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Consider the function y = x^2 − 18x. Enter the values for the variables to complete the inverse
Given the equation:
y = x^2 – 18x
Rewrite in vertex form:
y = x^2 – 18x + (18/2)^2 – (18/2)^2
y = (x – 9)^2 – 81
Swap x and y:
x = (y – 9)^2 – 81
Solve for y:
x + 81 = (y – 9)^2
y – 9 = sqrt (x + 81)
y = sqrt (x + 81) + 9
or
y = (x + 81)^(1/2) + 9
Why does dividing by a fraction make a number bigger?
A number dividing by a proper fraction always make the number bigger.
What is Fraction?Fractions are a kind of real numbers where we express a number as a part of a whole.
Fractions are of the form p/q, where p is called the numerator and q is called the denominator.
Algebraically speaking when a number is divided by a fraction, then actually the number is getting multiplied by it's reciprocal.
For example [tex]\frac{5}{1/2}[/tex] = 5 × [tex]\frac{2}{1}[/tex] = 10
That is a number when get divided by a proper fraction, operation is changed into the multiplication of the reciprocal.
In other words, we have to find that 5 is divided into how many equal 1/2
parts or 0.5 equal parts. Now, 1/2 part is actually the half part of 1.
Since 1/2 is half part of 1, 1 can be divided into 2 equal 1/2 parts.
We know that 5 when divided into equal 1 parts, we will get 5 parts.
So 5 can be divided into 5 × 2 = 10 equal 1/2 parts.
Hence, dividing by a fraction make a number bigger.
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y=9x+4 is translated 4 units , what would be the equation on a graph?
Consider the equation 2y−5x=30 . Determine the x-intercept
2 ⋅
−5x=30
−5x=30
=30
x=
The x-intercept for the equation 2y - 5x = 30 is found when y is set to zero and the equation is solved, resulting in the x-intercept being -6.
Explanation:To find the x-intercept of a given equation, you need to set y equal to zero and solve for x. So, for the equation 2y - 5x = 30, you set y = 0 which leads to the adjusted equation of -5x = 30
To isolate x, you should divide both sides of the equation by -5, which gives x = -6. Therefore, the x-intercept of the equation 2y - 5x = 30 is -6.
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Solve the following inequality.
-2/3x>8
A) x < - 4
B) x > - 4
C) x > -12
D) x < -12
She could tell of the Crows, who she had never seen, and of the Black Hills, where she had never been. I wanted to see in reality what she had seen more perfectly in the mind’s eye... Which tone is conveyed by the language in this excerpt? a sense of respect for Aho misgivings about the future spiritual longing for the past disinterest in the present
Answer:
A sense of respect for Aho.
Explanation:
In N. Scott Momaday's memoir "The Way To Rainy Mountain", he narrates how he embarked on rediscovering his Kiowa heritage and the importance of preserving one's cultural background. Momaday uses a semi- autobiographical form of writing in providing the history and migration of the Kiowa people from their initial residence in Montana to Oklahoma.
In the given passage, the narrator is talking about his grandmother Aho who perfectly remembers the "Crows, who gave them the culture and religion of the Plains". But she was never a part of those who traveled, but rather the stories told by her forefathers. Her ability to remember and preserve those memories as if she had personally experienced them impressed the narrator, who have a huge respect for her. Her memory of the "crows,.... and the Black Hills where she had never been" shows how she values the stories and tales of her own forefathers and the culture and heritage of the Kiowa people as a whole.
Michael and Jacob are standing on two docks that are 20 miles apart. They are watching a ship that is out in the ocean. The angle between the dock and the line connecting Michael and the ship is 48°, and the angle between the other dock and the line connecting Jacob and the ship is 37°.
If the ship can travel to either dock, which dock would be closest? Explain your answer.
A.) Michael’s dock would be closer because the angle opposite is smaller.
B.) Jacob’s dock would be closer because the angle opposite is smaller.
C.) Michael’s dock would be closer because the docks are 20 miles apart.
D.) Jacob’s dock would be closer because the docks are 20 miles apart.
Based on the basic principles of trigonometry, the ship would be closer to Jacob's dock because the dock's angle is smaller.
Explanation:The question is asking which dock, Michael's or Jacob's, would be closer to the ship based on angles given. In the world of mathematics and specifically trigonometry, larger angles in a triangle usually indicate longer sides opposite that angle. This is because the length of the side of a triangle is directly proportional to sine of its opposite angle.
In this case, the angle between the dock and the line connecting Michael and the ship is given as 48° which is larger than the angle for Jacob (37°). When applying the basic principles of trigonometry, this tells us that the distance from the ship to Michael's dock would be greater than the one to Jacob's. Therefore, the ship would be closer to Jacob's dock. So, the answer is B: Jacob's dock would be closer because the angle opposite is smaller.
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Which Greek mathematician wrote the most definitive text on geometry, one that is still referred to today?
a.Thales
b.Pythagoras
c.Euclid
d.Archimedes
e.Hippocrates
Answer:
The correct answer is Euclid.
