added to a fraction will result in a rational number.
If the point (x, y) is on the y-axis, which of the following must be true? A). x=0 B). y=0
Answers
Answer:
X = 0
Step-by-step explanation:
Instructions: Find the angle measures given the figure is a rhombus.
Answers
Answer:
m∠1 = 90°
m∠2 = 55°
Step-by-step explanation:
1. m∠1 = 90° because by definition, the diagonals of a rhombus are perpendicular, or intersect at 90°.
2. Because of vertical angles, the angle opposite of ∠1 is also 90°. A triangle has a total of 180°.
m∠2 + 90 + 35 = 180
90 + 35 = 125
m∠2 + 125 = 180
subtract 125 from both sides to solve for m∠2
m∠2 = 55°
i’m not sure how to solve “system of equations”
Answers
Hey there! :)
Answer:
(2, -2)
Step-by-step explanation:
-2x + y = -6
4x + 3y = 2
We can begin by setting the first equation equal to y:
-2x + y = -6
Add 2x to both sides:
y = 2x - 6
Plug this equation for y into the second equation:
4x + 3(2x - 6) = 2
Distribute:
4x + 6x - 18 = 2
Combine like terms:
10x = 20
x = 2
Plug the value of 'x' into an equation to solve for 'y':
-2(2) + y = -6
-4 + y = -6
y = -2
Therefore, the solution is (2, -2)
U 3 4
Lucy buys 7 kg of nuts to sell.
She pays £10 for the nuts.
Lucy puts all the nuts into bags.
She puts 350 g of nuts into each bag.
She then sells each bag of nuts for 75p.
Lucy sells all the bags of nuts.
Work out her percentage profit.
Answers
Answer: 50%
Step-by-step explanation:
I'm converting 7kg to grams to make it easier. So £10 = 7000g
£1 = 7000÷10 = 700g
700g÷2 = 350g and if you follow the ratios on top, she payed 50p per 350g
She sells a bag of 350g for 75p.
Percentage profit=[tex]\frac{Change in cost}{original cost}[/tex] × 100
75p - 50p = 25p = change in cost
Percentage profit= [tex]\frac{25}{50}[/tex] × 100
= 50%
find the solution of pair of equation y=0 and y= -6
Answers
Answer:
Step-by-step explanation:
there is no soltion because it is not intersects
Answer:
No solution as it will not intersect.
Find the area. Use Pi = 3.14 a. 15.1976 cm2 c. 13.816 cm2 b. 6.908 cm2 d. 60.7904 cm2
Answers
Answer:
A.
Step-by-step explanation:
Diameter = 4.4 cm
Radius = 2.2 cm
Now
Area of the circle = πr²
= (3.14)(2.2)²
= (3.14)(4.84)
= 15.1976 cm²
Answer:
A.
Step-by-step explanation:
D=4.4, therefore, the Radius is equal to 2.2, half of the diameter.
The formula for Area:
A=pir^2.
A=(3.14)(2.2)^2
A=(3.14)(4.84)
A=15.1976
A=15.1976, which is identical to option A.
In a survey, the ratio of the number of people who preferred tea to those who preferred coffee was 9:5
36 more people preferred tea to coffee.
How many people were in the survey?
Answers
Answer:
45 people prefered coffee, 81 people prefered tea. A total of 126 people were surveyed.
Step-by-step explanation:
Let t be the people who prefer tea, and let c be the people who prefer coffee.
The ratio between tea and coffee is 9:5, thus we have t/c=9/5. Cross products give us 5t=9c.
Also, we have 36 more people prefer tea than coffee, so we have c+36=t
Thus we have: 5(c+36)=9c
5c+180=9c
180=4c
c=45
c+36=t
45+36=81
At work Bret must check and record the internal temperature of the freezer on an hourly basis when working properly the temperature should remain constant over time.What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly
Answers
Answer:
The slope of the line will be ZERO.
From the question given above, we are told that when the freezer is working perfectly that the temperature will remain constant over time. This means that if the graph of temperature and time is drawn, the slope of the graph will be constant from one point of the graph to the other, which means that the values will cancel each other out and will be zero.
What is the value of x in the equation 8x - 2y = 48, when y = 4?
O 6
07
O 14
O 48
Answers
Answer:
The answer is option 2.
