Answer:
f-¹(x) = (x + 6)/2
Step-by-step explanation:
Replace f(x) with y.
y = 2x – 6
Interchange x and y.
x = 2y – 6
Solve for y.
y = (x + 6)/2
Replace y with f-¹(x)
f-¹(x) = (x + 6)/2
There are seven roads that lead to the top of a hill. How many different ways are there to reach the top and come back ( you dont have to go on the same road there and back)?
Answer:
49 different ways
Step-by-step explanation:
If there are seven roads that lead to the top, you have seven possible choices to go to the top of the hill.
Then, to come back to the start, you also have seven possible choices (seven roads), and you can pick any road.
So, if you have seven ways to go up and seven ways to go down, the number of different ways of going to the top and coming back is the product of these numbers of possible choices.
N(total) = N(up) * N(down)
N(total) = 7 * 7
N(total) = 49 different ways
Brainliest pls and tysm!
Need it solved correctly for khan academy
The tiger population loses 3/5 of its size every 2.94 decades
Rate of change using differential calculus
The given equation is:
[tex]N(t)=710(\frac{8}{125} )^t[/tex]
Find the derivative of the given function
[tex]\frac{dN}{dt} =710(0.064)^tln(0.064)\\\\\frac{dN}{dt} =-1951.7(0.064)^t[/tex]
When the tiger loses 3/5 of its population
dN/dt = 3/5
Solve for t
[tex]\frac{3}{5} =-1951.7(0.064)^t\\\\-0.0003=(0.064)^t[/tex]
Take the natural logarithm of both sides
[tex]ln(-0.0003)=t(ln0.064)\\\\-8.087=-2.75t\\\\t=\frac{-8.087}{-2.75} \\\\t=2.94[/tex]
The tiger population loses 3/5 of its size every 2.94 decades
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Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive? 48 mph 104 mph 0.019 mph 53 mph
Answer:
53 mph
Step-by-step explanation:
We need to give the answer in terms of miles per hour. This means that we need to find out how many miles Joe needs to travel in one hour. Therefore, this is a ratio problem.
We can set up a proportion where the unknown variable is the number of miles driven in one hour:
[tex]\frac{106}{2} =\frac{x}{1}[/tex]
x is just 106/2, or 53. Therefore, Joe needs to travel 53 mph
When figuring out the sign of a fraction as a
whole, you use the rules for dividing negatives.
At a charity fundraiser, each female attendant donated $1,200 and each male attendant donated $800. If the average donation at the fundraiser was $900, what was the ratio of the number of female attendants to the number of male attendants.
Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem:
There were f + m donations.The sum was of 1200f + 800m.The average was of 900.Hence:
[tex]\frac{1200f + 800m}{f + m} = 900[/tex]
1200f + 800m = 900f + 900m
100m = 300f
[tex]\frac{f}{m} = 3[/tex]
Hence the ratio was of 3.
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What is the solution to the system of equations? (7, 4) (7, startfraction 13 over 3 endfraction) (8, startfraction 14 over 3 endfraction) (9, 7)
The points are (7, 13/3).
Lets simplify the equation,
The equation of first line: y = 1/3 x + 2
the equation of second line: y= 4/3x - 5
Solve the system of equations by elimination,
Multiply equation A by -4 both sides
-4y = -4(1/3x +2)
-4y = -4/3x-8
After eliminating the equation we get,
y = 13/3
So now have to find x
13/3 = 1/3x + 2
Lets multiply above by 3
x = 13-6
x = 7.
Hence the points are (7, 13/3)
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Answer:
B
Step-by-step explanation:
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
What is the nth term of the sequence below?
2, 6, 12, 20, . . .
A. [tex]n {}^{2} \: + \: 1[/tex]
B. [tex]3n[/tex]
C. [tex]n(n \: + \: 1)[/tex]
D. [tex] {n}^{2} \: - \: 1[/tex]
Answer:
Option C
Kindly award branliest
Step-by-step explanation:
Tn = n(n + 1)
T1 = 1(1 +1) = 1(2) = 2
T2 = 2(2+1) = 2(3) =6
T3 = 3(3 + 1) = 3(4) = 12
T4 = 4(4 + 1) = 4(5) = 20
... It obeys
3 is subtracted from the product of 8 and a number
Answer: (8 * x) -3
Step-by-step explanation:
The term product refers to multiplication, so let the unknown number be x and multiply it by 8. Then you can subtract 3 afterwards.
*= multiplication
What does the following expression mean? x <= y
As per inequality, it means that the value of x can be less than or equal to y.
Inequality in Mathematics
The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >, <, ≤, or ≥ are used to denote an inequality, when the two expressions aren't always equal.
