The inverse of a function is its opposite
The values of the unknown are: b = 1, c = 81 and d = 9
The function is given as:
[tex]y = x^2 - 18x[/tex]
Rewrite the equation in vertex form as:
[tex]y = (x - 9)^2 - 81[/tex]
Swap the positions of x and y
[tex]x = (y - 9)^2 - 81[/tex]
Add 81 to both sides
[tex](y - 9)^2 = x + 81[/tex]
take the square roots of both sides
[tex]y - 9 = \pm\sqrt{x + 81}[/tex]
Add 9 to both sides
[tex]y = \pm\sqrt{x + 81} + 9[/tex]
By comparison, the values of the unknown are:
b = 1, c = 81 and d = 9
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Find the value of each expression. Show your work.
18.) ₉P₃
Answer:
The value of the expression is 504.
Step-by-step explanation:
We are given the expression [tex]9P3[/tex].
Now, [tex]9P3[/tex] represents the permutations of 9 objects which are taken 3 at a time.
Also, its value is given by,
[tex]9P3=\dfrac{9!}{(9-3)!}\\\\9P3=\dfrac{9!}{6!}[/tex],
where ! represents the factorial given by,
[tex]n!=n(n-1)(n-2)...3.2.1[/tex]
Thus, evaluating the expression, we get,
[tex]9P3=\dfrac{9!}{6!}\\\\9P3=\dfrac{9\times 8\times 7\times 6!}{6!}\\\\9P3=9\times 8\times 7\\\\9P3=504[/tex]
Thus, the value of the expression is 504.Gaff has used 331/3 of his monthly minutes on his cell phone plan. If he already used 200 mintues, how many does he have left this month?
The first step to solve this problem is to compute for the total minutes allowable in his cell phone plan. To compute for this, you have to divide the number of minutes consumed by the fraction of the time consumed.
200 minutes / 33 1/3% = 600 minutes
To compute for the remaining minutes left for this month, you have to deduct the consumed minutes to the total allowable minutes in his plan.
600 minutes – 200 minutes = 400 minutes left
Write the first four terms in the multiplication pattern given by the formula 10*5n
(The n is exponent)
There are 84 students in the glee club there are 12 more boys than girls what is the ratio of the number of girls to the number of boys
How many MP3 players in the shipment would you predict to be damaged if 6 MP3s in the sample had been damaged
Quick help!! If you not sure of the answer PLEASE DON'T COMMENT
Which transformation gives the same result as a reflection over the y-axis followed by a reflection over the x-axis?
a.A rotation of 180° around the origin
b.A rotation of 270° around the origin
c.A translation to the left and then down
d.A rotation of 90° around the origin
Answer:
a. A rotation of 180° around the origin.
Step-by-step explanation:
A rotation of 180° around the origin would give us the same result as a reflection over the y-axis followed by a reflection over the x-axis. When we perform this rotation, we take each of its points through the transformation (x,y) ---> (-x, -y). This means that we would multiply the coordinates of each of the points on the shape by a negative. This is equivalent to reflecting a shape over the x-axis and the y-axis.
The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56 cm. Find the lengths of the sides of the rectangle.
Answer:
length is 18 and width is 10
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A stadium has a total of 18000 seats. Of these 7500 are field seats and the rest are grandstand seats. Write an equation that can be used to find the number of standsteats s
How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50-foot radius?
A circular garden with a 50-foot radius needs 628 flowers spaced every 6 inches.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that, flowers are spaced every 6 inches, are needed to surround a circular garden with a 50-foot radius.
As we know that, their is 12 inches in 1 foot.
1 foot = 12 inches
50 foot = 50 × 12 inches
50 foot = 600 inches
Circumfereeence of circle is obtained as,
C= 2πr
C=2×3.14×600
C=3768
If the floweres are spaced flowers, spaced every 6 inches, the number of are needed to surround a circular garden with a 50-foot radius,
n = C / 6
n=3768 / 6
n=628
Thus, a circular garden with a 50-foot radius needs 628 flowers spaced every 6 inches.
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Nancy builds a hollow wooden ramp for an obstacle course as part of an athletic event. The ramp and the net of the ramp are shown below. Units are in feet. The surface area of the ramp is square feet. Nancy wants to sell the wooden ramp at a price based on the surface area. If each square foot of wood of the ramp is sold for $3, the ramp would sell for $.
Nancy can sell the wooden ramp for $486 based on the surface area.
What is Area of Rectangle?The area of Rectangle is length times of width.
The area of each rectangular face is length times width, so the top and bottom faces have an area of:
2 x (8 feet x 3 feet) = 48 square feet
The side faces also have an area of:
2 x (8 feet x 6 feet) = 96 square feet
The area of each triangular face is one-half the product of the base and the height, so the front and back faces have an area of:
2 x (0.5 x 3 feet x 6 feet) = 18 square feet
The total surface area of the ramp is the sum of the areas of all the faces:
48 + 96 + 18 = 162 square feet
If each square foot of wood of the ramp is sold for $3, then the ramp would sell for:
162 square feet x $3/square foot = $486
Therefore, Nancy can sell the wooden ramp for $486 based on the surface area.
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check all that apply
Brian is playing a video game. He earns the same number of points for each star he picks up. He earns 2400 points for 6 stars, 4000 points for 10 stars, and 5,200 points for 13 stars. What is the independent and dependent value?
The equation of the circle whose center is at (3, 7) and whose radius is 6 is a. (x + 3)² + (y + 7)² = 6 b. (x + 3)² + (y + 7)² = 36 c. (x - 3)² + (y - 7)² = 36
Simlify the sum 4/m+9 + 5/m^2-81
What is one way to determine if a quadrilateral has parallel sides
A line has the following vector equation.
