Function composition exists a mathematical procedure where two functions, f and g, are taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)).
If the function be f(x) = 10x - 10 then the value of (f ⁰ f⁻¹)(d) is 99.
What is meant by composition?Function composition exists a mathematical procedure where two functions, f and g, exists taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)). The function g is used in this operation on the outcome of applying the function f to x.
Let the function be f(x) = 10x -10
We want to find (f ⁰ f⁻¹)(d)
To differentiate with respect to X, then we get
[tex]F^{-1}[/tex](x) = 10
To find the value of (f ⁰ f⁻¹)(d)
F([tex]f^{-1}[/tex](x)) = F(10)
F([tex]f^{-1}[/tex](x)) = 10x - 10
substituting the values in the above equation, then
F([tex]f^{-1}[/tex](x)) = 10(10) - 10
simplifying the above equation, we get
F([tex]f^{-1}[/tex](x)) = 100 -10
F([tex]f^{-1}[/tex](x)) = 99
Therefore, the value of (f ⁰ f⁻¹)(d) = 99
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pls help.. A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change in the bird’s altitude. Give your answer to the nearest hundredth.
The bird settles on the branch at the rate of 2.33 meters per second.
What is the rate of change?The rate of change refers to the traveling speed of the bird when perching on the branch.
The rate of change (which is speed) is the distance (altitude) divided by time.
Data and Calculations:The bird's flying altitude above ground = 10 meters
Time in seconds to settle on a branch = 3 seconds
The altitude above ground after settling on the branch = 3 meters
The change in altitude = 7 meters (10 - 3)
Rate of change = 2.33 meters per second (7/3)
Thus, the rate of change that the bird used to settle on the branch is 2.33 meters per second.
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Answer:
-2.33
Step-by-step explanation:
Use a table to solve each equation. Round to the nearest hundredth.
3x⁻¹=72
3[tex]x^{-1}[/tex] = 72 => x = 0.4167, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.Given: 3[tex]x^{-1}[/tex] = 72
=> [tex]x^{-1}[/tex] = [tex]\frac{72}{3} =[/tex] 24
=> [tex]\frac{1}{x}=24[/tex]
=> x = 0.4167
Hence, 3[tex]x^{-1}[/tex] = 72 => x = 0.4167, by basic algebra.
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Find 6y + 10z - 2yz, use y=2 and z=3
Answer:
30
Step-by-step explanation:
6(2) + 10(3) - 2(2)(3)
12 + 30 - 2(6)
42 - 12
30
The value of the expression 6y + 10z - 2yz when y = 2 and z = 3 is 30.
What is the value of the expression when y=2 and z=3?Given the expression in the question:
6y + 10z - 2yz
y = 2
z = 3
To determine the value of the expression 6y + 10z - 2yz, we simply substitute y = 2 and z = 3 into the expression and then simplify.
6y + 10z - 2yz
Plug in y = 2:
6( 2 ) + 10z - 2(2)z
Plug in z = 3:
6( 2 ) + 10( 3 ) - 2(2)(3)
Simplifying, we get:
12 + 30 - 12
Add 12 and 30:
42 - 12
Subtract 12 from 42:
30
Therefore, the value of the expression is 30.
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Which statement is true of the numbers 39/7 and-0.3287 A Only 39/7 is rational. B Only -0.328 is rational. C Both numbers are rational. D Both numbers are not rational.
Both numbers are rational numbers, so the correct answer is (C).
What are rational numbers?An irrational number cannot be expressed using fractions, whereas a rational number can be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating decimals. It is now possible for 12 rational numbers between -1 and 2 to be: 0, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, -0.1, -0.2, and -0.3. It's important to remember that there are other solutions besides the 12 rational numbers listed above.So,
39/7 is already a rational number as it is already in a fraction with a denominator not equal to zero.
And -0.3287 can also be expressed in fractions where the denominator will not be equal to 0. (Refer to the image below for work)So, we can say that both numbers are ratio numbers.Therefore, both numbers are rational numbers, so the correct answer is (C).
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According to the given solving we can say that both numbers are rational.
