Answers
Given:
The function is:
[tex]f(x)=x^2[/tex]
The graphs of functions [tex]f(x)[/tex] and [tex]g(x)[/tex].
To find:
The function [tex]g(x)[/tex].
Solution:
We have,
[tex]f(x)=x^2[/tex]
The function [tex]f(x)[/tex] is vertically compresses to get the graph of the function [tex]g(x)[/tex]. So, the function [tex]g(x)[/tex] is:
[tex]g(x)=kf(x)[/tex]
[tex]g(x)=kx^2[/tex] ...(i)
From the given graph it is clear that the graph of the function [tex]g(x)[/tex] passes through the point (3,3). So, putting [tex]x=3[/tex] and [tex]g(x)=3[/tex] in the above function, we get
[tex]3=k(3)^2[/tex]
[tex]3=9k[/tex]
[tex]\dfrac{3}{9}=k[/tex]
[tex]\dfrac{1}{3}=k[/tex]
Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get
[tex]g(x)=\dfrac{1}{3}x^2[/tex]
Therefore, the correct option is D.
Related Questions
The average weight of a particular box of crackers is 37.0 ounces with a standard deviation of 0.5 ounce. The weights of the boxes are normally distributed.
What percent of the boxes weigh more than 36.0 ounces?
What percent of the boxes weigh less than 36.5 ounces?
Answers
Find the
surface area of the
prism.
Answers
Answer:
D. 972 ft^2
Step-by-step explanation:
SA = 2B + PH
where SA = total surface area of the prism,
B = area of a base
P = perimeter of the base
H = height of the prism
SA = 2 * bh/2 + (15 ft + 12 ft + 9 ft)(24 ft)
SA = (9 ft)(12 ft) + (15 ft + 12 ft + 9 ft)(24 ft)
SA = 972 ft^2
1:Under what condition will the line px+py+r=0 mat be a normal to the circke x²+y²+2gx+2fy+c=0
2:prove that the two circles x²+y²+2ax+c²=0 and x²+y²+2by+c²=0 touch if
[tex]\frac{1}{a²}+\frac{1}{b²}=\frac{1}{c²}[/tex]
Answers
Answer:
#1The normal overlaps with the diameter, so it passes through the center.
Let's find the center of the circle:
x² + y² + 2gx + 2fy + c = 0(x + g)² + (y + f)² = c + g² + f²The center is:
(-g, -f)Since the line passes through (-g, -f) the equation of the line becomes:
p(-g) + p(-f) + r = 0r = p(g + f)This is the required condition
#2
Rewrite equations and find centers and radius of both circles.
Circle 1
x² + y² + 2ax + c² = 0 (x + a)² + y² = a² - c²The center is (-a, 0) and radius is √(a² - c²)Circle 2
x² + y² + 2by + c² = 0 x² + (y + b)² = b² - c²The center is (0, -b) and radius is √(b² - c²)The distance between two centers is same as sum of the radius of them:
d = √(a² + b²)Sum of radiuses:
√(a² - c²) + √(b² - c²)Since they are same we have:
√(a² + b²) = √(a² - c²) + √(b² - c²)Square both sides:
a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)2c² = 2√(a² - c²)(b² - c²)Square both sides:
c⁴ = (a² - c²)(b² - c²)c⁴ = a²b² - a²c² - b²c² + c⁴a²c² + b²c² = a²b²Divide both sides by a²b²c²:
1/a² + 1/b² = 1/c²Proved
Answer:
Answer is in the picture
Phineas puts $600 into a certificate of deposit that earns 3.09%. If the money is
compounded monthly, how much will it be worth in 4 years?
Answers
Answer: $678.83
Step-by-step explanation:
A = P(1 + r/n)nt
A = 600.00(1 + 0.0309/12)(12)(4)
A = 600.00(1 + 0.002575)(48)
A = $678.83
Draw the next five shapes in this pattern.
Answers
Answer:
what next five shapes in the pattern
Answer:
I can make one up for you
Square , Circle , Square , Prism , Sphere , Cone , Semi-Circle , Square , Circle,
What are the next 5 shapes ?
Step-by-step explanation:
The sum of the numbers x, y, and z is 50. The ratio of x to y is 1 : 4, and the ratio of y to z is 4 : 5. What is the value of y?
A. 4
B. 8
C. 10
D. 20
Answers
Answer:
x：y：z
1：4
4：5
-------------
1：4：5
-------------
let a:b:c＝k:4k:5k
k+4k+5k=50
10k=50
k=5
y=4(5)
=20(D)
Answer:
D. 20
Step-by-step explanation:
x:y:z
1:4:5
1+4+5=10
50÷10=5
1=5
4=?
4=4×5
=20
What type of solutions does the quadratic equation, 8v2 + 8 = -11v, have?
