The resulting expressions for [tex](f\,\circ\,g)(x)[/tex] and [tex](g\,\circ\,f)(x)[/tex] are [tex]5- 2\cdot x^{2}[/tex] and [tex]-4\cdot x^{2} + 12\cdot x -5[/tex], respectively.
A composition is a operation two functions in which the independent variable of the first function is substituted by the entire second function. In other words, we have the following expressions:
[tex](f\,\circ\,g) (x) = f(g(x))[/tex] (1)
[tex](g\,\circ \,f)(x) = g(f(x))[/tex] (2)
If we know that [tex]f(x) = 2\cdot x - 3[/tex] and [tex]g(x) = 4 - x^{2}[/tex], then we have the following compositions:
[tex](f\,\circ\, g) (x) = 2(4-x^{2})-3[/tex]
[tex](f\,\circ\,g)(x) = 5-2\cdot x^{2}[/tex]
[tex](g \circ f) (x) = 4 - (2\cdot x-3)^{2}[/tex]
[tex](g\,\circ f) (x) = -4\cdot x^{2} +12\cdot x -5[/tex]
The resulting expressions for [tex](f\,\circ\,g)(x)[/tex] and [tex](g\,\circ\,f)(x)[/tex] are [tex]5- 2\cdot x^{2}[/tex] and [tex]-4\cdot x^{2} + 12\cdot x -5[/tex], respectively.
We kindly invite to check this question on composition between functions: https://brainly.com/question/15070966
A frog leaps off of a ledge and lands on the ground below. The function
f(x) = -1.6x2 + 2.3x + 3.2 represents the frog's path.
a. How high is the ledge where the frog starts?
b. How high is the frog at its highest point?
c. What is the frog's horizontal distance from the ledge when it
reaches its highest point?
Answer:
-1.6x2 + 2.3x + 3.2 = f(x) to solve this you do -1.6 x 2 = -3.2 + 2.3x = -0.9 + 3.2 = 2.3
Step-by-step explanation:
For A the height of ledge is 3.2
for b - the frogs highest point 2.30x
and c is 12.3x
There are 16 boys and 18 girls in a grade 6 math class . write the ratio of girls to boys in words as simply as possible
Answer:
8:9 = eight to nine
Step-by-step explanation:
16:18 - divide each by 2 in order to simplify
= 8:9
Tell the mistake that was made in solving this equation. Tell the answer and one thing that is important to remember when simplify.
-8y+5x+3y-9x
-11y+5x+-9x
-11y+14x
Answer:
-8y + 5x +3y-9x
-8y+3y+5x-9x
-5y-4x
What are the combining like terms ?
Answer: 6 + 3 − 9
− 3 + 3
-3+3m
3m-3
Step-by-step explanation:
PLEASEEE help!!! i dont remember how to do these
Answer:
22. the answer is 27n^2 m^5 s^6 / 32
23. the answer is -7
Step-by-step explanation:
select the expression that is equivalent to (3d^4)^2
A. 6d^6
B. 9d^8
C. 9d^6
D 3d^8
Answer:
9d^8
Step-by-step explanation: found it online
A store sells notepads in packages of 24 and packages of 6. The organizers of a conference needs to prepare at least 200 notepads for the event. Would they have enough notepads if they bought five packages of 24 and fifteen packages of 6 ?
Answer: Yes they would have enough notepads
Step-by-step explanation:
24 * 5 = 120
15 * 6 = 90
120 + 90 = 210
The organizers will have enough notepads if they bought five packages of 24 and fifteen packages of 6.
Given that, a store sells notepads in packages of 24 and packages of 6.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of note pads with five packages of 24
24 × 5 = 120
The number of note pads with fifteen packages of 6
15 × 6 = 90
Total number of note pads
= 120 + 90 = 210
Therefore, the organizers will have enough notepads if they bought five packages of 24 and fifteen packages of 6.
To learn more about the unitary method visit:
brainly.com/question/22056199.