The correct option is C.
Why are rational number?The ratio or fraction among two numbers, p/q, where both p and q are the numerator and denominator, respectively, can be expressed as a rational number. For example, 3/7 and any integer represent rational numbers..
Why are numbers irrational and rational?Rational numbers can really be expressed as ratios (such P/Q and Q0), while irrational numbers can indeed be expressed as a fraction. Both of these numbers, nevertheless, are real and can be displayed on a number line.
According to the given data:39/7 and-0.3287
The decimal number as a fraction:
0.3287 = 0.3287/1
this can be written as:
[tex]\frac{0.3287}{1}[/tex] x [tex]\frac{1000}{1000}[/tex] = [tex]\frac{3287}{1000}[/tex]
So we can say that:
-0.3287 = [tex]\frac{-0.3287}{1000}[/tex]
According to the given solving we can say that both numbers are rational number.
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solve the equation for y. 2/5x+y=7
Which values, when substituted for x in the expression _/x , will result in an irrational number? Select all that apply.
The values, which when substituted for x in the expression √x , would result in an irrational number are:
x = 168x = 2x = 8x = 21x = πThe types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbersWhole numbersRational numbersIrrational numbersReal numbersIntegersWhat is an irrational number?An irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 168, 2, 8, 21, π, 11.
In conclusion, when a perfect square or 4 is substituted for x in the expression √x, the result is not an irrational number because it is neither a terminating nor a repeating decimal.
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Complete Question:
Which values, when substituted for x in the expression √x, will result in an irrational number? Select all that apply.
x = 168
x = 2
x = 8
x = 21
x = π
x = 4
when x is a perfect square.
Si por el consumo de 80m de agua se pagan $57 ¿cuánto se pagaron por 50m de agua?
6m=-12n-10 I was wondering if anyone could help me
Answer:
Check options down below!
Step-by-step explanation:
If solving for n:
n = -m/2 - 5/6
If solving for m:
m = -2n - 5/3
If f(x)=x+1 and g(x)=x²-3 x-4 , what is (f ⁰ g)(x) ?
(F) x²-3 x-3 (G) x²-x-6 (H) x²-x (I) x²-x-3
The value of the composite function f o g (x) is x² - 3 x - 3.
We have the functions:
f (x) = x + 1 and g (x) = x² - 3 x - 4
We need to find the composite function:
f o g (x)
= f ( g (x) )
Substituting the values, we get that:
= ( x² - 3 x - 4 ) + 1
= x² - 3 x - 4 + 1
= x² - 3 x - 3
Therefore, the value of the composite function f o g (x) is x² - 3 x - 3.
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Question 1 of 10
The equation y =
[25x
OA. $950
B. $30
OC. $38
OD. $25
0≤x≤38
represents Michelle's regular
30(x-38)+950 x > 38
hourly and overtime wage. Based on this equation, what is Michelle's
overtime hourly pay?
Michelle’s overtime hourly payment is 35.22
Given that ,
Equation represents Michelle’s regular hourly and overtime wage
= 130 (x – 38) + 950% > 38
We have to find Michelle’s overtime hourly payment.
Let’s solve the above given equation:
130 (x – 38) + 950% x 38 = 0
130x – 4940 + (950/100) x 38 = 0
130x – 4940 + 9.5 x 38 = 0
130x – 4940 + 361 = 0
130x – 4579 = 0
130x = 4579
X = 4579 / 130
X = 35.22
That is, Michelle’s overtime hourly payment is 35.22.
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which of the following expressions is equivalent to 2^4x-5
The relationships in the table below are functions. Write a function rule.
Answer: y = 25x + b
Step-by-step explanation:
Which of these are examples of deductive reasoning? Select the correct answer. Milk costs $2.99 per gallon at the first three grocery stores that Gema visited. She concludes that milk costs costs $2.99 per gallon everywhere. Most tulips grow to between 6 and 24 inches tall. Janelia concludes that the flowers in her garden will be shorter than 24 inches. Felix knows that everything that fits in his bookbag will fit in his suitcase. His laptop fits in his bookbag, so he concludes that the laptop will fit in his suitcase. Everytime Matthew has left for school at 7 am, he has been on time. Matthew concludes that if he leaves the house at 7 am today, he will be on time. The school's schedule states that lunch period is from 12 p.m. to 1 p.m. Eric concludes that it is after 12:00 p.m. because it is currently the lunch period. Sammy notices that the ants around his house all have 6 legs. He concludes that all ants must have 6 legs.
