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.
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Given m||n, find the value of x.
(7x+6)° (9x-24)°
Answer:
X=15
I hope this helps also I would appricate brainliest if possible :)
Please help asap, correct answer will get brainliest
Answer:
im not sure if my answer is correct
The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) are shown to the right.
The expected number of mortgages approved per week and the standard deviation of the distribution are 2.019 and 0.024 respectively.
The expected number of mortgages approved per week :
Mean = (Σfx ÷ Σf)Expected Number approved = 210 ÷ 104 = 2.019
Hence, it is expected that 2.019 mortageahes would be approved per week.
The standard deviation :
Variance = [Σ(Xi - x)² ÷ Σf] Standard deviation = √VarianceVariance = (59.5414 ÷ 104) = 0.0005698
Standard deviation = √0.0005698
Standard deviation = 0.024
Therefore, the expected value and standard deviation are 2.019 and 0.024 respectively.
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please check the picture!!
find the indefinite integral of:
Answer:
x = 23
Step-by-step explanation:
please help me solve x please
Answer:
x = 5
Step-by-step explanation:
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.
In the given problem, the exterior angle is < B, and the non-adjacent interior angles are < D and < C.
Given that:
< B = 12x + 8
< D = 8x + 8
< C = 20°
Set up the following formula to solve for x:
(8x + 8) + 20 = 12x + 8
Combine like terms:
8x + 28 = 12x + 8
Subtract 8 from both sides:
8x + 28 - 8 = 12x + 8 - 8
8x + 20 = 12x
Subtract 8x from both sides:
8x - 8x + 20 = 12x - 8x
20 = 4x
Divide both sides by 4 to solve for x:
20/4 = 4x/4
5 = x
Therefore, x = 5.
A function has zeros at -5, 1, and 3.,
f(-7), f(-3), and (4) are negative. f(2) is
positive. Sketch a graph of f.
Answer:
Step-by-step explanation:
Haa
help me asap I have 5min to send it in plss
Answer
A) Morning: 2:45am. / afternoon: 2:45pm
B) Morning: 6:05am / afternoon: 6:05pm
c) Morning: 9:15am. / afternoon: 9:15pm
d) Morning: 11:35am. / afternoon: 11:35pm
Step-by-step explanation:
What is the measure of the angle of rotation for the polygon?
Answer:
360 degrees divided by that order
someone to give me the answer to this ...? please!
Answer:
1.
a. x = 2
b. x = 6
c. x = 5/4 or 1.25
2. You have to do it on your own. sorry!
3. slope = +3
4. y = 1/3x + 4
5. y = 2x + 3
6. pattern = +8
39, 47, 55
7.You have to do it on your own. sorry!
8. You need a protractor so I am guessing
a.60*
b.95*
c.145*
Step-by-step explanation:
Have a nice day! :-)
Sample Question...........4x + 5x=
Answer:
4x+5x=0
sample question
or it can be a quadratic equation
4x^2+5x=0
solved
PLZZZ HELPPPP ILL MARK BRAINLIEST TO FIRST AND CORRECT ANSWER THAT HAS WORK AND A THX TO SECOND AND CORRECT ANSWER.
Answer:
3.9 - C
Step-by-step explanation:
This forms a triangle with a base of 2.5 and a height of 3.
Using the Pythagorean Theorem, 2.5^2 + 3^2 = c^2
This gives you the answer 3.91.
Solve this plz ill give your brainly
Answer:
1) 280
There are 60 minutes in an hour. 60/15 is four. 4*70 is 280
2)384
640/5=128
128*3=384
3) 24
216/9=24
4)3
4.5=18/4
six times as many as you need.
1/2 times 6 is 3.
5)1120
280*4=1120
Hope this helps!
It took a dog groomer 72 minutes to wash 2 dogs. How long will it take him to wash 9 more dogs if he continues to wash at the same pace?
Help me please. You get brownies.
Which expressions represent the product of a variable and a coefficient?
Answer:
dfhlfbfuewbbfv
Step-by-step explanation:
Answer: There is not variables?
Step-by-step explanation:
You are selling flowers for a fundraiser . You pay $ 1.50 for each flower plus a flot rate delivery fee of $ 15 . You are selling the flowers for $ 3 . At least how many flowers do you need to sell to make a profit ?
Answer:
15÷1 .50=10
Because you are already paying a flat rate of $15. You make 1.50 off of each flower. So you have to sell over 10 flowers to make a profit.
At least 11 flowers should be sold to make a profit.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.