[x, y] = [2, -3] + t[5, 1]
a) State the coordinates of three other points on the line. Can you show your work please.
b) Write another vector equation of this line.
An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. find the dimensions of such a box if the amount of material used in its construction is to be minimal. hint: let the dimensions of the box be x in. by y in. by z in. then, xyz = 108 and the amount of material used is given by
Given that the volume of a rectangular box is a product of its length, breadth, and height, we define our problem using the given volume of 108 cubic inches and the formula for the surface area of an open box. To find the dimensions that will use minimal material requires the application of calculus and optimization techniques.
Explanation:In this problem, we know that the volume of the open rectangular box is 108 cubic inches. The volume of a rectangular box can be calculated with the formula V = xyz where x, y, and z are the length, width, and height. If we let the dimensions of the box be x, y, and z inches respectively, it means that the volume V = 108 = x*y*z.
The amount of material used or the surface area S of an open box (a rectangular box without a top) is given by the formula S = xy + 2xz + 2yz. Here, our task is to minimize this surface area.
To minimize the surface area, we need to employ calculus, specifically the concept of optimal control. However to apply calculus, we need to express S in terms of one variable. We can get this by expressing y in terms of x and z using the volume formula. This leads to a complex optimization problem that involves calculus.
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Write an absolute value equation that has the solutions x=23
One side of a regular hexagon is 4 cm. What is the length of one other side?
a. 4 cm
b. 5 cm
c. 6 cm
d. can't be determined.
Answer:
Your Answer is 4 CM
Step-by-step explanation:
the length of a rectanglr exceeds its width by 5 inches, and the area is 84 square inches. what are the length and width of a a rectangle
The area is the product of length and width, which is to say that the length and width are factors of the area.
Assuming the dimensions are integers, you want factors of 84 that differ by 5.
... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12
The last of these pairs differ by 5, so ...
the length is 12 inchesthe width is 7 inches.Answer:
The answer is l=12, w=7
Step-by-step explanation:
Maya's penny bank is 3/10
full. After she adds 520
pennies, it is
4/5 full. How many pennies can Maya's bank hold?
Maya's bank can hold 1733 pennies.
Explanation:To find out how many pennies Maya's bank can hold, we can set up an equation using the given information. Let's start with the fact that Maya's bank is 3/10 full before adding 520 pennies. This means that 3/10 of the bank's capacity is equal to 520 pennies. We can use this information to find the total capacity of the bank.
Since 3/10 of the bank's capacity is equal to 520 pennies, we can set up the equation (3/10)x = 520, where x represents the total capacity of the bank in pennies.
To solve for x, we can multiply both sides of the equation by 10/3 to cancel out the fraction. This gives us x = (10/3) * 520 = 1733.33. Since we cannot have a fraction of a penny, we round down to the nearest whole number. Therefore, Maya's bank can hold 1733 pennies.
A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.
What is the experimental probability of the arrow stopping over Section 1?
Section 1 Section 2 Section 3
28 36 16
Answer: [tex]\frac{7}{20}[/tex]
Step-by-step explanation:
From the given table, The number of times arrow comes results in section 1= 28
The total number of times spinner spins =80
Now, the experimental probability of the arrow stopping over Section 1 is given by:-
[tex]\text{P(Section 1)}=\frac{28}{80}=\frac{7}{20}[/tex]
Hence, the experimental probability of the arrow stopping over Section 1 is [tex]\frac{7}{20}[/tex]
divide 56 in the ratio 5 3
Jalla's hourly wage is $11.791. Round her salary to the nearest cent
Jalla's hourly wage, when rounded to the nearest cent, is $11.79.
Explanation:To round Jalla's wage to the nearest cent, we must look at the numbers following the decimal. In this case, Jalla's hourly wage is $11.791. Decimal rounding rules tell us that if the number following the decimal is equal to 5 or more, round up; otherwise, round down. In this case, the number after the decimal is 9, more than 5, so we round the second decimal place up. Therefore, rounding to the nearest cent, Jalla earns $11.79 per hour, her rounded wage.
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Mario was given some birthday money. He puts the money in an account. Every month after that, he deposits the same amount of money.The equation that models this situation is y = 75x + 50, where y is the amount of money in the account and x is the number of deposits.What does the y-intercept mean in this situation? A. He puts $75 in the account each month. B. He puts $50 in the account each month. C. He was given $75 for his birthday. D. He was given $50 for his birthday.
The y intercept in the equation y=75x+50 shows that he was given $50 for his birthday which is option D.
What is equation?Equation is like a relationship between two variables in equal to form which is simplified in order to get the value of both variables.
How to evaluate an equation?The given equation is y=75x+50 where y is the amount of money in the account and x is the number of deposits. Put the value of x=0 and we get y=50 means when deposit is 0 means no deposits then the amount of money in account is equal to 50 which concludes that Mario was given 50 on his birthday.
Hence y intercept in the equation y=75x+50 shows that he was given $50 for his birthday.
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Brayden is simplifying the expression 4n – (n – 3)2. He begins by distributing the negative to the terms inside the parentheses. What should he have done instead? combine like terms square the binomial cube the binomial rewrite the expression as a fraction
The correct step is to square the binomial (n - 3)² before combining like n terms.
Brayden is working on simplifying the expression 4n – (n - 3)². The correct initial step is not to distribute the negative inside the parentheses, but rather to square the binomial. This involves applying the binomial square formula [tex](a - b)^2 = a^2 - 2ab + b^2[/tex], to the expression inside the parentheses. Therefore, simplification should start with (n - 3)² resulting in [tex]n^2 - 6n + 9[/tex]. After this, Brayden should combine like n terms by adding or subtracting them to simplify the expression further.
You roll a single die numbered from 1 to 6. What is the probability of rolling a number greater than 3 and then a number less than 3?