Which equation is the inverse of y = 9x^2 - 4?

Answers

Answer 1

keep in mind that, to get the inverse expression of any relation, we start off by doing a quick switcharoo on the variables, and then solve for "y", so let's do so,

[tex]\bf y=9x^2-4\qquad \stackrel{inverse}{\boxed{x}=9\boxed{y}^2-4}\implies x+4=9y^2 \\\\\\ \cfrac{x+4}{9}=y^2\implies \sqrt{\cfrac{x+4}{9}}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer 2

Final answer:

The inverse of

[tex]y = 9x^2 - 4[/tex]

can be mathematically given by y = +/- sqrt((x + 4) / 9), yet it is not considered a function because it does not pass the horizontal line test.

Explanation:

The inverse of a function flips the x and y values such that each x becomes a y and vice versa. However, it's important to mention that not all functions have an inverse that is also a function. Your provided function,

[tex]y = 9x^2 - 4[/tex]

, is a quadratic function (a type of polynomial function), and it does not have an inverse that can also be called a function because it does not pass the horizontal line test.

Yet, mathematically it can be found by swapping x and y and solving for y. If we do that, we have:

Switch the roles of y and x, we get: x = [tex]9y^2 - 4[/tex].Solving for y, we have: y = +/- sqrt((x + 4) / 9), where "sqrt" denotes the square root.

Again, this is not a function due to the presence of the plus/minus symbol.

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Related Questions

11x−6y=5 −4x−6y=13 How many solutions does this system have

Answers

x=1.2 therefore the system only has ONE solution.

tickets to a play cost $11 each. There is also a service charge of $4 per order. Write ab equation for the relationship that gives the total cost y in dollars for an order of x tickets.

Answers

y=11x+4. formula: y=mx+b. insert the number of tickets where x is times 11 then add 4 to your total

Final answer:

The equation representing the total cost of an order of tickets is y = 11x + 4, where y is the total cost and x is the number of tickets.

Explanation:

The problem involves a constant service charge and a variable cost that depends on the number of tickets bought. In this case, the constant cost is the $4 service fee and the variable cost is the $11 per ticket. We express this relationship with the equation y = 11x + 4, where y is the total cost and x is the number of tickets purchased.

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20 POINTS!!! Of 35 jewelers in her town, Naomi polled the 5 biggest to learn about the latest jewelery trends. Her sample is (biased; Not biased).The sample is (representative; not representative) PLZ ANSWER IN THAT ORDER!! I NEED THIS ASAP

Answers

Answer:

Biased / Not Representative

Step-by-step explanation:

The answer is biased because she is asking only the 5 biggest jewelers in her whole town, not the whole 35. It is also not representative because it is not representing allts of of the though every jeweler. Hope this helps <3

PS. Brainliest is wrong.

Answer:

I hope this helps

Step-by-step explanation:

In certain county, the number of charter schools is 4vless than twice the numbervof alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?

Answers

Let us assume that the number of alternative schools in the county are x in number.

It is given that the number of charter schools is 4 less than twice the number of alternative schools. So we can write, the number of charter schools is 4 less than twice of x. In equation form this can be written as:

Number of Charter Schools = 2x - 4

It is given that number of charter schools is 48. So we can write:

48 = 2x - 4
2x = 52
x = 26

x was the number of alternative schools. Therefore, there are 26 alternative schools in the county.

1. Let's call the number of carter school: "x" and "y" the number of alternative school. Then, you have that:
- The number of charter schools is 4 less than twice the number of alternative schools.
- There are 48 charter schools in the country.
2. So, you have:
x=2y-4 (i)
x=48 (ii)
3. Then, when you substitute x=48 into the equation (i), you obtain:
x=2y-4
48=2y-4
4. Now, you must clear "y, as below:
48+4=2y
2y=52
y=52/2
y=26

How many alternative schools are in the county? The answer is: There are 26 alternative schools.

what are the slope and why intercept shown on the graph below

Answers

Hello!