Given:
Total cost for the buying flower = 1.5 * number flowers + 15
For n=10 = 1.5 * 10 + 15
= 30
By selling 10 flowers =10 * 3
= $30
For n =11 = 1.5 * 11 + 15
= 31.5
By selling 11 flowers = 11 * 3
= 33
Therefore, At least 11 flowers should be sold to make a profit.
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6x+10=30x+135 solve for "x"
Answer:
x=-125/24
Step-by-step explanation:
(6x+10)+(-10-30x)=(30x+135)+(-10-30x)
(6x+10)+(-30x-10)=(30x+135)+(-30x-10)
6x+10-30x-10=30x+135-30x-10
6x-30x+10-10=30x-30x+135-10
-24x=125
24x/24=-125/24
x=-125/24
if f (x)=4x+1 and g(x)=x+3 find (g. g) (7)
Evaluate (m^4 + 5)−n^3 if m=−2 and n=−4 .
Answer:
85
Step-by-step explanation:
m = -2 and n = -4, Plug in:
(m^4 + 5) - n^3
( (-2)^4 + 5 ) - (-4)^3
( 16 + 5 ) - (-64)
21 + 64
85
Solve for x !!!!plzzzzz
Answer:
12x-4=80
12x=80+4
=84
x=84÷12
=7
}
3) At a restaurant, Imani and her six friends
decided to divide the bill evenly. If each
person paid $12 then what was the total bill?
Answer:
$84 was the original bill.
Step-by-step explanation:
12 x 7 = 84
Pls help! Consider graphing the linear inequality y>2x-1 on the coordinate plane. Which statement is true?
A. The graph will have a SOLID boundary line, with shading ABOVE.
B. The graph will have a SOLID boundary line, with shading BELOW.
C. The graph will have a DASHED boundary line, with shading ABOVE.
D. The graph will have a DASHED boundary line, with shading BELOW.
Step-by-step explanation:
given the linear inequality y >2x-1 on the coordinate plane.
the true statement is:
C. The graph will have a DASHED boundary line, with shading ABOVE.
for '>' meaning dashed line
Answer:
C. The graph will have a DASHED boundary line, with shading ABOVE.
Step-by-step explanation:
When graphing inequalities:
< or > : dashed line≤ or ≥ : solid line< or ≤ : shading under the line> or ≥ : shading above the lineGiven inequality:
[tex]y > 2x-1[/tex]
Therefore, the graph will have a dashed boundary line and shading above the line.
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Someone please help me
I went to the mall with $75 and bought a pair of shoes and a few candy bars for $1.25 each. How much did I spend?
Write an expression for the situation.
75 - X - 1.25y
75 - x - 1.25
75 + x + 1.25y
Answer:
75 - x - 1.25y
Step-by-step explanation:
Someone please help me! Will mark brainliest!
Answer:
F
(
x
)
=
−
x
2
−
3
x
+
C
Step-by-step explanation:
The number of termites in a nest in any given month can be represented by the
function f(t) = 4(3)^t where t represents the number of months.
The number of ants in a box can be represented by the function represented by the
table:
Months
0-1-2-3-4
Number 20-45-101-228-513
What is the positive difference in the number of termites and the number of ants in
the fourth year?
im pretty sure the answer is 189
The positive difference in the number of termites and the number of ants in the fourth month will be 189. Option B is correct.
What is the application of subtraction?In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
It is given that, the number of termites in a nest in any given month can be represented by the function [tex]\rm f(t) = 4(3)^t[/tex].
For the fourth month,
f(4) = 4(3)⁴
f(4) = 324
From the table, it is observed that the number of ants in four months is 513.
The positive difference in the number of termites and the number of ants in the fourth month is found as,
=513-324
=189
Thus, the positive difference in the number of termites and the number of ants in the fourth will be 189. Option B is correct.
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What is the value of one over 10 divided by 3 over 5.?
Answer:
0.00666666666
Step-by-step explanation:
- by nævis
Answer:
1/6
Step-by-step explanation:
Solve the following equation:
5x - 3(x - 2) = -2
-
A) -4
B 2
C) -2
D
0
Can you make EXACTLY $20 by using a total of seven $1, $5, or $10?
Answer: No, you cannot.
1*7=7
5*7=35
10*7=70
None are equal to 20.
10L is repacked into 6DL bottles. how many bottles are filled ??
Answer:
16
Step-by-step explanation:
1L=10DL
10L=100DL
100DL÷6DL=16.67