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The width of a rectangle is three units less than the length. The area of the rectangle is 4 units. What is the length, in units, of the rectangle
length is 4
area= l*w
4-3=1
4*1= 4
Can anyone answer with an explanation?
Answer:
x=0.136
Step-by-step explanation:
4x^3-6x^2+16x-6=0
64x-36x+16x-6=0
28x+16x-6=0
44x-6=0
+6 +6
44x= -6
/44 /44
x=0.136
The function f(x)=260−55 x represents the distance, in miles, remaining on a trip x hours into the trip. What is the value of f(3)
ASAP PLZ
Melissa is driving on the highway at the legal speed of 65 mi/h. She notices there is an accident ahead approximately 200 feet away. Her reaction time is 0.75 of a second. Is she far enough away to bring the car to a safe and complete stop?
*Round your answers to 2 places after the decimal!
1 Reaction distance =
2 Breaking distance =
3 Total Stopping Distance =
4 yes or no
Answer:
You are asked to find the skid distance given the speed,
the drag factor, and the braking efficiency.
Step-by-step explanation:
Use the skid speed formula. S = √
_______
30Dfn
Substitute 50 for S, 1.2 for f,
and 0.9 for n. 50 =√
___________________
30 × D × 1.2 × 0.9
Simplify the expression under the radical. 50 = √
_______
32.4D
Expand the following
Answer:
There are multiple ways to expand but I did it by using sum/difference formulas.
3(x-2) = 3x-6
8(2x+2) = 16x+16
5(x-1) = 5x-5
2(6x+3y) = 12x+6y
What is matter?
Anything that has mass and takes up space
Something that has volume and takes up space
Things that have energy and take up space
Things that take up space but don't have mass
Did I choose the right answer to this
Answer:
honestly, i think it would be d
Step-by-step explanation:
i could be wrong, but i hope this helps :)
Math experts please provide the product in standard form thank you so much
Answer:
[tex]2x^{3} -11x^{2} +18x-9[/tex]
Step-by-step explanation:
use foil thn combine like terms
HELLPPPPPPPPPPPPPPPPPPPPPPPPP If you get this right you get branilest
Answer:
D.
Step-by-step explanation:
-1 + 1 = 0
[tex]6^{4x-9} =(\frac{1}{36} )^{x-4}[/tex]
[tex]\displaystyle \large \boldsymbol {} 6^{4x-9} =\bigg(\frac{1}{36} \bigg)^{x-4} \\\\\\ 6^{4x-9}=(6^{-2})^{x-4 }\\\\\\ 6^{4x-9}=6^{-2x+8} \\\\\\ 4x-9=-2x+8 \\\\\\ 4x+2x=9+8 \\\\\\ \boxed{x=\frac{17}{6}=2\frac{5}{6} }[/tex]
The graph of the exponential function f(x) = 4(0.5)* + 2 is shown.
Answer:
g(x)=0.5(0.8)^x+2
Step-by-step explanation:
What percent is 7 out of 20?
Step-by-step explanation:
35%Therefore, 7/20 in terms of percentage is 35%
Now, let us express 7/20 in terms of decimals. To convert any fraction to a decimal, we divide the numerator by the denominator.
Step-by-step explanation:
35%
Therefore, 7/20 in terms of percentage is 35%
Now, let us express 7/20 in terms of decimals. To convert any fraction to a decimal, we divide the numerator by the denominator.
Simplify 6 to the 3rd power
Answer:
216Step-by-step explanation:
6 · 6 · 6 = 216
Hope this helped. A brainliest would be very much appreciated. (I need 5 brainliest so I can level up) :)
Answer:
2 √ 3 or 3.46410161
Step-by-step explanation:
I don't know math I just look it up tbh. Hope it helps ya though.
solve the inequality -179 greater than or equal to 9v - 8
Answer:
v ≤ -19
Step-by-step explanation:
which number is irrational
Answer:
Any real number that cannot be expressed as a ratio of two integers.Step-by-step explanation:
OPTIONS R NOT HERE
HOPE IT HELP
Answer: i didn't get enough detail but you can use this to help
Step-by-step explanation:
Irrational numbers are the real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.
