The value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Composite functionsComposite function is also known as function of a function. They are determined by representing x with the other function.
Given the following functions
f(x)=4x+1
g(x)=2x^2+1
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(2x^2+1)
(f∘g)(x) = 4(2x^2+1) + 1
(f∘g)(x) =8x^2 + 5
For the composite function (g∘f)(x)
(g∘f)(x) = g(f(x))
(g∘f)(x) = g(4x+1)
Replace x wit 4x+1 to have:
(g∘f)(x) = 2(4x+1)^2 + 1
(g∘f)(x)= 2(16x^2+8x+1) + 1
(g∘f)(x) = 32x^2 + 16x + 3
Hence the value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
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taking test needing answers asap
Answer:
(4,8)
Step-by-step explanation:
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Find the missing side length in the image below 12 18 and 10
The missing length of the right triangle is 13.41 inches.
How to find the side of a right triangle?A right angle triangle has one of its angles as 90 degrees.
The side length of a right triangle can be found using Pythagoras theorem.
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legs.Therefore,
x² = 18² - 12²
x² = 324 - 144
x² = 180
x = √180
x = 13.416407865
x = 13.41 inches
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A bank ATM system has a pad with 10 digits (0 to 9). Find the number of possible 4-digit pin codes
if digits can be repeated.
if digits cannot be repeated.
a.
1. 10 000 ; 2. 5 040.
b.
1. 5 040; 2. 10 080.
c.
1. 10 000; 2. 210.
d.
1. 3 125; 2. 15 120.
Answer:
A
Step-by-step explanation:
If digits can be repeated, that means there are 10 options for each place in the pin code. 10*10*10*10 = 10,000
If digits can not be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit. 10*9*8*7 = 5040
plssssssssssssssssssssssss help
Hello and Good Morning/Afternoon!
Let's take this problem step by step:
Let's consider some facts:
⇒ angles are opposite each other
⇒ by the Vertical Angle Theorem
⇒ angles opposite each other are equal in measure
So:
[tex]\hookrightarrow 4x + 12 = 64[/tex]
Let's solve
[tex]4x + 12 = 64\\4x = 52\\x = 13[/tex]
x's value is 13
Answer: 13
Hope that helps!
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Consider rolling a six-sided die. Let A be the set of outcomes where the roll is an even number. Let B be the set of outcomes where the roll is greater than 3. Calculate and compare the sets on both sides of De Morgan’s law.
1. [tex](A \cup B)^c = A^c \cap B^c[/tex]
2. [tex](A \cap B)^c = A^c \cup B^c[/tex]
Answer:
See below
Step-by-step explanation:
[tex]A = \{2, 4, 6\}[/tex]
[tex]A^c =\{1, 3, 5\}\\B = \{4, 5, 6\}\\B^c = \{ 1,2, 3\}[/tex]
To prove 1 we have
[tex](A \bigcup B) = \{2, 4, 6\} \bigcup \{4, 5, 6\} = \{2, 4, 5, 6\}\\(A \bigcup B) ^c =\bold{\{1,3\}}\\A^c \bigcap B^c = {\{1, 3, 5\} \bigcap \{1, 2, 3\} =\bold{\{1,3\}}\\[/tex]
Hence proved
To prove 2
[tex](A \bigcap B) = \{2, 4, 6\} \bigcap \{4, 5, 6\} = \{4, 6\}\\\\(A \bigcap B)^c = \bold{\{1,2, 3, 5\}}\\A^c \bigcup B^c = \{1, 3, 5\} \bigcup \{1, 2, 3\} = \bold{\{1,2,3,5\}}\[/tex]
Hence proved
Notes
The complement of a set is the set of all elements not in the set
Here the set of all outcomes is {1, 2, 3,4,5, 6}
So if A = {2, 4, 6} then the complement of A s=is the set of outcomes not in A ie the set {1, 3, 5} which is the set of odd numbers on a die throw
The union of two sets is the set of all elements in both sets without duplication
The intersection of two sets is the set of all elements common to both sets
1+r+r²+...........+r^n+1=1-r^n/1-r
mathematical induction mesthod
Answer + Step-by-step explanation:
the correct question:
For r ≠ 1 ,Prove using the mathematical induction method that :
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
………………………………………………………………………………………………………………
for n = 0 :
1⁰ = 1 and (1 - r⁰⁺¹)/(1 - r) = (1 - r)/(1 - r) = 1
Then the property is true for n = 0.
