Given:
The functions are:
[tex]f(x)=\dfrac{1}{2}x[/tex]
[tex]f^{-1}(x)=2x[/tex]
To find:
The values of [tex]f(2),f^{-1}(1),f^{-1}(f(2))[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{1}{2}x[/tex] ...(i)
[tex]f^{-1}(x)=2x[/tex] ...(ii)
Putting [tex]x=2[/tex] in (i), we get
[tex]f(2)=\dfrac{1}{2}(2)[/tex]
[tex]f(2)=1[/tex]
Therefore, the value of [tex]f(2)[/tex] is 1.
Putting [tex]x=1[/tex] in (ii), we get
[tex]f^{-1}(1)=2(1)[/tex]
[tex]f^{-1}(1)=2[/tex]
Therefore, the value of [tex]f^{-1}(1)[/tex] is 2.
Now,
[tex]f^{-1}(f(2))=f^{-1}(1)[/tex] [tex][\because f(2)=1][/tex]
[tex]f^{-1}(f(2))=2[/tex] [tex][\because f^{-1}(1)=2][/tex]
Therefore, the value of [tex]f^{-1}(f(2))[/tex] is 2.
Fern bought groceries that cost $14.38. She paid the
store clerk, Ping, with a $20 bill. Ping makes change by
saying
2 pennies makes the total $14.40.
6 dimes makes it $15.00, and
6 dollars makes it $20.
pril
Did the clerk make a mistake in giving Fern her change?
You may use the scratchpad to show your work.
No, she received $6.62 in change.
8
Yes, Ping should give Fern 6 pennies and 2
dimes.
Yes, Ping should give Fern 3 dimes and 8
pennies.
Yes, Ping should give five one-dollar bills, not
SIX
I NEED HELP ASAP SOMEONE ANSWER AS SOON AS YOU CAN MAYBE YEA THANKS BYE
Answer:
Yes, Ping should give five one-dollar bills, not
SIX
Step-by-step explanation:
I answered this question on
https://brainly.com/question/23795763
It wasn't the same question but yes
3 of 12 The perimeter of a rectangular piece of cardboard is 7 feet, and the area is 3 square feet. The length and width of this piece are each multiplied by 6. What is the perimeter of the new enlarged piece of cardboard?
A. 34 ft.
B. 42 ft.
C. 54 ft.
D. 68 ft.
Answer:
B. 42 ft.
Step-by-step explanation:
2L+2W=7
LW=3
L=3/W
2(3/W)+2W=7
6/W+2W=7
6+3W=7W
6=4W
W=3/2
L=2
12(2)+12(3/2)=42
What is the simplest radical form of the expression? (8x5y3)23
This may be incorrect, so sorry if it is! The answer I got is 2760y.
choose the pair of sets which is equivalent
Answer:
set ={Sunday,Monday,Tuesday,Wednesda,Thursda,Friday, Saturday} and set={1,2,3,4,5}
Step-by-step explanation:
To be equivalent, the sets should have the same cardinality.The organizers want the zip line to have two platforms (towers / anchors). The first platform (on the higher ground) should be about 50 m away from the second platform. The slope length from the top of platform one to the top of platform two should be about 70 m. What would be the angle of depression from platform one to two to the nearest degree?
Answer:
The angle if depression is 44.4 degree.
Step-by-step explanation:
horizontal distance, d = 50 m
slope length, L = 70 m
The angle of depression is given by
[tex]cos\theta=\frac{d}{L}\\\\cos \theta = \frac{50}{70}\\\\cos \theta = 0.714\\\\\theta = 44.4^o[/tex]
what is factorial of 100
Answer:
9.332621544^157
Step-by-step explanation:
formula to calculate factorial : n×(n-1)×(n-2)×(n-3)...3×2×1
So,
100×(100-1)(×100-2)×(100-3)...3×2×1
100×99×98×97×3×2×1
=564,656,400 Answer
6. Find JL.
Please and thank you. 5x-16=3x+4
Answer:
JL = 68
Step-by-step explanation:
JM = ML
Hence, 3x + 4 = 5x - 16
Subtract 3x from both sides
4 = 2x - 16
Add 16 to both sides
20 = 2x
Divide both sides by 2
10 = x
Now we want to find JL
Note that JL = JM + ML
JM = 3x + 4 and x = 10
Substitute 10 for x
3(10) + 4
Multiply
30 + 4
Add
JM = 34
Because JM = ML
We simply multiply 34 times 2 to find the length of JL
34 * 2 = 68
JL = 68
two dice are rolled write the sample space and number of sample points also write events and number of sample points in the event according to the given condition sum of the digits of upper faces is a prime number , sum of the digits on the upper face is a multiple of 5 , sum of the digits on the upper face is 25 and digit on the upper face at the first die is less then then the digit on the second die
Answer:
S={(1,),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),}n(S)=36
E = { (1,1), (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,6), (6,1), (6,5)}, n(E) = 15
Step-by-step explanation:
thats the answer
how much work is done when you lift an object that weighs 150 N to a height of 5 meters
Answer:
Work done = 150 x 5 = 750 J
Step-by-step explanation:
Work done is the measure of energy transferred to an object when a force is added causing the object to move a distance in the direction of the force.