Irrational numbers are expressed usually in the form of R\Q, where the backward slash symbol denotes ‘set minus’. it can also be expressed as R – Q, which states the difference between a set of real numbers and a set of rational numbers.
3 1/6 x 1/7 reduce to lowest terms
Answer:
19/42
Step-by-step explanation:
Adam Zetts is an aerospace engineer. He earns $78,000 a year
and is paid on a semimonthly basis. How much is deducted
per pay period for Social Security? How much for Medicare?
Answer:
Social Security: $201.50, Medicare: $47.13
Step-by-step explanation:
divide 78,000 by 24(semimonthly) - $78000/24 = $3250(gross semimonthly basis)
multiply 3250 by .062(social security) - 3250 x .062 = $201.50
multiply 3250 by 0.0145(medicare) - 3250 x 0.0145 = $47.13
Find the area of the kite
A) 660 mm2
B) 744.5 mm2
C) 630 mm2
D) 106 mm2
F) 1260 mm2
Answer:
C) 630 mm²
Step-by-step explanation:
area of kite = pq
2
= 28x45
2
= 630 mm²
moniquemfv
me responde prv
te peço
Answer:
Que?
Step-by-step explanation:
x^2-25y^2+6x+18=0
help me
Answer:
im not very good at that but my best problematic ratio is deviding the x ponet by the ^ and then using your y ponet multiplyed by your first couple of numbers which are "x^2"
Current rules for telephone area codes allow the use of digits 2-9 for the first digit, and 0-9 for the second and third digits, but the last two digits cannot both be 1 (to avoid confusion with area codes such as 911). How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately preceding the last four digits of a phone number. Given both of those rules, how many 10-digit phone numbers are possible? Given that these rules apply to the United States and Canada and a few islands, are there enough possible phone numbers? (Assume that the combined population is about 400,000,000.)
Using the fundamental counting theorem, we have that:
648 different area codes are possible with this rule.There are 6,480,000,000 possible 10-digit phone numbers.The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.The fundamental counting principle states that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are ways to do both things.
For the area code:
8 options for the first digit.9 options for the second and third.Thus:
[tex]8 \times 9 \times 9 = 648[/tex]
648 different area codes are possible with this rule.
For the number of 10-digit phone numbers:
7 digits, each with 10 options.648 different area codes.Then
[tex]648 \times 10^7 = 6,480,000,000 [/tex]
There are 6,480,000,000 possible 10-digit phone numbers.
The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.
A similar problem is given at https://brainly.com/question/24067651
Answer: Number of possible area codes: 792
Amount of 10-digit phone numbers: 6,273,640,000
Step-by-step explanation:
Find the slope of the line
Answer:
Slope = 3
Step-by-step explanation:
(2, 0)
(0, -6)
(-6-0)/(0-2) = -6/-2 = 3 = m
Solve B=1/4m(s+z) for s
Answer:
[tex]s = \frac{-mz+4B}{m}[/tex]
Step-by-step explanation:
Step 1: Distribute.
[tex]B = \frac{1}{4}m * s + \frac{1}{4}m * z[/tex] [tex]B = \frac{1}{4}ms + \frac{1}{4}mz[/tex] [tex]\frac{1}{4}ms + \frac{1}{4}mz = B[/tex]Step 2: Subtract 1/4(mz) from both sides.
[tex]\frac{1}{4}ms + \frac{1}{4}mz - \frac{1}{4}mz = B - \frac{1}{4}mz[/tex] [tex]\frac{1}{4}ms = -\frac{1}{4}mz + B[/tex]Step 3: Divide both sides by m/4.
[tex]\frac{1}{4}ms/\frac{m}{4}=(\frac{-1}{4}mz + B)/\frac{m}{4}[/tex] [tex]s = \frac{-mz+4B}{m}[/tex]