For n ≥ 0 :
Suppose
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
And prove that
[tex]1+\cdots+r^{n+1} =\frac{1-r^{n+2}}{1-r}[/tex]
Since :
[tex]1+\cdots+r^{n+1} =(1+\cdots+r^n)+r^{n+1}[/tex]
Then
[tex]1+\cdots+r^n+r^{n+1} =\frac{1-r^{n+1}}{1-r}+r^{n+1}[/tex]
[tex]= \frac{1-r^{n+1}+r^{n+1}(1-r)}{1-r}[/tex]
[tex]= \frac{1-r^{n+2}}{1-r}[/tex]
Then according to the mathematical induction method
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
Where n is a natural number and r ≠ 1.
To reduce their expected estate tax liability prior to either spouse's death, the Hansens could?
If the Hansens want to reduce their expected estate tax liability prior to the death of either of the spouses, they could initiate a Marital Transfer.
What is a marital transfer?A Marital transfer simply means that the Hansens should bequest their assets to each each other in case either of them die.
If this happens, the surviving spouse will not be charged any estate taxes because bequests to spouses are not subject to taxation.
To do this, the Hansens should put it into both of their wills that they plan to gift/ bequest their assets to their spouse if they die.
The big disadvantage of using a marital transfer however, is that the estate will still be subject to taxes when the surviving spouse dies. All the estate taxes that had been avoided would then be incurred by the estate but only after the death of both spouses.
In conclusion, they should use a marital transfer.
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Solve the inequality for 3y+1 is less than -11 . Simplify your answer as much as possible.
MY LAST ONE PLEASE HELP
the inequality gives the 'y' value as -4
What is inequality?An inequality is a mathematical tool that compares two values, expressing when one is less than, greater than, or not equal to the other value.
For instance,
a ≠ b says that a is not equal to b
a < b says that a is less than b
a > b says that a is greater than b
From the information given, that 3y+1 is less than -11 . It can be expressed as;
3y + 1 ∠ -11
Let's collect like terms
3y ∠ -11 - 1
add like terms
3y ∠ -12
make 'y' the subject of formula
y ∠ -12/3
y ∠ -4
The inequality gives the 'y' value as -4
Thus, the inequality gives the 'y' value as -4
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Given AD is the median of △ABC find x, CD, and DB. i need step by step
Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.
What is the Median of a Triangle?The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.
Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:
Side CD equals side DB.
Side CD = 5x - 17
Side DB = 3x + 1
Make both segments equal to each other. Therefore, we would have the equation:
5x - 17 = 3x + 1
Solve for x
Add both sides by 17
5x - 17 + 17 = 3x + 1 + 17
5x = 3x + 18
Subtract 3x from both sides
5x - 3x = 3x + 18 - 3x
2x = 18
Divide both sides by 2
2x/2 = 18/2
x = 9
CD = 5x - 17
Plug in the value of x
CD = 5(9) - 17
CD = 45 - 17
CD = 28 units.
DB = 3x + 1
Plug in the value of x
DB = 3(9) + 1
DB = 27 + 1
DB = 28 units.
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athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the medals be distributed?
Using the permutation formula, there are 157,410 ways for the medals to be distributed.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:
P(55,3) = 55!/52! = 157,410
157,410 ways for the medals to be distributed.
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i need help with this people be posting fake answers for these
The value of the probability P(A and D) is 0.30
How to determine the probability P(A and D)?Using the probabilities on the tree diagram, we have the following parameters
P(A) = 0.5
P(D/A) = 0.6
The probability P(A and D) is then calculated using the following formula
P(A and D) = P(A) * P(D/A)
Substitute the known values in the above equation
P(A and D) = 0.5 * 0.6
Evaluate the product
P(A and D) = 0.30
Hence, the value of the probability P(A and D) is 0.30
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Teresa earns a weekly salary of $825 and a 6% commission on her total sales.
Ramón earns a weekly salary of $1,350 and a 2% commission on sales. What
amount of sales, x, will result in each of them earning the same amount for the
week?
To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:
T = R
825 + 0.06x = 1350 + 0.02x
Simplifying the equation, we get
x = 13125
We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.
How to estimate the number of sales, x, that will result in each of them gaining the exact amount for the week?
For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x
Where x represents the number of sales. And similarly the total salary of Ramon we have:
R = 1350 + 0.02x
We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:
T= R
825 + 0.06x = 1350 + 0.02x
Multiply both sides by 100
[tex]$825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$[/tex]
82500 + 6x = 135000 + 2 x
Subtract 82500 from both sides
82500 + 6x - 82500 = 135000 + 2x - 82500
6x = 2x + 52500
Subtract 2x from both sides
6x - 2x = 2x + 52500 - 2x
4x = 52500
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{52500}{4}$[/tex]
x = 13125
So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.
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14. In a right triangle, if one acute angle has measure 10x + 6 and the other has measure 2x + 7, find the larger of these two angles.
Answer:
421/6 degrees
Step-by-step explanation:
The acute angles of a right triangle are complementary, so
[tex]10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}[/tex]
So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.
