Answers
Answer:
[tex]{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) = {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =( \frac{a}{a'})x {}^{2} + ( \frac{b}{b'}) x} + \frac{c}{c'} } = 0[/tex]
Related Questions
Evaluate for x=2 and y=3: x^2y^-3/x^-1y
Answers
Answer:
8/81
Step-by-step explanation:
It's most efficient to simplify the quotient algebraically before inserting the values of the variables x and y.
The given expression reduces to x³ / y^4.
Substituting 2 for x and 3 for y, we get:
(2)³ 8
--------- = ---------- (Agrees with first given possible answer)
(3)^4 81
Help differentiate this
Answers
Answer:
[tex]\displaystyle y' = 20x^3 + 6x^2 + 70x + 9[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsExpand by FOILFunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (x^3 + 7x - 1)(5x + 2)[/tex]
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(x^3 + 7x - 1)](5x + 2) + (x^3 + 7x - 1)\frac{d}{dx}[(5x + 2)][/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle y' = (3x^{3 - 1}+ 7x^{1 - 1} - 0)(5x + 2) + (x^3 + 7x - 1)(5x^{1 - 1} + 0)[/tex]Simplify: [tex]\displaystyle y' = (3x^2+ 7)(5x + 2) + 5(x^3 + 7x - 1)[/tex]Expand: [tex]\displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5(x^3 + 7x - 1)[/tex][Distributive Property] Distribute 5: [tex]\displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5x^3 + 35x - 5[/tex]Combine like terms: [tex]\displaystyle y' = 20x^3 + 6x^2 + 70x + 9[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Mark draws one card from a standard deck of 52. He receives $ 0.30 for a heart, $ 0.55 for a queen and $ 0.90 for the queen of hearts. How much should he pay for one draw
Answers
Answer
$0.1346
Explanation:
Find probability of each card and the value of each card and then add them together.
Probability of getting a heart = 13/52
Price of one heart =$0.30
Pay for one heart = 13/52×0.30=$0.075
Probability of getting a queen =4/52
Price of one queen =$0.55
Pay for one queen =4/52×$0.55=$0.0423
Probability of getting a queen of hearts =1/52
Price of one queen =$0.90
Pay for one queen =1/52×$0.90=$0.0173
Therefore the pay for one draw= $0.075+$0.0423+$0.0173=$0.1346
Solve the following system of equations
Answers
Answer:
Given Two equations :-
[tex]3x {}^{2} - 2 {y}^{2} = 57 .\: .\: .\: . \:(i) \\ - 2 {x}^{2} + 3 {y}^{2} = -23.\: .\: .\: . \:(ii)[/tex]
multiplying eq.(i) by 2 eq.(ii) by 3.[tex](3x {}^{2} - 2 {y}^{2} = 57 ) \times 2 .\: .\: .\: . \:(i) \\ ( - 2 {x}^{2} + 3{y}^{2} = - 23) \times 3.\: .\: .\: . \:(ii)[/tex]
[tex]6x {}^{2} - 4 {y}^{2} =114 .\: .\: .\: . \:(i) \\ - 6 {x}^{2} + 9 {y}^{2} = - 69.\: .\: .\: . \:(ii)[/tex]
[tex]0 + 5 {y}^{2} = 45 \\ 5y {}^{2} = 45 [/tex]
diving both sides by 5[tex] {y}^{2} = 9[/tex]
taking Square root[tex]y = + - 3[/tex]
placing this value of y² in eq. (i)3x²- 2×9 = 57
3x² - 18 = 57
adding 18 to both sides3x² = 57 + 18
3x²= 75
diving both sides by 3x² = 25
x = ± 5
So, the values of x are +5 and -5 and the values of y are +3 and -3The slope of diagonal AB is ___ , and it’s equation is ___.
Answers
Answer:
The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].
Step-by-step explanation:
Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.
Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].
Divide: (2n3+4n−9)÷(n+2).
Answers
Answer:
2n+2
_____
9 2n
what is the domain of f(x)
Answers
Answer:
Values of x
Step-by-step explanation:
The domain of a function is the set of all possible inputs for the function while the co-domain is the set of all possible outputs of the function.
In other words, domain is the set of x-values that you can put into any given equation while co-domain is the sex of f(x)-values that you get from substituting the values of x.
Hope it's clear
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 7 minutes and the standard deviation of the waiting time is 1 minute. Find the probability that a person will wait for more than 6 minutes. Round your answer to four decimal places.
Answers
Answer:
0.15866
Step-by-step explanation:
6-7/1
=-1
p(x>-1)=1-p(x<1)
=0.15866
Sarah invests £2000 for 2 years in a saving account. She earns 3% per annum in compound interest.
How much did Sarah have in her saving account after 2 years?