Step-by-step explanation:
Euclid was a Greek mathematician, who is referred as the father of geometry and founder of geometry.
One of Euclid's most notable work, in the form of 'The Elements' has the strongest fundamental texts on geometry.
Apart from geometry, Euclid also developed many mathematical theories.
How much time will Alex need to walk to his school, which is 2 1 /4 miles away from his house, if he would walk with the speed of 3 3/4mph
Evi what to make to pottery she needs 3/5 pounds of clay for one piece and 7/10 Pound of clay for the other piece she has three bags of clay that wiegh 4/5 pound each.how many bags of clay will Eva need to make both pieces of pottery?How many pounds of clay will she have left over ?
The product of 3 and a number subtracted from 16 is 7. Find the number.
A spinner is numbered 1 through 5 is spun 3 times. What is the probability of spinning a number less than 3, then a number greater than 3, and then the number 3? Write your answer as a decimal. Do not round.
please help with math
One number is two less than three times another. if their sum is decreased by one, the result is nine. find the numbers.
steve saved $2000. he saved $100 in june. what percent of the total amount did her save in june?
What is the inverse of the following statement? If at first you don’t succeed, try, try again. Select the best answer from the choices provided. If you try, try again, then you did not succeed at first. If at first you succeed, then do not try, try again. If you don’t try, try again, then you succeeded at first. Try, try again if at first you don’t succeed. NextReset
Answer:
Try, Try again if at first you dont
exceed
Step-by-step explanation:
Can you find the missing angle measurements
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
Right triangle ABC is shown.
a to c is 3m
c to b is a
b to a is c and ab is 50 degrees
Which equation can be used to solve for c?
sin(50o) =
sin(50o) =
cos(50o) =
cos(50o) =
Answer:
The required equation which can be used to solve for the value of c is given by :
[tex]\bf\sin 50=\frac{3}{c}[/tex]
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
AC = 3 meter
CB = a meter
BA = c meter
m∠ABC = 50°
Now, to find the value of c.
In right angle triangle right angled at C, we need to find the length of hypotenuse, so using the sine rule in the ΔABC
[tex]\implies \sin\theta=\frac{Perpendicular}{Hypotenuse}\\\\\implies \sin 50=\frac{3}{c}[/tex]
Hence, the required equation which can be used to solve for the value of c is given by :
[tex]\bf\sin 50=\frac{3}{c}[/tex]
How do you write 7 to the fourth power in exponential form using exponents?
A large adult elephant weighs 24,000 pounds. A baby elephant, on the other hand, weighs only 260 pounds. How much more does the adult elephant weigh?
24,000 - 260 = 23,740
23,740 + 260 = 24,000
The adult elephant weighs 23,740 more pounds than the baby elephant.
8 cakes cost £4.00 how much do three cakes cost
What is the y-intercept of the line that has a slope of -1/2 and passes through the point (2, 3)?
y=-1/2x+
Dimitri is paid 8 percent commission on his total sales every pay period. Last pay period, he sold $6,300 worth of items. After a state tax of 6 percent is deducted from his commission, how much is left to the nearest dollar?
Answer:
$ 474 is left.
Step-by-step explanation:
Given,
The amount at which the items are sold = $ 6,300,
Also, commission percentage = 8 %,
Thus, commission = 8% of 6300
[tex]=\frac{8\times 6300}{100}[/tex]
[tex]=\frac{50400}{100}[/tex]
[tex]=\$ 504[/tex]
Now, deducted tax percentage on commission = 6%,
Hence, the left amount of commission = commission - 6% of the commission
[tex]=504-\frac{6\times 504}{100}[/tex]
[tex]=504-\frac{3024}{100}[/tex]
[tex]=504-30.24[/tex]
[tex]=\$ 473.76[/tex]
[tex]\approx \$ 474[/tex]
The volume of a box with a square base can be written as V = s² x h where V is the volume, s is one side of the square base, and h is the height. Find the volume of a rectangular prism where s = 6 cm and h = 9 cm.
A.108 cm³
B.54 cm³
C.486 cm³
D.324 cm³
In the game Kazoo, teams lose one point each time they skip a turn. They earn one point each time their team guesses correctly. Maria's team skipped 888 turns. They guessed correctly 666 times.
Which line has a slope of 2?
if y+1 is an even integer, what is the next consecutive even integer?
The next consecutive even integer will be y + 3
What is Arithmetic Progression?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.
The nth term of an AP is given be aₙ = a₁ + ( n - 1 ) d
where a₁ = first term
d = common difference between terms
Given data ,
y + 1 = even integer
The next consecutive even integer can be calculated by adding 2 because the difference between two consecutive even or odd integers is always two.
Therefore , y + 1 + 2 = y + 3
Hence , the next consecutive even integer will be y + 3
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ou are cycling around Europe with friends.
A famous cycling race is taking part in the north of Spain. You want to travel there from France, but it will take too long by bike. You decide to catch the train.
You need to take 2 trains to get to Spain. On one website the first train will cost £64.98 and the second train will cost £32.88. There is also a £6.99 charge for cycle storage for the whole trip.
How much would the journey cost you?