The inverse function of the function 5y + 4 = (x + 3)² + 0.5 is shown below. Then the correct option is D.
[tex]\rm y= \pm \sqrt{5x + \dfrac{7}{2}} - 3[/tex]
What is the inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means, the inverse of 'f' is a reverse operator, that takes back the effect of 'f'
The equation is given below.
[tex]\rm 5y + 4 = (x+3)^2 + \dfrac{1}{2}[/tex]
Then y will be
[tex]\rm 5y = (x+3)^2 + \dfrac{1}{2} - 4\\\\\rm y \ \ = \dfrac{(x+3)^2}{5} - \dfrac{7}{10}[/tex]
The replace y by x and x by y, then we have
[tex]\begin{aligned} x &= \dfrac{2(y+3)^2}{10} - \dfrac{7}{10}\\\\\dfrac{10x + 7}{2} &= (y + 3)^2 \\\\\sqrt{5x + \dfrac{7}{2}} &= y + 3\\\\y &= \pm \sqrt{5x + \dfrac{7}{2}} - 3 \end{aligned}[/tex]
More about the inverse function link is given below.
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Answer: D
Step-by-step explanation:
The 2022 Russian Invasion of Ukraine began due to the cause of the collapse of the Soviet Union, which was sped along by the independence of the baltic states in 1990. When Ukraine left the USSR in 1991 and gave it's nuclear weapons to Russia in 2006, it began clear that Ukraine needed to be returned back into the hands of Moscow, before becoming another frontline for the NATO Army to invade the Russian Federation from the west, with more support from Japan in the east. Oh and I did the Edge test in 2022 so thats how I know it's D.
Trees that are cut down and stripped of their branches for timber are
approximately cylindrical. A timber company specializes in a certain type
of tree that has a typical diameter of 50 cm and a typical height of about
10 meters. The density of the wood is 380 kilograms per cubic meter, and
the wood can be sold by mass at a rate of $4. 75 per kilogram. Determine
and state the minimum number of whole trees that must be sold to raise
at least $75,000. *
From the calculations, the number of whole trees that can be sold at $75,000 is 21 trees.
What is density?Density is defined a the mass per unit volume. Now we have the following;
Diameter = 50 cm or 0.5 m
height = 10 meters
volume = ?
Density of the cylinder = 380 Kg/m^3
Now;
We can get the volume from;
V = πr^2h
V = 3.142 * (0.5/2)^2 * 10
V = 1.96m^3
From;
D = m/V
m = DV
m = 1.96m^3 * 380 Kg/m^3
m = 744.8 Kg
If 1 Kg of wood is sold at $4. 75
744.8 Kg is sold at 744.8 Kg * $4. 75/ 1 Kg
= $3537.8
Number of whole trees to be sold at $75,000= $75,000/$3537.8
= 21 trees
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Which term is defined as two intersecting lines that form four right angles in a plane?.
Answer:
Perpendicular.
Step-by-step explanation:
Two lines that come together and form 4 angles are known as perpendicular lines.
The radius and center of circle C are shown. Use 3.14 for pi . Round to the nearest tenth.
Answer:
See below
Step-by-step explanation:
Circumference = pi * d = 18 pi inches
Area = pi r^2 = pi * 9^2 = 81 pi in^2
Can you tell us what the missing number is in this sequence? 7,10,15,22, ?, 42
Answer:
31
the difference between the numbers is the number, plus 2, so for example, the difference between 7 and 10 is 3, add two and you have 5, and ten plus 5 equals 15. Using this formula, we have 5+2=7, which is 15+7=22. For the missing number, we have 7 (the last number used) +2=9, so, 22+9=31.
Step-by-step explanation:
im kinda bad at explaining things, but i really hoped this helped :)
Della bout a tree seedling that was two and one 4th feet tall during the first year it grew one and 16 feet after two years it was 5 feet tall how much did see thing go during the second year
Answer:
sorry i'm having an exam and its rlly hard so i'm looking for answers myself
Step-by-step explanation:
...
hope it helps
the answer is
What’s The Answer Of This? Please Answer ASAP
Answer:
c) 80⁰
isosceles triangle, two sides and angels are equal.
Step-by-step explanation:
180⁰= full triangle
80⁰+20⁰=100⁰
180-100=80⁰
Veronica painted 6 doghouses. She used 5 quarts of paint. If she used the same amount of paint for each doghouse, how many quarts of paint did she use on each doghouse?
Answers:
A 1/5
B 5/6
C 1/6
D 6/5
Answer:
A. 1/5
Step-by-step explanation:
First, you do 6 and divide it by 5. 6 divided by 5 is 1/2. 1/5 times 6 equals 1/2.
Rosa earns $120 per week tutoring math. Each week, she puts 36$ from her paycheck in a bank account to save for college. Find the amount Rosa saves out of $100.
Answer:
30
Step-by-step explanation:
You can do 36*100=3600 and do 3600/120. This is a very simple way to get 30 out of 100
Answer: $30
Step-by-step explanation: If she saves $36 when she earns $120, then she saves *amount =36/120 ×100
Amount saved with $100 earning is $30
4. Mindy has two secret numbers. Her numbers are prime numbers and they are between the
numbers 18 and 25. List Mindy's two numbers.