Answers
Answer:
Complex roots
Step-by-step explanation:
Given
[tex]8v^2 + 8 = -11v[/tex]
Required
The type of solution
Rewrite as:
[tex]8v^2 +11v+ 8 = 0[/tex]
To determine the type of solution, we simply calculate the discriminant (D)
[tex]D = b^2 - 4ac[/tex]
Where
[tex]a = 8;\ \ \ b =11\ \ \ c = 8[/tex]
So, we have:
[tex]D = 11^2 - 4 * 8 * 8[/tex]
[tex]D = 121 - 256[/tex]
[tex]D = -135[/tex]
The above value implies that:
[tex]D<0[/tex]
When [tex]D<0[/tex], the solution of the equation is: complex roots
i need help with this one plz! (marking BRAINLIST) :)
Answers
Answer:
cosθ = 7/25
Step-by-step explanation:
To find hypotenuse, you use Pythagorean's Theorem.
a^2+b^2=c^2
7^2+24^2=c^2
625=c^2
25=c
This means cosθ = 7/25
PLEASE HELP GEOMETRY!!!!!
Based on geometric properties, which statements are correct?
A) The formula V = lwh can be used to model the shape of a cake.
B) The formula V = 1/2bhl can be used to model the shape of a tent
C) The formula V = 1/2r³ can be used to model the shape of an apple
D) The formula V = r²h can be used to model the shape of a tree trunk
E) The formula V = 4/3r²h can be used to model the shape of a funnel
Answers
Answer:
I reckon it's B ........
Answer: The answer is A, B, and D.
Step-by-step explanation: I just did it on USATestPrep
Please help it's for my test.
The area of a parallelogram is 108 square inches. What is the length of the parallelogram if the height is 6 inches?
Answers
Answer:
18 inches
Step-by-step explanation:
just FYI this is using base and height this is not trigonometry or diagonals but whenever you want to find the area of a parallelogram you have the base times the height and so you have the formula A= B * H but here you want to find the base so we divide the area by the height since those are your givens
A/H=B
108/6=18
Need help with this equation if anyone can respond
Answers
Answer:
120 yards is the answer to the equation
please help. no links!
Answers
Answer:
I think B
Step-by-step explanation:
121.346° is more close to 121.3°, than 121.4°
if i'm wrong, the i'm sorry
PLS SOLVE!! e2 = d^2+f^2 -2df(cosE)
Answers
9514 1404 393
Answer:
e = 25.7 m
Step-by-step explanation:
Put the given numbers in the given formula and do the arithmetic.
[tex]e^2=d^2+f^2-2df(\cos{E})\\\\e^2=11.9^2+18.5^2-2(11.9)(18.5)\cos{114^\circ}\approx 662.946\\\\e\approx\sqrt{662.946}\approx25.74774\\\\\boxed{e\approx25.7\text{ m}}[/tex]
whats the value of 13C11
Answers
Answer:
78
Step-by-step explanation:
[tex]nC_k = \frac{n!}{k!(n-k)!}[/tex]
[tex]13 C_{11} = \frac{13!}{11! \times (13-11)!}[/tex]
[tex]= \frac{13!}{11! \times 2!}[/tex]
[tex]= \frac{ 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10\times 11 \times 12 \times 13}{(1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10\times 11 )\times ( 1 \times 2)}[/tex]
[tex]=\frac{12 \times 13}{2} \\\\= 6 \times 13\\\\=78[/tex]
select all the names appropriate for the angle indicated by the arc mark
Answers
Answer:
The answers are
angle KHM and
angle MHK
9/50 percents and decimals
Answers
Answer:
18% and 0.18
Step-by-step explanation:
converting fraction 9/50 as a percent leaves u with 18%
helpppp y’all sososososo
Answers
Answer:
3/4
Step-by-step explanation:
Answer:
I think the answer is 4/8 ✨
The base of a solid right pyramid is a square with an
edge length of n units. The height of the pyramid is n
1 units
Which expression represents the volume of the
pyramid?
VA
on(n-1) units
on(n-1)2 units
or’n - 1) units
on*(n − 1) units
(n-1)
n
Answers
Answer:
C
Step-by-step explanation:
Base area = n^2
V = (base area * height)/3 = (n^2 *(n-1)/3 = 1/3n^2(n-1)
The expression for the volume of pyramid is V = ( 1/3 )n² ( n - 1 ) units³
What is the volume of a pyramid?The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.
Volume of Pyramid = ( 1/3 )a²H
Given data ,
Let the base edge length of the solid pyramid be = n units
So , the base area of the pyramid = n² units²
Let the height of the pyramid be = ( n - 1 ) units
And , Volume of Pyramid = ( 1/3 )a²H
On simplifying , we get
V = ( 1/3 ) n² ( n - 1 ) units³
Hence , the expression is V = ( 1/3 ) n² ( n - 1 ) units³
To learn more about volume of pyramid click :
https://brainly.com/question/17615619
#SPJ7
O TRIGONOMETRIC FUNCTIONS
Arc length and central angle measure
Na
A circular arc has measure 18 in and is intercepted
a central angle of
radians. Find the radius r of the circle.
Do not round any intermediate computations, and round your answer to the nearest tenth.
?
Answers
Answer:
r = 22.9 in.
Step-by-step explanation:
Central angle in radians, ∅ = π/4
Length of arc, S = 18 in.
radius (r) = ?