The equation for work done is force time the distance and is measured in Joules. Therefore the formula is W = F x D
work done (W) is measured in joules (J)
force (F) is measured in newtons (N)
distance (d) is in the same direction as the force and is measured in
metres (m)
W = F x D
w = 150 x 5
W = 750 J
How do you ratify the denominator for 2/ 2(sqrt2)? When I multiply by sqrt2/sqrt 2 I'm still left with a radical in the denominator.
Answer: [tex]\dfrac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
Given
The fraction is [tex]\dfrac{2}{2\sqrt{2}}[/tex]
Making denominator a number, multiply and divide by [tex]\sqrt{2}[/tex]
[tex]\Rightarrow \dfrac{2}{2\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\\Rightarrow \dfrac{2\sqrt{2}}{2\sqrt{2}\times \sqrt{2}}=\dfrac{2\sqrt{2}}{2\sqrt{2\times 2}}\\\\\text{cancel out the common term 2}\\\\\Rightarrow \dfrac{\sqrt{2}}{2}[/tex]
Un político Envía un cuestionario a sus votantes para determinar sus intereses acerca de 6 asuntos de importancia nacional: desempleo, medio ambiente, impuestos, tasas de interés, defensa nacional y seguridad social. Los votantes deben seleccionar cuatro asuntos de interés personal y colocarlos en orden: o un número1, 2, 3 0 4 después de cada asunto para indicar el grado de interés, donde 1 indica el mayor interés y 4 el menor interés ¿ En cuantas formas se puede responder al cuestionario.
Answer:
El cuestionario puede ser respondido de 360 formas diferentes.
Step-by-step explanation:
Dado que un político envía un cuestionario a sus votantes para determinar sus intereses acerca de 6 asuntos de importancia nacional: desempleo, medio ambiente, impuestos, tasas de interés, defensa nacional y seguridad social, y los votantes deben seleccionar cuatro asuntos de interés personal y colocarlos en orden 1, 2, 3 y 4 después de cada asunto para indicar el grado de interés, donde 1 indica el mayor interés y 4 el menor interés, para determinar en cuantas formas se puede responder al cuestionario se deben realizar los siguientes cálculos:
6 x 5 x 4 x 3 = X
30 x 4 x 3 = X
120 x 3 = X
360 = X
Por lo tanto, el cuestionario puede ser respondido de 360 formas diferentes.
If θ is in standard position and -180° < θ <-90°, then θ terminates in Quadrant _____.
Answer:
Quadrant III
Step-by-step explanation:
-180° is a 180° rotation clockwise, which will end up between Quadrant II and III. -90° is a 90° rotation clockwise, which will end up between Quadrant III and Quadrant IV. The range of possible angles are contained in Quadrant III, in conclusion.
Helppppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeee
Answer:
1/ 3^6
Step-by-step explanation:
We know that a^b / a^c = a^(b-c)
3^-7 / 3^-1 = 3^(-7 - -1) = 3^(-7+1) = 3^(-6)
We know that a^ -b = 1/ a^b
3^-6 = 1/ 3^6
The circumference of circle T is 180 units.
What is the area of the shaded sector?
A. 2 square units
B. 900 square units
C. 3240 square units
D. 8100 square units
Round to the nearest tenth. I need help
Answer:
118.0
Step-by-step explanation:
using Trigonometry,
[tex]x = 99tan(50) \\ = 118.0[/tex]
Find d^2y/dtheta^2 if y=sin^5
Answer:
20 sin³O. cos²O - 5sin⁵O
Step-by-step explanation:
y = sin⁵O
Using the Chain Rule
dy/dO = 5 sin⁴O cosO
Using the Product / Chain rules:
d²y/dO² = 20 sin³O.cosO . cos O+ 5 sin⁴O * - sin O
= 20 sin³O. cos²O - 5sin⁵O
WILL GIVE BRAINIEST ONLY IF YOU GET IT RIGHT!!!!
Marlon buys a sweater for $28 that has $17 off its usual price in sale. Write an equation to describe the cost of the sweater in the sale compared with its usual price. Then solve the equation to find the usual price of the answer.
x - 17 = 28
so
28 + 17 = x
28 + 17 = $45
so
x = $45
(I'm pretty sure)
Esmerelda flips a coin and draws a card. What is the possibility that she gets “heads” and a black card?
Answer:
1/4
Step-by-step explanation:
The probability of flipping a coin and landing a heads is 1/2. Their are 26 black cards in a standard deck of 52 cards- 26/52 (1/2). Multiply the fractions to get the probability.
1/2 * 1/2 = 1/4
A golf ball has a diameter of 42.67 millimeters and a mass of 45.93 grams.what is the number of grams per cubic millimeter of the material used to make the golf ball?
The density of golf ball is 0.000113 gm/mm³
What is volume ?