Let's start by finding the slope of the line. You can calculate the slope by dividing the change in y-values by the change in x-values using the following formula:

[tex] \frac{ y_{1}- y_{2} }{ x_{1} - x_{2} } [/tex]

The plotted coordinates are (0, 5) and (4, -5); let's plug those into the formula:

[tex] \frac{5(-5)}{0-4} [/tex]

Simplify:

[tex] \frac{5+5}{-4} [/tex]

[tex] \frac{10}{-4} [/tex]

[tex] \frac{-5}{2} [/tex]

The slope is [tex] \frac{-5}{2} [/tex].

Now, the y-intercept is where the line intersects the y-axis, or when x equals 0. x equals 0 when y equals 5, so the y-intercept is 5.

I hope this helps!

Hi there! The formula for finding the slope is y2 - y1/ x2 - x1, where the first x and y-coordinates are subtracted from the second x and y-coordinates. We have the two points on the graph marked. We will use (0, 5) and (4, -5) in this case. Here are the numbers that represent each:

y2 = -5
y1 = 5
x2 = 4
x1 = 0

Let's subtract. -5 - 5 is -10. 4 - 0 is 4. -10/4 is -2 1/2 in simplest form or -5/2 as a mixed number. We found the slope. The y-intercept is where the line crosses, where the x-axis is 0. In this case, we can see by the point given out that the slope intercept is 5. There. The slope is -5/2 and the slope-intercept is 5. The answer is B.

mrs. west is 14 years younger than her aunt. if mrs. west’s age in years is as much below 60 as her aunt’s age is over 40, how old is each?

Answers

Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.

Let's represent Mrs. West's age as W and her aunt's age as A.

Given that Mrs. West is [tex]14[/tex] years younger than her aunt, we can write the equation:

[tex]W=A-14[/tex]

Also, it's given that Mrs. West's age is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex] . This can be represented as:

[tex]W=60-(A-40)[/tex]

Simplify the equation:

[tex]W=60-A+40\\W=100-A[/tex]

Now, we have two equations for [tex]W[/tex]:

[tex]W=A-14\\W=100-A[/tex]

Since both equations equal [tex]W[/tex], we can set them equal to each other:

[tex]A-14=100-A[/tex]

Now, solve for A:

[tex]A+A=100+14\\2A=114\\A=57[/tex]

Now, plug the value of [tex]A[/tex] into either equation to find [tex]W[/tex]:

[tex]W=57-14\\W=43[/tex]

So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.

COMPLETE QUESTION:

Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], how old is each?

Solve this problem using the proper formula

A gardener is installing a circular garden. The circumference of the circle 132 feet. What radius should he use to layout the circle if he uses p=22/7?

The radius is feet.

Answers

C = 2πr
132 ft = 2(22/7)r
r = (132 ft)*7/44 = 21 ft

The radius is 21 feet.

Given that the garden should be in a circular shape.

And the circumference of the circle would be, C = 132 feet.

It says to find the radius of the circular garden, r = ?

We know the formula for Circumference of the circle is given as follows :-

Circumference of circle = 2π x radius

C = 2·π·r

Hint:- It says to use pi = 22/7.

[tex] 132=2*\frac{22}{7}*r \\\\
132=\frac{44}{7}*r \\\\
r=132*\frac{7}{44} \\\\
r= \frac{924}{44} \\\\
r= 21 \;feet [/tex]

Hence, Radius would be r = 21 feet.

The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle? 5, 10, or 25?

Answers

You know the hypotenuse of a right triangle with sides 3 and 4 has length 5, so the radius of this circle will be 5. The diameter is twice that.

The diameter of the circle is 10.

tossing a number cube numbered from 1 to 6 and getting an odd number that is less than or equal to 3

Answers

1/3 bc only 1 and 3 are odd and less than/equal to 3, and there’s 6 total outcomes.