19, 25
18, 25
24, 25
19, 23
Answer:
19 23
Step-by-step explanation:
19 and 23 are the only primes in her range
7 times what equals 12
Answer:
12/7Step-by-step explanation:
Let the required number be 'n'.
Then, we need to find what the value of n is.
According to the question,
7 x n = 12Multiply both sides by 1/7.
7 x n x 1/7 = 12 x 1/77/7 x n = 12/7n = 12/7A right rectangular prism has a square base, with sides that are each 2 meters in length. The height of the prism is 34 meters. Find the volume of the prism in cubic meters
Answer:
136m
Step-by-step explanation:
The formula for the volume of a rectangular prism is V = L · W · H
We can take the given values and multiply them to find our answer.
L = 2
W = 2
H = 34
2x2x34 = 136
The volume of the rectangular prism will be 136 cubic meters.
What is a rectangular prism?A rectangular prism is a solid three-dimensional shape with six faces and rectangular bases. A rectangular prism is also a cuboid. A cuboid and a rectangular prism have the same cross-section.
Given that a right rectangular prism has a square base, with sides that are each 2 meters in length. The height of the prism is 34 meters.
The formula for the volume of a rectangular prism is V = L · W · H
We can take the given values and multiply them to find our answer.
L = 2
W = 2
H = 34
The volume of the prism will be calculated as,
V = 2x2x34
V = 136 cubic meters
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Akira's dog will be having four puppies. Akira performs a
simulation by tossing a coin to model whether these
puppies will be male or female.
• Let heads (H) = female puppy
• Let tails (T) = male puppy
The results of the simulation are:
1. THHT 6. HHHT
2. HTHH 7. HHTT
3. HTTH 8. THTH
4. TTTH 9. HHTT
5. TTTH 10. HTHH
What is the estimated probability that at least two of the puppies will be
female?
Answer:
u didnt put the anwsers but its 80% percent now can i have brainliest pls ty
Step-by-step explanation:
Which best describes the resulting three-dimensional figure? a cone with a base radius of 26 cm a cone with a base radius of 14 cm a cylinder with a base radius of 26 cm a cylinder with a base radius of 14 cm
The best description of the resulting three-dimensional figure when the considered figure is revolved is: A cylinder with height 24 cm.
What is solid of revolution?When a figure is revolved around some fixed axis, the whole three dimensional solid formed from the area that it swaps out is called solid of revolution.
Since no image is specified, we will work on the image attached below.
We can visualize and imagine that the horizontal line is still and just rotating on its place. The rectangle will revolve around, and therefore will swap out a cylindrical shape.
Since the length of the rectangle is 24 cm, and it is rotated on its length, so that will serve as height of the formed cylinder.
Thus, the best description of the resulting three-dimensional figure when the considered figure is revolved is: A cylinder with height 24 cm.
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The teacher of a seventh-grade class flipped a coin 100 times. The students recorded the results in the table shown below:
Side of Coin Landed On Heads Tails
Number of Flips 54 46
Which of the following best describes the experimental probability of getting heads?
The experimental probability is the same as the theoretical probability.
The experimental probability is 4% lower than the theoretical probability.
The experimental probability is 4% higher than the theoretical probability.
The experimental probability cannot be concluded from the data in the table.
Answer: Answer: Third option is correct.
Step-by-step explanation: Step-by-step explanation:
Since we have given that
Number of heads = 56
Number of tails = 44
Total number of flips = 100
So, Probability of getting head is given by
Theoretical probability of getting head is given by
There is a difference of
0.54-0.50=0.04 = 4%
Hence, the experimental probability is 4% higher than the theoretical probability.
Therefore, Third option is correct.
Answer:
The experimental probability is 4% lower than the theoretical probability.
Step-by-step explanation:
because i took this before and got it right
A standard deck of playing cards is shuffled and three people each choose a card. Find the probability that the first two cards chosen are diamonds and the third card is black if the cards are chosen without replacement.
Answer:
don't worry about this question
Learning task 1: Conduct a survey of the favorite fruit of your classmates and/or friends 10 boys and 10 girls by sending a message on messenger or sms use the table to record the data.
help me pls
nonsense=report
nice answer=brainles
pls dont waste my points
What is trigonometry and where is it used?
Answer:
Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding.
Find angle hif angle 46
Answer:
Step-by-step explanation:
find the area of the triangle. please show all the work.
Answer:
Step-by-step explanation:
If triangle equilateral, then h = 3 × 4√3 = 12√3
If side of triangle is "x" , then length of the base is
x² - ( [tex]\frac{x}{2}[/tex] )² = ( 4√3 )²
4x² - x² = 192
x² = 64
x = 8
[tex]A_{triangle}[/tex] = 8 × 12√3 = 96√3
solve 7^x-2 =30.
Type the correct answer in the box. Round your answer to three decimal places.