Volume is a three dimensional space occupy by the body of particular shape such as here :
volume (V) of sphere with radius r : 4πr³/3
it is given that :
golf ball has a diameter d of = 42.67 millimeters
r = d/2 = 21.33 mm
golf ball has a mass m of = 45.93 grams
First, let us find the volume of the golf ball can be determined using the formula:
V = 4πr³/3
Substituting r = 21.33mm, we get;
V = 4π(21.33)³/3
V = 40650 mm³
Now, to find the number of grams per cubic millimeter of the material used to make the golf ball we find the density of golf ball :
ρ = m/V
ρ = 45.93/40650
ρ = 0.000113 gm/mm³
Therefore, the density of golf ball is 0.000113 gm/mm³
Learn more about volume here:
brainly.com/question/16017437
#SPJ2
W is the midpoint of VX and Z is the midpoint of VY . If XY=p and WZ=p–30, what is WZ?
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
You'll have to know : Mid-point theorem states that A straight line segment joining the mid-points of any two triangle is parallel to the third side and it is equal to half of the length of the third side.We're provided : XY = p , WZ = p - 30 & we're asked to find out the value of WZ. For that , firstly we have to find out the value of p.[tex] \large{ \tt{❁ \: LET'S \: START }: }[/tex]
Set up an equation & solve for p :[tex] \large{ \bf{☄ \: p - 30 = \frac{1}{2} p }}[/tex]
[tex] \large{ \tt{↦ \frac{1}{2} p = p - 30}}[/tex]
[tex] \large{ \tt{↦ \frac{1}{2} p - p = - 30}}[/tex]
[tex] \large{ \tt{↦ \frac{p - 2p}{2} = - 30 }}[/tex]
[tex] \large{ \tt{↦p - 2p = - 60}}[/tex]
[tex] \large{ \tt{ ↦ \: - p = - 60}}[/tex]
[tex] \large{ \tt{↦p = 60}}[/tex]
The value of p is 60[tex] \large{ \tt{❇ \: REPLACING \: VALUE}} : [/tex]
[tex] \large{ \tt{↬ \: wz = p - 30 = 60 - 30 = \boxed{\boxed{ \tt{30 }} }✔}}[/tex]
Hence , WZ = 30 .♪ Success is not a magic or miracle , it's not a luck , it's full of late night hard work , compromises & sacrifices.
♡ Hope I helped ! ツ
☼ Have a wonderful day / night ! ☃
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Slope of (-5,12), ( -9, 16)
somebody help me out !
Answer:
224
Step-by-step explanation:
Hello!
To find f(-7) you simply plug the value, -7, into the function.
This will get you:
f(-7) = 4(-7)^2 - 4(-7)
Remember that the square of a negative number is a positive! Also, remember to use the order of operations (PEMDAS)!
This will get you:
f(-7) = 4(49) - 4(-7)
f(-7) = 196 - (-28)
f(-7) = 224
Hope this helps!
If 22 = 26, which must be true about 22?
Answer:
Angle 2 is supplementary to angle 8 because the two angles create a supplementary angle (180 degrees angle).
Step-by-step explanation:
In circle D with m \angle CDE= 76m∠CDE=76 and CD=13CD=13 units find area of sector CDE. Round to the nearest hundredth.
Answer:
112.03sq. units
Step-by-step explanation:
The area of a sector = theta/360 * πr²
The area of a sector = 76/360 * 3.14 * 13²
The area of a sector = 76/360 * 530.66
The area of a sector = 40,330.16/360
The area of a sector = 112.03sq. units
This gives the area of the sector
Answer:
Step-by-step explanation:
Evaluate the expression below when y = 3. If needed, answer as a fraction or a decimal.
y⋅5y+2
Answer:
-10
Step-by-step explanation:
y-5y+2
=3-5 x 3+2
Using the rule of BODMAS
=3-15+2
=3-13
= -10
OladipoSeun♡˖꒰ᵕ༚ᵕ⑅꒱What is the equation of a circle with center (-4, 7) and radius 6?
Answer:
(x +4)^2 + (y-7)^2 = 36
Step-by-step explanation:
The equation of a circle is of the form
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
(x- -4)^2 + (y-7)^2 = 6^2
(x +4)^2 + (y-7)^2 = 36
Holly has $125. She spends $35 on gas for her car. Which model represents how
much money Holly has left?
Answer:
160 is the answer pls mark me as brainlist
Answer:
3rd model
Step-by-step explanation:
Well 125-35=90 and the 3rd model shows 125-35=90 so the correct answer is the t3rd model
Brainliest, 50 points
10y+50
Answer:
10(y+5)=10y+50
just
multiplying both by 10.Use distribute property.
Answer:
10 y + 50
Step-by-step explanation:
10 ( y + 5 )
multiplying both by 10
10 × y + 10 × 5
10 y + 50
Anyone know the answer to this?
Answer:
Diameter : 22.568 cm
Step-by-step explanation:
Hope this Helps!