Length of arc, C = r∅
Plug in the values and find r
18 = r*π/4
18 = (πr)/4
Multiply both sides by 4
4*18 = πr
72 = πr
Divide both sides by π
72/π = r
r = 22.9183118
r = 22.9 in. (Nearest tenth)
Which number is GREATEST?
0.27
0.046
0.297
0 0.3
Answers
Answer:
0.3
Step-by-step explanation:
Go left to right for each digit, which one is greater. They all have a decimal so for right now we can’t eliminate any. Next digit we two 2s a 0 and a 3. Whch number is greater? The three! So the greatest number is 0.3.
PLEASE ANSWER!! Find EF using Pythagorean theorem. Express answer to one decimal place.
Answers
Answer:
115.5 cm
Step-by-step explanation:
A^2 + B^2 = C^2
41^2 + 108^2 = C^2
C^2 = 13345
C = 115.5 cm
can anyone help with this trig question?? any help would be greatly appreciated! :)
Answers
Answer:
Step-by-step explanation:
Hope this helps u!!
Find the x- and y-intercepts of the graph of the function f(x)=−4|x+5|+4.
Answers
Answer:
See image below:)
Step-by-step explanation:
The x and y intercept is -4 or -6 and -16 respectively.
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given function: f(x)=- 4|x+5|+4
To find the x- intercept take f(x)=0So, 0= -4|x+5|+4
-4|x+5|=-4
|x+5|=1
x= -6 or -4.
For y-intercept take x=0
then y=-20+4
y=-16
Hence, the intercepts are -6 or -4 and -16.
Learn more about intercepts here:
https://brainly.com/question/14180189
#SPJ2
Given the diagram below, find the value of x. Then find AC,
Answers
Answer:
[tex]x=5,\\AC=14[/tex]
Step-by-step explanation:
Since one triangle is inscribed in another, the two triangles are similar. As marked in the diagram, the sides of the larger triangle are exactly two times larger than the corresponding sides of the smaller triangle.
Therefore, we have:
[tex]2(x+2)=4x-6,\\2x+4=4x-6,\\10=2x,\\x=\boxed{5}[/tex]
Since AC is marked by [tex]4x-6[/tex]:
[tex]AC=4(5)-6,\\AC=20-6,\\AC=\boxed{14}[/tex]
Geri runs a total of3.1 miles, how many feet is this
Answers
4-9+8+7+9+10+11+21+33+25-3 minus -50-55+50
Answers
the height of a tower is 15m more than tiwce the height of a building find the height of the building if tower is 255m tall
Answers
Answer: 120m
Step-by-step explanation:
Let the height of the building be represented by x.
Since the height of a tower is 15m more than tiwce the height of a building, the height of the tower will be:
= (2 × x) + 15
= 2x + 15
Since the tower is 255m tall, therefore,
2x + 15 = 255
2x = 255 - 15
2x = 240
x = 240/2
x = 120
The height of the building is 120m
Which drink has more sugar per fluid ounce? 11 POINTS
Answers
Answer:
essentially the question is if
[tex] \frac{14}{8} or \ \: \frac{12}{7} [/tex]
is more
we can express the two fractions as 98/56 and 96/56
(56 is just 7*8)
now we can see that 14/8 is slightly more than 12/7, Drink a is your answer
PLEASE HELP WITH ALGEBRA HOMEWORK.WILL MARK BRAINLIEST
Answers
[tex] {36}^{2x + 5} = {216}^{x - 1} [/tex]
[tex] {6}^{2(2x + 5)} = {6}^{3(x - 1)} [/tex]
[tex] {6}^{(4x + 10)} = {6}^{(3x - 3)} [/tex]
Since bases i.e 6 are same exponents are equal
4x+10= 3x-3
4x-3x = -3-10
x= -13
Answer:
x = -13
Step-by-step explanation:
36 = 6^2
216 = 6^3
36^(2x + 5) = 6^(2)^(2x + 5)
When taking an exponent to an exponet: multiply the exponents
36^(2x + 5) = 6^(4x + 10)
216^(x - 1) = 6^(3)^(x - 1)
When taking an exponent to an exponet: multiply the exponents
216^(x - 1) = 6^(3x - 3)
-----------------------------
Therefor
6^(4x + 10) = 6^(3x - 3)
Since the bases are the same the exponents are equal
4x + 10 = 3x - 3
Subtract 3x from both sides
x + 10 = -3
subtract 10 from both sides
x = -13
PLS HELP!
Two angles are complementary. Draw a diagram that illustrates the complementary angles. One angle measures 35° and the other measures (x + 15)°. What is the value of x?
Answers
Answer:
40°
Step-by-step explanation:
Isolate x. Complementary angles sum up to 90°, so that’s where you start
35+(x+13) = 90
35+(x+15)-35 = 90-35 (subtract 35)
x+15=55
x+15-15=55-15 (subtract 15)
x=40
To find the secong angle’s measure, just substitute x for 40. 40+15=55
I can’t draw a diagram, but two angles put together with measurements 40° and 55° should do the trick