An example of deductive reasoning is Most tulips grow to between 6 and 24 inches tall. Janelia concludes that the flowers in her garden will be shorter than 24 inches.
What is a deductive reasoning?Deductive reasoning can be described as the mental process that involves the the act of drawing deductive inferences.
It should be noted that this inference can be valid in the case whereby the conclusion is seen to be in line with logic from its premises, hence option B is correct because it follows a logical sequesnce before amking a conclusion.
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Answer:
Step-by-step explanation:
It's C and E
Felix and The school's schedule
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Answer:
AWSOME IMAGE!
Step-by-step explanation:
You make it??!!!
Answer: AIght thx for the points
Step-by-step explanation:
Find the inverse of each function.
y=log₂4 x
The inverse function of the function y = log₂ 4x is f ⁻¹(x) = 2ˣ/4.
Given the function is :
y = log₂4x
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now interchange the positions of x and y in the function.
x = log₂4y
the next step is to isolate the dependent variables.
f ⁻¹(x) = 2ˣ/4
hence, we get the inverse of the given function as f ⁻¹(x) = 2ˣ/4
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simplify the expression (-3m^-4)(-5m^7). Explain your process and justify each step by naming the appropriate property
help
By the use of algebra properties, the expression (- 3 · m⁻⁴) · (- 5 · m⁷) is equivalent to 15 · m³.
How to simplify an algebraic expression
In this question we find a product of two monomials, each monomial has a constant, a variable and a grade and the entire expression must be simplified by means of algebra properties. The complete procedure of simplification is now presented:
(- 3 · m⁻⁴) · (- 5 · m⁷) Given[(- 3) · (- 5)] · [(m⁻⁴) · m⁷] Commutative and associative properties15 · m³ Multiplication of two negative numbers / Multiplication of powers with the same base / ResultTo learn more on algebraic expressions: https://brainly.com/question/21443100
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A point on the edge of a symmetrical canyon is 4500 feet above a river that cuts through the canyon floor. The angle of depression from each side of the canyon to the canyon floor is 60o.
a) Find the length of the canyon wall (from the edge to the river).
feet
b) Find the distance across the canyon.
feet
c) Is it more or less than a mile across the canyon? (5280 feet = 1 mile) more or less
The length and distance across the canyon is 5196.15 feet and it is more than 1 mile.
a) To find the length of canyon, we will sine function. As per the sine theta = length of opposite side ÷ hypotenuse. Keep the values in formula to find the hypotenuse, which is the length of the canyon wall.
sin 60 = 4500 ÷ hypotenuse
Hypotenuse = 4500 ÷ (✓3/2)
Hypotenuse = 4500 × 2 ÷ ✓3
Hypotenuse = 9000 ÷ ✓3
Hypotenuse = 5196.15 feet
The length of the canyon wall is 5196.15 feet.
b) To find the distance across the canyon, we will use cosine function. As per the cos theta = base ÷ hypotenuse. Keep the values in formula to find the base, which is half the length of the distance across the canyon.
cos 60 = base ÷ 5196.15
cos 60 × 5196.15 = base
Base = (1/2) × 5196.15
Base = 2958.075 feet
Total distance across the canyon = 2958.075 + 2958.075
Tota distance across the canyon = 5196.15 feet
c) Using the relation, 5280 feet = 1 mile
5196.15 feet = 5196.15 ÷ 5280 mile
5196.15 feet = 1.12 miles
So, distance across the canyon is more than 1 mile.
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The height of the house is 26 ft. What is the height of each r story
The height of each story based on the information is 10 feet.
How to calculate the value?It should be noted that from the information given, the storey building as a roof of 6 feet and the height of the house is 26 ft.