Factor problems 9 - 12 by using the difference of squares method.
9. x2 – 4
A. This polynomial cannot be factored by using the difference of squares method.
B. (x – 2)(x – 2)
C. (x – 2)(x – 1)
D. (x – 2)(x + 2)
E. (x – 1)(x – 4)
F. (x + 2)(x + 2)
10. x2 – 25
A. (-x – 5)(x - 5)
B. This polynomial cannot be factored by using the difference of squares method.
C. (-x + 5)(x + 5)
D. (x – 5)(x + 5)
E. (x + 5)(-x - 5)
F. (x – 5)(x - 5)
11. 36x4 – 4x2
A. (6x2 – 2x)(6x2 - 2x) = 4x2(3x - 1)(3x - 1)
B. (6x2 + 2x)(6x2 + 2x) = 2x2(3x + 1)(2x + 1)
C. This polynomial cannot be factored by using the difference of squares method.
D. (-6x2 – 2x)(-6x2 - 2x) = 4x2(-3x - 1)(-3x - 1)
E. (6x2 – 2x)(6x2 + 2x) = 4x2(3x - 1)(3x + 1)
F. (-6x2 + 2x)(6x2 - 2x) = 2x2(-3x + 1)(3x - 1)
12. x2 + 100
A. (x + 10)(x – 10)
B. (-x + 10)(x – 10)
C. (x + 10)(x + 10)
D. This polynomial cannot be factored by using the difference of squares method.
E. (x - 10)(x – 10)
F. (-x + 10)(-x – 10)
Answer:
Step-by-step explanation:
9. D
10.D
11.E
12.D
Answer:
9.
[tex]x^2-4\\(x-2)(x+2)[/tex]
10.
[tex]x^2-25\\(x-5)(x+5)[/tex]
11.
[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]
12.
[tex]x^2+100\\[/tex]
This polynomial cannot be factored by using the difference of squares method
Using plane K, name a point that is not on the line.
Answer:
H
Step-by-step explanation:
Plane K is shown with two lines. Points on one of them are A, B, G. Points on the other one are G, M, N.
The point in plane K that is not shown on any line is point H.
Which expression is equivalent to (9x8)^4
A candle on pauline’s dresser is 10 inches tall and burns at a rate of 0.75 inches per hour. how many hours will it take for the candle to burn down to a height of .25 inches?
Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:
h(t) = 10 - 0.75t
The height will be of 0.25 inches when h(t) = 0.25, hence:
0.25 = 10 - 0.75t
0.75t = 9.75
t = 9.75/0.75
t = 13 hours.
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695 is a hundred times smaller than
Answer:
69500
Step-by-step explanation:
695 x 100 = 69500
to check answer divided 69500 by 100
which is equals to 695
695 is a hundred times smaller than 69500
What is Multiplication?multiplication is a method of finding the product of two or more numbers.
We need to find the number which 695 is a hundred times smaller than
Six hundred ninety five times smaller than
Let us consider the number to be x.
Let us multiply 695 with 100 to get the value or answer of the above question.
Six hundred ninety five into hundred is sixty nine thousand five hundred
695 x 100 = 69500
To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct
69500/100=695
Hence 695 is a hundred times smaller than 69500
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Steve weatherspoon, a super salesman contemplating retirement on his 50th birthday, decides to create a fund on an 11% basis that will enable him to withdraw 14,570 per year on June 30th, beginning in 2024 and continuing through 2027. To develop this fund, Steven intends to make equal contributions on June 30th of each of the years 2020 through 2023. How much must the balance of the fund equal on June 30th 2023 in order for Steve to satisfy his objective?
Based on the amount that Steve Weatherspoon wants to withdraw every year beginning in June 30, 2024, and the interest rate, the balance on June 30th 2023 should be $45,203.
What should the balance be in 2023?The fact that Steve Weatherspoon wants to be able to withdraw a particular amount every year, this makes this amount an annuity.
The value in 2023 would therefore be the present value of the annuity that will then accrue to the required amounts as the years go by.
The present value of an annuity is:
= Annuity amount per year x Present value interest factor of an annuity, 11%, 3 years between 2024 and 2027
Solving gives:
= 13,126.25 x 3.44371
= $45,203
In conclusion, the balance on the fund in 2023 should be $45,203 in order for Steve Weatherspoon to achieve his objectives.
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Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x+11 >12
Answer:x>1
Step-by-step explanation:
Subract 11 from both sides
Find the value of x in the triangle shown below.
x =
98°
27°
Answer: 55
Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.
Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.
Thus, we could label the points A, B, and C, and set up an algebraic expression.
Let A = 27, B = 98, and C = x.