£
Use the formula:
A=P(1+r100)n
Where;
A = the amount of money accumulated after n years, including interest
P = the principal sum (the initial amount borrowed or invested)
r = the rate of interest (percentage)
n = the number of years the amount is borrowed or invested
Answers
Answer:
£2120.27
Step-by-step explanation:
A = P (1 + r100)
A = 2000 (1+ 0.03/365)^365(2)
A = 2000 ( 1.00008)^730
A = 2000 (1.060)
A = £2120.27
5
12
of the pupils in Year 9 say their favourite colour is red.
There are 240 pupils in Year 9.
How many students said red is their favourite colour?
Answers
Answer:
100
Step-by-step explanation:
I assume you mean [tex]\frac{5}{12}[/tex] of the students in Year 9.
Basically, first you need to work out 1/12 of the students, which is just 240 divided by 12, equals 20.
So, we know 1/12 of 240 is 20, therefore, in order to work out 5/12, we must do 20 x 5, which is 100.
We are testing a new drug with potentially dangerous side effects to see if it is significantly better than the drug currently in use. If it is found to be more effective, it will be prescribed to millions of people.
1.
a. What does it mean in context to make a type I error in this situation?
b. What does it mean in context to make a type Il error in this situation?
c. Which error do you think is worse? Now we are testing to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the supplement.
2.
a. What does it mean in context to make a type I error in this situation?
b. What does it mean in context to make a type Il error in this situation?
c. Which error do you think is worse? For a given situation, what should you do if you think that committing a type l error is much worse than committing a type Il error?
A. Increase the significance level.
B. Decrease the significance level.
C. Nothing, just be careful to take a good sample.
Answers
Answer:
1) a) accepting the new drug is better based on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects
b) Accepting and using the current drug in use when it is not as effective as the new drug
c) Type 1 error
2) a) rejecting the vitamin supplement based on not knowing the harmful side effects
b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.
c) Type II error
3) Increase the significance level ( A )
Step-by-step explanation:
1)
a) To make a type 1 error in this situation is accepting the new drug is better and prescribing it to the millions of people based only on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects
b) A type II error in context is :Accepting and using the current drug in use when it is not as effective as the new drug
c) Type I error
2)
a) Type 1 error is rejecting the vitamin supplement based on not knowing the harmful side effects
b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.
c) Type II error
3) If committing a type 1 error is much worse
Increase the significance level
helppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
the total square footage = 194
1.88 x 194 = 364.72
Step-by-step explanation:
Area for triangle ends.
A = [tex]\frac{2.5 (8)}{2}[/tex] (Times two, because there are two ends.)
Base of prism = 8 x 10 = 80
Sides of prism = 2(10 x 4.7 ) = 94 (What's the 2? There's two of them)
Add all together : 10 + 10 + 80 + 94 = 194
1.88 x 194 = 364.72
What is A∪ϕ and A∩ϕ for a set A?
Answers
Answer:
1 ans A second phi okay yed
21. The mean salary of twelve men is $58,000, and the
mean salary of eight women is $42,000. Find the
mean salary of all twenty people.
Answers
(58000 + 42000)/2 = 50000
A rectangular prism has a volume of 60cm^3. What could the length, width and
height be? Explain how you know. "Recall, the formula for the volume of a prism
is V=lwh.
Can you guys help
Answers
H: 10
W: 2
3x10x2=60
Rearrange height length width if needed for your answer
Hope this helps!
Solutes in the bloodstream enter cells through a diffusion process called
osmosis, the diffusion of fluid through a semi-permeable membrane. Let C = C(t)
be the concentration of a certain solute inside a particular cell. The rate at which
the concentration inside the cell is changing is proportional to the difference in the
concentration of the solute in the bloodstream and the concentration within the cell.
Suppose the concentration of a solute in the bloodstream is maintained at a constant
level of L gm/cm?
(a) Write a differential equation involving
dc\dt
Answers
Answer:
en la calasa ni esta en la estacion
When converting 5 1/4% to decimal, Mark wrote 5.25. Explain why his answer is wrong and write the correct answer.
Answers
Answer:
Below
Step-by-step explanation:
It is 5 1/4 PERCENT not just 5 1/4.
5 1/4 % = 5.25%
= 5.25/100
= 0.0525.