Therefore, the height of each story will be:
= (26 - 6) / 2
= 20 / 2
= 10 feet
Therefore, the height of each story based on the information is 10 feet.
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A 2 storey building as a roof of 6 feet.. The height of the house is 26 ft. What is the height of each story
I which of the numbers
are solutions to the
equation x² = 100? Select all that apply.
-10,000
-50
-10
0
10
50
10,000
The numbers that fits into the equation X² = 100 are -10 and 10.
How to illustrate the information?It should be noted that squares simply means multiplying a number by itself.
In this case, X² = 100.
Therefore, the numbers that fits X will be:
X² = 100
Square root both sides
X = ✓100
X = 10
Also, it should be noted that (-10)² = 100
Therefore, the numbers that fits into the equation X² = 100 are -10 and 10.
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how do i rate an answer
Answer:
press the stars.
Step-by-step explanation:
If the Social Security tax is 6% of a person's wages, what would the Social Security tax on wages of $80 be?
Answer: $4.8
Step-by-step explanation:
80*0.06=4.8
If there are 30 dogs and 36 cats at a pet daycare, fill out all of the possible ratios of
dogs to cats that could be made.
There are 30 dogs for every 36 cats (30:36 ratio)
There are
dogs for every cats try
Type in an equivalent ratio of dogs and cats.
8
(14)
19 (20)
(25) (26)
13
15
6
10 11 (12)
(16
(18)
23 (24)
28 (29) (30
17
(18)
(19) (20) (21) (22) (23) (24
(25)
(31)
(22)
(30)
(35) (36)
Answer:
1:2
Step-by-step explanation:
During this basketball season trey took 250 shots and made 72 baskets what was his shooting percentage
Justin borrowed money from a credit union for 2 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $840. How much money did he borrow?
Justin borrow $6,000 from a credit union for 2 years.
What is Principal amount?
The amount of money initially borrowed from the lender, and as the loan is repaid, it can also refer to the amount of money still owed, is called Principal amount.
Given that;
Simple interest = $840
Time = 2 years
Annual rate = 7%
Now, The formula for calculate the principal amount is,
Simple interest = Principal amount × Rate × time / 100
Principal amount = Simple interest × 100 / Rate × time
Hence,
Principal amount = 840 × 100 / 7 × 2
Principal amount = 84,000 / 14
Principal amount = $6000
So, Justin borrow $6,000 from a credit union for 2 years.
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PLEASE HELP! INEQUALITY PROBLEM!
unit 3 parallel and perpendicular lines, homework 1
Answer:
Not enough info.
Step-by-step explanation:
Is it possible to have a Triangle with
3cm , 6cm , 7cm ?
Answer:
yesStep-by-step explanation:
Is it possible to have a Triangle with
3cm , 6cm , 7cm ?
the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. so your answer is YES (obtuse Triangle)
If your SF = 6/5, what type of dilation is it?
Answer:
enlargement
Step-by-step explanation:
if scale factor > 1 then enlargement
if scale factor 0 < SF < 1 then reduction
here SF = [tex]\frac{6}{5}[/tex] = 1.2 > 1 so enlargement
Answer:
Enlargement
Step-by-step explanation:
Due to the scale factor properties stating that a SF value must be more than one to become an enlargement factor, we know that 6/5 is more than one whole. Thus, the SF is enlargement.
What is the length of HN?
Answer:
Given the length of all 3 segments is 38, we are counting two-thirds of 38. You would find this by multiplication.
Step-by-step explanation:
Conversion to improper fractions/Simplification
[tex]\frac{38}{1} \times \frac{2}{3} = \frac{76}{3}\\\\\frac{76}{3} = 76 \div 3 = 25\frac{1}{3}[/tex]
Therefore, HN = [tex]\sf 25\frac{1}{3}[/tex]
Question 10 of 10
Which of the following is most likely the next step in the series?
Answer:
A
Step-by-step explanation:
each step has added one extra side you might have trouble thinking it’s d but the pattern is x color (I’m colorblind) blue x blue so your answer is a