A + B + C = 180°.
Substituting A, B, and C we get:
27 + 98 + x = 180°.
Adding, we get:
125 + x = 180°
Subtracting 125 by 180, we get:
x = 55°
Thus, the angle X is 55°.
We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.
3. What is a variable?
numbers that represent letters
a combination of letters and numbers
Oletters that represent numbers
O a operation between different letters
19. What is the probability that the student only plays football?
(a) 35 /66 (b) 20 /33 (c) 13 /33 (d) 5 /33
20. What is the probability that the student plays baseball, but not football?
(a) 3 22 (b) 7 22 (c) 411 (d) 8 33
Using the probability concept, we have that:
The probability that the student only plays football is: (c) 13 /33.The probability that the student plays baseball, but not football is: (d) 8/33.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The total number of students is given by:
26 + 3 + 9 + 10 + 6 + 5 + 7 = 66
Of those, 26 play only football, hence the probability is:
p = 26/66 = 13/33
Which means that option c is correct for question 19.
Of those same 66 students, 9 + 7 = 16 play baseball but not football, hence the probability is:
p = 16/66 = 8/33
Which means that option d is correct for question 20.
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Please help! Need em doneee
(2) Veena made 5 frocks of the same size out of 14 metres of cloth. How many metres of cloth did she use for each frock? Ans.
Answer:
2.8 metres each
Step-by-step explanation:
14/5
2.8
How many gold medals have been awarded for the 1500-meter race from 1896 - 2000 ?
Answer:
Hola disculpa no me acuerdo
Step-by-step explanation:
De verdad que me encantaria ayudar pero no me acuerdo :(
Answer:
6
Step-by-step explanation:
Solve -7(m-1)= -(3m-1)
Please give work
Answer:
m = 3/2
Step-by-step explanation:
-7(m-1)= -(3m-1)
-7m + 7 = -3m + 1
-4m = -6
m = 3/2
Check.
-7(m-1)= -(3m-1)
-7(3/2 - 1) = -(3*3/2 - 1)
-7(1/2) = -(4.5 - 1)
-3.5 = -3.5
Use the distributive property to multiply −7 by m−1.
−7m+7=−(3m−1)To find the opposite of 3m−1, find the opposite of each term.
−7m + 7 = −3m −( − 1 )The opposite of −1 is 1.
−7m + 7= −3m + 1Add 3m to both sides.
−7m + 7 + 3m = 1Combine −7m and 3m to get −4m.
−4m + 7 = 1Subtract 7 from both sides.
−4m = 1 − 7Subtract 7 from 1 to get −6.
−4m = −6Divide both sides by −4.
m = -6/-4Reduce the fraction -6/-4 to its lowest expression by extracting and canceling −2.
Answer: m=3/4 ✅
Which equation can be simplified to find the inverse of y = 5x^2 + 10?
Answer:
Step-by-step explanation:
Here's the solution
f^(-1)(x)=(\sqrt(5(x-10)))/(5), -(\sqrt(5(x-10)))/(5)
hey can you help me answer this question by giving me the answer?
The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
Given a function f(x)=4-2x+6[tex]x^{2}[/tex].
We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.
Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.
f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).
f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]
=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])
=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]
=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]
[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h
=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]
=[tex](6h^{2} -2h+12ah)/h[/tex]
=6h+12a-2.
Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
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please I need help in these exercises and I tried to solve them but I can't, crown to the best answer <'3
(a) The result of the long division is a - b + c.
(b) The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).
How to find an algebraic expression by long division
Long division is an algebraic procedure with which we can find the result of a division of two polynomials. Now we proceed to present the entire procedure explained:
(a) a² - b² + 2 · b · c - c² divided by a + b - c.
1) Multiply a + b - c by a and subtract it from a² - b² + 2 · b · c - c²: Result: a / Remainder: - b² - a · b + 2 · b · c + a · c - c²
2) Multiply a + b - c by - b and subtract it from the result of 1): Result: a - b / Remainder: b · c + a · c - c²
3) Multiply a + b - c by c and subtract it from the result of 2): Result: a - b + c / Remainder: 0
The result of the long division is a - b + c.
(b) 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4 divided by m⁴ - 3 · m² + 4.
1) Multiply m⁴ - 3 · m² + 4 by 3 · m³ and subtract it from 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4: Result: 3 · m³ / Remainder: 2 · m⁵ + m⁴ + 6 · m³ - 8 · m + 3 · m² + 4.
2) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 1): Result: 3 · m³ + 2 · m / Remainder: m⁴ + 12 · m³ - 16 · m + 3 · m² + 4.
3) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 2): Result: 3 · m² + 2 · m + 1 / Remainder: 12 · m³ - 16 · m + 6 · m².
The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).
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