Find the standard normal area for each of the following (Round your answers to 4 decimal places.): Standard normal area a.P(1.26 < Z < 2.16) b.P(2.05 < Z < 3.05) c.P(-2.05 < Z < 2.05) d.P(Z > .55)
Answers
Answer:
The correct answer is:
(a) 0.0884
(b) 0.0190
(c) 0.9596
(d) 0.2921
Step-by-step explanation:
(a)
= [tex]P(1.26<Z<2.16)[/tex]
= [tex]P(Z<2.16)-P(Z<1.26)[/tex]
= [tex]0.9846-0.8962[/tex]
= [tex]0.0884[/tex]
(b)
= [tex]P(2.05<Z<3.05)[/tex]
= [tex]P(Z<3.05)-P(Z<2.05)[/tex]
= [tex]0.9989-0.9798[/tex]
= [tex]0.0190[/tex]
(c)
= [tex]P(-2.05<Z<2.05)[/tex]
= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]
= [tex]0.9798-0.0202[/tex]
= [tex]0.9596[/tex]
(d)
= [tex]P(Z>0.55)[/tex]
= [tex]1-P(Z<0.55)[/tex]
= [tex]1-0.7088[/tex]
= [tex]0.2912[/tex]
Find the perimeter of a rectangular tile with length 1/5ft and width 3/14ft
Answers
Answer:
[tex]\frac{29}{35}[/tex] ft (29/35 ft)
Step-by-step explanation:
1. LCDPerimeter: [tex]2w+2l[/tex]
[tex]2(\frac{1}{5})+2(\frac{3}{14})=\frac{2}{5} +\frac{6}{14}[/tex]
Since [tex]\frac{6}{14} = \frac{3}{7}[/tex], the LCD would be 35
2. SolvingNew equation: [tex]\frac{14}{35} +\frac{15}{35} =\frac{29}{35}[/tex]
[tex]\frac{29}{35}[/tex]
Hope this helped! Please mark brainliest :)
Write an equation that represents the line.
Answers
Answer:
Y = 2/3X + 4/3
Step-by-step explanation:
(1,2) (4,4)
M = 2/3
Y = 2/3X + b
4 = 8/3 + b
12 = 8 + 3b
4 = 3b
B = 4/3
Y = 2/3X + 4/3
Time Remaining 59 minutes 49 seconds00:59:49 PrintItem 1 Time Remaining 59 minutes 49 seconds00:59:49 At the end of Year 2, retained earnings for the Baker Company was $2,950. Revenue earned by the company in Year 2 was $3,200, expenses paid during the period were $1,700, and dividends paid during the period were $1,100. Based on this information alone, what was the amount of retained earnings at the beginning of Year 2?
Answers
Answer:
$2550
Step-by-step explanation:
Calculation to determine the amount of retained earnings at the beginning of Year 2
Using this formula
Beginning Retained Earnings + Revenue − Expenses − Dividends = Ending Retained Earnings
Let plug in the formula
Beginning Retained Earnings + $3,200 − $1,700 − $1,100 = $2950
Beginning Retained Earnings= $2,950-$400
Beginning Retained Earnings = $2,550
Therefore the amount of retained earnings at the beginning of Year 2 is $2550
If f(x) = 4^x-8 and g(x) = 5x+6, find (f + g)(x)
A. (F+g)(x) = -4^x - 5x + 2
B.(F+g)(x) = 4^x + 5x - 2
C.(F+g)(x) = 4^x - 3x + 6
D.(F+g)(x) = 9x - 2
Answers
Hey there!
We are given two functions - one is Exponential while the another one is Linear.
[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]
1. Operation of Function
(f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]
2. Substitution
Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]
3. Evaluate/Simplify
Cancel out the brackets and combine like terms.[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]
4. Final Answer
(f+g)(x) = 4^x+5x-2Solve for y.
5y – 10 = 10
y = [?]
What is y?
Answers
Answer:
y = [ 4 ]
Step-by-step explanation:
5y - 10 = 10
+10 +10
5y = 20
/5 /5
y = 4
hope this helps ! ^^
Answer:
[tex]5y-10=10[/tex]
[tex]Add ~10[/tex]
[tex]5y=10+10[/tex]
[tex]5y=20[/tex]
[tex]divide ~by ~5[/tex]
[tex]y=4[/tex]
[tex]ANSWER: y=4[/tex]
-----------------------------
HOPE IT HELPS
HAVE A GREAT DAY!!
More math sorry. But I honestly don’t know any of these
Answers
Answer: A
Step-by-step explanation:
The main parent functions are x, and x raised to the power of something (examples: [tex]x^2, x^3, x^4[/tex], etc)
Find the difference.
(3x3−2x2+4x−8)−(5x3+12x2−3x−4)=
Answers
Answer:
-2x³ - 14x² + 7x - 4
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(3x³ - 2x² + 4x - 8) - (5x³ + 12x² - 3x - 4)
Step 2: Simplify
[Distributive Property] Distribute negative: 3x³ - 2x² + 4x - 8 - 5x³ - 12x² + 3x + 4Combine like terms (x³): -2x³ - 2x² + 4x - 8 - 12x² + 3x + 4Combine like terms (x²): -2x³ - 14x² + 4x - 8 + 3x + 4Combine like terms (x): -2x³ - 14x² + 7x - 8 + 4Combine like terms: -2x³ - 14x² + 7x - 4When 50% of a number is added to the number, the results is 165
Answers
Answer:
this would look like
0.5x+x=165
1.5x=165
x=110
Hope This Helps!!!