Type of Inequality
The given expression, x <= y denotes the type of inequality where the possible values of x are either less than y or equal to less. The value of x cannot be greater than y in any case.
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A zoologist researched the feeding habits of lemurs. she collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. what kind of statistical study did the zoologist conduct?
The kind of statistical study the zoologist conducted was D. observational study.
What is observational study in research?An observational study serves as a study whereby the researcher simply observes the subjects without interfering with it.
This is different from carrying out experiment on them or just a theoretical approach.
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CHECK THE COMPLETE QUESTION BELOW:
A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study
Which expresses the correct factorization
of….? look at pic
Answer:
Option 1
Step-by-step explanation:
Find 2 numbers that multiply to give 16 and sum to give +8 :
These numbers are 4 and 4
Now split +8x into +4x and +4x and factor each part :
x²+4x+4x+16 = 0
x(x+4)+4(x+4) = 0
Keep 1 bracket and the terms outside the brackets make their own :
(x+4)(x+4) = 0
(x+4)² = 0
Therefore answer will be Option 1
Hope this helped and have a good day
Members of a softball team raised $1353 to go to a tournament. They rented a bus for
$943.50 and budgeted $31.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Equation:
Answer: x =
Submit Answer
attempt 1 out of 2
The equation which can be used to determine x, the number of players the team can bring to the
tournament is 1353 = 943.50 + 31.50x and x = 13 players
EquationTotal amount raised = $1353Cost of renting a bus = $943.50Cost of each player's meal = $31.50Number of players in the team = x1353 = 943.50 + 31.50x
1353 - 943.50 = 31.50x
409.50 = 31.50x
x = 409.50 / 31.50
x = 13 players
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solve -9 2/7 - (-10 3/7)
Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he prepared 20 cupcakes in 30 minutes.
A) Does the scenario represent a direct variation?
B) If yes, explain the meaning of the constant of proportionality in the scenario.
take your time if you want :)
a) As the constants are equal, the situation represents a proportional relationship.
b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the constants for each situation are:
k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.
Since the constants are equal, the situation represents a proportional relationship.
The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
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[tex]4(x+y)^{2} -20(x+y)^{2} +25z^{2}[/tex]
Answer:
I am pretty sure that it is 625.
Answer:
Step-by-step explanation:
please make sure you indicate whether to factorize , simplify, fatorize by grouping , evaluate, or finding the derivative
Find the distance between the pair of points: (-3,-6) and (1,2).
d² = (y2 - y1)² + (x2 - x1)²
..............
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
The polynomial approximate values are
a. The linear approximating polynomial is p1(x) = 2 - x
b.The quadratic approximating polynomial is p2(x) = x² - 3*x + 3
c. The approximating polynomial value is p1(0.97) = 1.03; p2(0.97) = 1.0309
According to the statement
we have given that the f(x) = 1/x
And we have to find that polynomial approximate values which are written below
The linear approximating polynomial And quadratic approximating polynomial And approximate the given quantity of polynomials obtained in parts a. and b.
So, the given function is f(x) = 1/x
And
f'(x) = -1/x²
f''(x) = 2/x³
a = 1
Now, we find the linear approximating polynomial
So,
a. The linear approximating polynomial is:
p1(x) = f(a) + f'(a)*(x - a)
p1(x) = 1/1 + -1/1² * (x - 1)
p1(x) = 1 - x + 1
p1(x) = 2 - x
And Now, we find the quadratic approximating polynomial
So,
b. The quadratic approximating polynomial is:
p2(x) = p1(x) + 1/2 * f''(a)*(x - a)²
p2(x) = 2 - x + 1/2 * 2/1³ * (x - 1)²
p2(x) = 2 - x + (x - 1)²
p2(x) = 2 - x + x² - 2*x + 1
p2(x) = x² - 3*x + 3
And Now, we find the approximating polynomial value
So,
c. approximate 1/0.97 using p1(x)
p1(0.97) = 2 - 0.97 = 1.03
approximate 1/0.97 using p2(x)
p2(0.97) = 0.97² - 3*0.97 + 3 = 1.0309
So, The polynomial approximate values are
a. The linear approximating polynomial is p1(x) = 2 - x
b.The quadratic approximating polynomial is p2(x) = x² - 3*x + 3
c. The approximating polynomial value is p1(0.97) = 1.03; p2(0.97) = 1.0309.
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Disclaimer: This question was incomplete. Please find the full content below
Question:
A. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centeredat the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
f(x)=1/x, a=1; approximate 1/0.97
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A polynomial function has a root of 0 with multiplicity 1, and a root of 2 with multiplicity 4. If the function
has a negative leading coefficient, and is of odd degree, which of the following are true?
The function is positive on (-∞, 0).