X=
Answer:
x = 3.748
Step-by-step explanation:
this problem requires logs
[tex]log_{7} 30 = x-2[/tex]
x = 2 + log_7 (30) or 3.7479
What is the additive inverse of the polynomial –9xy2 6x2y – 5x3? –9xy2 – 6x2y 5x3 –9xy2 – 6x2y – 5x3 9xy2 6x2y 5x3 9xy2 – 6x2y 5x3
The additive inverse of the given polynomial is
-f(x,y)=-9xy^2+6x^2y-5x^3
You have the polynomial f(x,y)=-9xy^2+6x^2y-5x^3.
What is the additive inverse of a polynomial?Additive inverse means changing the sign of the number and adding it to the original number to get an answer equal to 0.
The additive inverse of a polynomial f(x,y) is a polynomial that makes zero when it is added to polynomial f(x,y).
So additive inverse of polynomial f(x,y) will be -f(x,y).
Thus, the additive inverse will be
-f(x,y)=-9xy^2+6x^2y-5x^3
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Answer:
D
Step-by-step explanation:
:) Which division problem is modeled by the picture? A) 30 + 7 = 4 with a remainder of 2 B) 30 + 4 = 4 with a remainder of 2 C 30 + 2 = 7 with a remainder of 4 D) 30 = 4 = 2 with a remainder of 7
Cooper gave out a survey to some students in his school about their favorite color. Students could choose between red and blue. 129 of those surveyed said their favorite color was red. 57% of the students surveyed said their favorite color was blue. How many students were surveyed in total?
Using proportions, it is found that since 43% of the total amount is 129, 300 students were surveyed in total.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, since 57% of the students surveyed said their favorite color was blue, hence 100 - 57 = 43% said it was red, and this amount is of 129 students, hence:
0.43n = 129
n = 129/0.43.
n = 300.
300 students were surveyed in total.
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Answer number 9 pleaseeee
Answer:
No 9.
[tex]120 \: \times \frac{5}{100} [/tex]
SOMEONE HELP I NEED THE WHOLE ANSWER WITH WORK FOR TONIGHT
Answer:
325 or 325/1
Step-by-step explanation:
The formula for slope is:
y1 - y2/x1 - x2
Plugging the numbers in gives you:
40 - 690/0-2
Do subtraction first:
-650/-2
Two negatives make a positive and simplifying the fraction gives you:
325 or 325/1
Whichever makes you happier
(Also, remember that slope is rise/run, which is why it is y/x not the other way around(When graphing you go left/right then up/down))
Hope this helps you :)
help please fast!!!!!!!!
Answer:
Step-by-step explanation:
If there is only ONE output for each INPUT it can be a function
From top
Y N Y Y N Y
b) look at the second one
put in 30 days out put = april jun aug nov one input 4 outputs
so it is not a function
Miguel and three of his friends went to the movies. They originally had a total of $40. Each boy had the same amount of money and spent $7.50 on a ticket. How much money did each boy have left after buying his ticket?
A. Draw a bar diagram that represents the situation.
B. Write and solve an equation that represents the situation.
C. Explain how you solved your equation.
D. Compare the arithmetic solution and the algebraic solution.
What is the value of x in the equation −25x−2=18?
Answer:
x = -0.8
Step-by-step explanation:
-25x - 2 = 18
-25x -2 - 2 = 18 - 2
-25x = 16
-25x/-25 = 16/-25
x = -0.8
Answer:x=4/5
Step-by-step explanation: First you add two to both sides to cancel out the -2.Next you simplify and add the numbers.Finally, you divide both sides and simplify.
find the inverse of the function
If h⁻¹(x) is the inverse of h(x), then by definition of inverse function,
h(h⁻¹(x)) = x
Given that h(x) = 6∛(2x + 5) - 1, we have
h(h⁻¹(x)) = 6∛(2 h⁻¹(x) + 5) - 1 = x
Solve for h⁻¹(x) :
6∛(2 h⁻¹(x) + 5) - 1 = x
6∛(2 h⁻¹(x) + 5) = x + 1
∛(2 h⁻¹(x) + 5) = (x + 1)/6
[∛(2 h⁻¹(x) + 5)]³ = [(x + 1)/6]³
2 h⁻¹(x) + 5 = (x + 1)³/216
2 h⁻¹(x) = (x + 1)³/216 - 5
h⁻¹(x) = (x + 1)³/432 - 5/2
Nicholas is 12 years old and he has collected 459 trading cards. Phillip is 14 years old and he has collected 721 trading cards. How many more cards does Phillip have than Nicholas?
Phillip has _____
more cards than Nicholas.
Answer: Phillip has 262 more cards than Nicholas
Step-by-step explanation:
Since we are looking for how many more cards Phillip has compared to Nicholas we can subtract Nicholas' amount from Phillip's amount to see how much more he has.
721-459=262
Taking a simple difference, we can see that Phillip has _262_
more cards than Nicholas.
How many more cards does Phillip have than Nicholas?To find this, we need to take the difference between the number of cards that Philip has and the number of cards that Nicholas has, so we just need to solve a subtraction:
Phillip's cards - Nicholas' cards
Where:
Phillip's cards = 721
Nicholas' cards = 459
Then the difference is:
721 - 459 = 262
So we can see that Phillip has 262 more cards than Nicholas.
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