Step-by-step explanation:
You have to substitute the value of y into the equation :
[tex]8x - 2y = 48[/tex]
[tex]let \: y = 4[/tex]
[tex]8x - 2(4) = 48[/tex]
[tex]8x - 8 = 48[/tex]
[tex]8x = 48 + 8[/tex]
[tex]8x = 56[/tex]
[tex]x = 56 \div 8[/tex]
[tex]x = 7[/tex]
The value of x in the equation 8x - 2y = 48 is 7.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
8x - 2y = 48
Now, for y=4 put the value of y as 4 in given equation we get
8x- 2(4)= 48
8x -8= 48
8x = 48+ 8
8x = 56
x= 56/8
x= 7
Thus, the value of x is 7.
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PLEASE ASAP FOR BRAINLIEST
Answers
Answer:
27°
Step-by-step explanation:
Angle ABC is 90°
ACB is 63 because it is vertically opposite angle GCJ
Angle CAB is 27° (90-63)
angle x is 27° (vertically opposite CAB)
In need everyone's help!!!! 6-y+3 Answers: A -1 B 0 C 3 D 6
Answers
Answer: y=3
Step-by-step explanation:
6-y+3
-3 -3
6-3=3 and 3-3 is 0
so the answey is y=3
hope this Helps :)
could any one explain this problem?
Answers
Answer:
C
Step-by-step explanation:
Δ AQP and Δ ACB are similar triangles, thus the ratios of corresponding sides are equal, that is
[tex]\frac{AQ}{AC}[/tex] = [tex]\frac{PQ}{BC}[/tex] ( note that AC = 3 + 6 = 9 ), substitute values
[tex]\frac{3}{9}[/tex] = [tex]\frac{4.5}{BC}[/tex] ( cross- multiply )
3BC = 40.5 ( divide both sides by 3 )
BC = 13,5 cm → C
Which statement is true?
Answers
Answer:B
Step-by-step explanation:
Answer:
The real correct answer is C
Step-by-step explanation:
Which expression can be used to determine the average rate of change in f(x) over the interval 2, 9? On a coordinate plane, a curve opens down and to the right. The curve starts at (0, 0) and goes through (1, 3), (4, 6), and (7, 8). f(9 – 2) f(9) – f(2) StartFraction f (9 minus 2) Over 9 minus 2 EndFraction StartFraction f (9) minus f (2) Over 9 minus 2 EndFraction
Answers
Answer:
(D) [tex]\dfrac{f(9)-f(2)}{9-2}[/tex]
Step-by-step explanation:
To determine the average rate of change in f(x) over the interval [a,b], we use the formula:
[tex]\text{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}[/tex]
Therefore, given a function f(x), the average rate of change in f(x) over the interval [2,9] is given as:
[tex]\text{Average rate of change}=\dfrac{f(9)-f(2)}{9-2}[/tex]
The correct option is D,
Answer:
D
Step-by-step explanation:
please help me for brainliest
Answers
Answer:
Step-by-step explanation:
A) These are the squares of another number or we can say the prime numbers
B) THE NEXT NUMBER IN THE SEQUENCE IS 9 BECAUSE ALL THESE ARE SQUARES OF 8 7 6 5 4 AND THE LAST ONE WILL BE 9
Plz HELP!!!!!!!!!!!!!!!!!!!!!
Answers
They are Parallel, Intersecting, and perpendicular, if it's helpful let me know
Help please :) much appreciated
Answers
Answer:
x^2 +2x -5
Step-by-step explanation:
f(x) = 2x+3
g(x) = x^2 -8
f(x)+g(x) = 2x+3+ x^2 -8
Combine like terms
= x^2 +2x -5
PLEASEEEE If z=-1-sqrt3i and z^6 = a+bi, then a=___ and b=___.
Answers
Answer:
a = 94
b = -66√3
Step-by-step explanation:
Given z = [tex]-1-i\sqrt{3}[/tex]
[tex]z^{6}=(z^{3})^{2}[/tex]
[tex](-1-i\sqrt{3})^6=[(-1-i\sqrt{3})^3]^2[/tex]
[tex]=[-(1+i\sqrt{3})^3]^{2}[/tex]
[tex]=[(1+i\sqrt{3})^3]^2[/tex]
[tex]=[(1)^3+(i\sqrt{3})^3+3(1)^2(i\sqrt{3})+3(1)(i\sqrt{3})^2]^2[/tex] [(a + b)³ = a³ + b³ + 3a²b + 3ab²]
= [1 + 3i² + 3i√3 + 9i²]²
= [1 - 3 + 3i√3 - 9]²
= [-11 + 3i√3]²
= (11)² -2(3i√3)(11) + (3i√3)²
= 121 - 66i√3 + 27i²
= 121 - 66i√3 - 27
= (94 - 66i√3)
Comparing it with (a + bi),
a = 94 and b = -66√3