The function is negative on (0, 2).
The function is negative on (2, ∞).
The function is positive on (0,0).
Using the Factor Theorem to find the function, the correct statement is:
The function is positive on (0,∞).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
The described roots means that:
[tex]x_1 = 0, x_2 = x_3 = x_4 = x_5 = 2[/tex]
Hence the function is:
f(x) = x(x - 2)^4
(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:
The function is positive on (0,∞).
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Which of the following is an arithmetic sequence where a₁ = 9 and d= 7?
A) 9, 16, 23, 30, 37, ...
B) 0, 9, 18, 27, 36,...
C) 7, 16, 25, 34, 43,...
D) 0, 7, 14, 21, 28, ...
Answer:
Option A
Step-by-step explanation:
Arithmetic sequence:In a arithmetic sequence, difference between any two consecutive term is constant.
a₁ = 9 & d = 7
t₁ = 9
t₂ = a₁ + d
= 9 + 7
= 16
t₃ = t₂ + d = 16+ 7
= 23
t₄ = t₃ + d
= 23 + 7
= 30
t₅ = t₄ + d
= 30 + 7
= 37
9,16,23,30,37,.......
Multiplica: (5 ft 6 in) x 4.
Answer: 22 ft
Step-by-step explanation:
Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".
What is Multiplicative rule?The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.
If A and B are dependent events, then the probability of both events occurring simultaneously is given by:
[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]
The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:
[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]
Multiplication Theorem of Probability:
The multiplication guidelines that we use in probability have already been taught to us, including;
[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]
Therefore, the relationship between two events is explained by the probability multiplication rule.
Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.
Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.
Using the characteristics of conditional probability, the likelihood of event AB is calculated.
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WILL MAKE BRAINLIEST!!Determine if the two triangles are congruent if they are state the postulate or theorem that provides they are congruent
Answer:
Yes they are congruent by SSS criterionStep-by-step explanation:
AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion.
Help with this word problem!
Answer:
2.0 km
Step-by-step explanation:
The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.
SetupThe law of cosines tells us ...
c² = a² +b² -2ab·cos(C)
Using the given values, we have ...
c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)
SolutionSimplifying the equation, we get ...
c² = 37.89 -37.8cos(26°) ≈ 3.91559
c ≈ 1.979 . . . . km
The width of the strait is about 2.0 km.
Which number(s) satisfy a ∩ c? 16, 81 1, 16, 81 1, 4, 9, 16, 25, 36, 49, 81, 100 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer:
Step-by-step explanation:
B: 1, 16, 81
WHY?
Set A is perfect squares from A to 100:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
Set A = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Set C is perfect fourths
1^4 = 1
2^4 = 16
3^4 = 81
4^4 = 254 (This is greater than 100)
Set C = 1, 16, 81
Hope this helps :)
the product of two numbers is 8933. If each of the two numbers is doubled the product of these larger numbers is?
The product of two numbers when doubled, the product of these larger numbers is 35,732
Productlet
The two unknown number = x and yproduct of x and y = 8933
x × y = 8933
If each of the two numbers is doubled2x × 2y = 8933
4xy = 4(8933)
4xy = 35,732
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how to simplify cos(6x) + 1
HELP PLEASE ASAP:<
Consider the expressions given below.
A. 2x³ - x² - 6x
B. 2x³ + 8x + 4
C. 3x^4+ x² + x - 7
D. 3x^4 - 3x^2 + 5x - 7
For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x³ 4 + 7x) - (2x³ 8)is equivalent to expression
(-3x² + x¹ + x) + (2x¹ - 7+ 4x)is equivalent to expression
(²2x) (2x + 3)is equivalent to expression
3x² + 5x - 7
Find the measure of each numbered angle.
Step-by-step explanation:
18z+10z+40z+5+1=360
68z+6=360
68z=360-6
68z=364
z≈5.353
Find the indefinite integral by making a change of variables. (hint: let u be the denominator of the integrand. remember to use absolute values where appropriate. use c for the constant of integration.) 1 9 2x dx
The value of the indefinite integral is
Given:- The integration of is given whose lower limit is and upper limit is .
To Find:- We have to find the value of the integration of is given whose lower limit is and upper limit is .
By using the concept of indefinite integral it will be solved.
According to the problem,
Therefore, the value of the indefinite integral is .
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Find the vertex and axis of symmetry of each quadratic equation.
Answer: Vertex (-2,-15) and therefore the axis of sym will be -2
Step-by-step explanation: Using -b/2a you can deduce that 4x^2 is a, 16x is b and 1 is c. So -b/2a = -16/8 = -2. Then you plug -2 for y and yu should get -15. Then x will be your axis of symetry to x=-2