The five-number summary of a data set is: 0, 4, 6, 14, 17
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
Answers
Answer:
Outlier therefore could only be values below - 12.75
or could only be values above + 121.125
Step-by-step explanation:
0, 4, 6, 14, 17
inner quartile range of 0 - 17 is 1/2 of 17 subtracted from the higher number = 17 - 1/2 of 8.5 = 8.5 - 4.25 = 4.25 - 4.25 x 3
= 4.25 to 12.75 for inner quartile
inner quartile range is 12.75-4.25 = 8.5
We then 1.5 x 8.5 to show the outlier
= 12.75 meaning there is no outlier if is below.
Lower quartile fences = 4.25 - 1.5 = 2.75
or -1.5 x 8.5 (the range) = -12.75
Upper quartile fence = 12.75 + 1.5 = 14.25 x 8.5 = 121.125 this would be an outlier if it is 12.75 higher than 121.125 or 12.75 lower than 5.50.
Outlier therefore could only be values below - 12.75
or could only be values above + 121.125
An observation is considered an outlier if it exceeds a distance of 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile. The values of the lower quartile - 1.5 x IQR and upper quartile + 1.5 x IQR are known as the inner fences.
An observation is an outlier if it falls more than above the upper quartile or more than below the lower quartile. The minimum value is so there are no outliers in the low end of the distribution. The maximum value is so there are no outliers in the high end of the distribution.
rom each corner of a square piece of sheet metal 18 centimeters on a side,we remove a small square and turn up the edges to form an open box. Whatis the largest volume this box could have
Answers
Answer:
The volume is maximum when the height is 3 cm.
Step-by-step explanation:
let the side of the removed potion is x.
length of the box = 18 - 2 x
width of the box = 18 - 2 x
height = x
Volume of box
V = Length x width x height
[tex]V = (18 - 2 x)^2 \times x\\\\V = x(324 + 4x^2 - 72 x)\\\\V = 4 x^3 - 72 x^2 + 324 x \\\\\frac{dV}{dx} = 12 x^2 - 144 x + 324 \\\\So,\\\\ \frac{dV}{dx} =0\\\\x^2 - 12 x + 27 = 0 \\\\x^2 -9 x - 3 x + 27 =0\\\\x (x - 9) - 3 (x -9) = 0\\\\x = 3, 9[/tex]
Now
[tex]\frac{d^2V}{dx^2}=24 x - 144 \\\\Put x = 3 \\\\\frac{d^2V}{dx^2}=24\times 3 - 144 = - 72\\\\Put x = 9\\\\\frac{d^2V}{dx^2}=24\times 9 - 144 = 72\\[/tex]
So, the volume is maximum when x = 3 .
Find an expression for the general term of each of the series below. Use n as your index, and pick your general term so that the sum giving the series starts with n=0.
A. x^3cosx^2=x^3-(x^7)/2!+(x^11)/4!-(x^15)/6!+...
general term =
B. x^3sinx^2=x^5-(x^9)/3!+(x^13)/5!-(x^17)/7!+...
general term =
Answers
Answer:
[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
Step-by-step explanation:
A
Let's start with the first function:
[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]
In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a
[tex](-1)^{n}[/tex].
This will guarantee us that the terms will always change their signs so that will be the first part of our expression.
next, the power of the x. Notice the given sequence: 3, 7, 11, 15...
we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.
so let's put the two things together:
[tex](-1)^{n}x^{4n+3}[/tex]
Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!
This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!
So let's put it all together so we get:
[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
So now we can build the whole series:
[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
B
Now, let's continue with the next function:
[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]
In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a
[tex](-1)^{n}[/tex].
This will guarantee us that the terms will always change their signs so that will be the first part of our expression.
next, the power of the x. Notice the given sequence: 5, 9, 13, 17...
we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.
so let's put the two things together:
[tex](-1)^{n}x^{4n+5}[/tex]
Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!
This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!
So let's put it all together so we get:
[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
So now we can build the whole series:
[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20
Answers
Answer:
(4, 2 )
Step-by-step explanation:
Given the 2 equations
3x + y = 14 → (1)
7x - 4y = 20 → (2)
Rearrange (1) making y the subject by subtracting 3x from both sides
y = 14 - 3x → (3)
Substitute y = 14 - 3x into (2)
7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side
7x - 56 + 12x = 20
19x - 56 = 20 ( add 56 to both sides )
19x = 76 ( divide both sides by 19 )
x = 4
Substitute x = 4 into (3) for corresponding value of y
y = 14 - 3(4) = 14 - 12 = 2
solution is (4, 2 )
Answer:
[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]