2/6=1/3

Since 3 is half of 6 and it is basically 50% or 1/2

solve for y
11x+7y=-35

Answers

Solve for y:
11 x + 7 y = -35

Subtract 11 x from both sides:
7 y = -11 x - 35

Divide both sides by 7:

Answer: y = -(11 x)/7 - 5

At 7:45 a.m. Mike began walking to school. He arrived at his school at 8:20 a.m. How long did it take him to walk to school?
A. 15 minutes
B. 25 minutes
C. 35 minutes
D. 40 minutes
E. 65 minutes

Answers

c, 35. if you add 15 to 7:45 that’ll get you to 8, then you just add 20.

Hello there!

7:45+15=8:00 = 15:00 minutes so far.

8:00+20= 8:20= 20+15= 35.

Your correct answer would be (option c).

35 is your answer!

the average adult human has approximately 2.5 x 10 ^ 13 red blood cells + 7 x 10 ^ 9 white blood cells about how many times as great is the number of red blood cells than the number of white blood cells

Answers

To solve this problem, what we must do is use the following equation:
N = (red blood cells) / (white blood cells)
Substituting values we have:
N = (2.5 * 10 ^ 13) / (7 * 10 ^ 9)
N = 3571.428571
Nearest whole number:
N = 3571
Answer:
The number of red blood cells is 3571 as great as the number of white blood cells

Jim Abbott purchased a $60,000 recreational vehicle (RV) with a 40 percent markup on selling price. a. What was the amount of the dealer’s markup? Markup amount $ b. What was the dealer’s original cost? Original cost $

Answers

$42,857.14

Hope this helped!

Answer:

24,000 dealer paid

mark up : 36,000

Step-by-step explanation:

60,000 * 0.40= 24,000

60,000-24,000= 36000

What is the y-intercept of the line that has a slope of -1/2 and passes through the point (2, 3)?

Answers

y - 3 = -1/2(x - 2)
y - 3 = -1/2(x) + 1
y = -1/2(x) + 4

y intercept is 4

answer
y intercept (0,4)

Indicate whether each of the following fractions is proper or improper. a. 4⁄16 b. 75⁄70 c. 2⁄15 d. 6⁄6

Answers

75/70 is an Improper Fraction

An proper fraction is a fraction where the denominator is larger than the numerator.
An improper fraction is a fraction where the numerator is larger than or equal to the denominator.

a. 4/16
The denominator is 16. The numerator is 4. The denominator is larger than the numerator; thus, this is a proper fraction.

b. 75/70
The denominator is 70. The numerator is 75. The numerator is larger than the denominator; thus, this is an improper fraction.

c. 2/15
The denominator is 15. The numerator is 2. The denominator is larger than the numerator; thus, this is a proper fraction.

d. 6/6
The denominator is 6. The numerator is 6. The numerator is equal to the denominator; thus, this is an improper fraction.

A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1/2 units.

How many 1/2 unit cubes does it take to fill the prism?

Answers

48. If the side length is 1/2, cube it to find the volume of the cube. Then divide 6 by 1/8. Remember that if you are dividing a fraction, you multiply by the reciprocal, in this case 8. 6 times 8 is 48.

Answer:

Step-by-step explanation:

Which function is the inverse of f(x)=4x-1?

Answers

The function f⁻¹(x) = x/4 + 1/4 is the inverse of f(x)=4x-1

What is a function?

The function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable). In maths and the physical sciences, functions are indispensable for formulating physical relationships.

The function is given as f(x)=4x-1

To determine the inverse of a function, switch the places of x and y (or f(x)).

f(x) = 4x - 1

y = 4x - 1

Switch the variables;

x = 4y - 1

Now, convert the equation back into y = mx + b form.

x + 1 = 4y

y = x/4 + 1/4

f⁻¹(x) = x/4 + 1/4

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solve the inequality -×/2 <4

Answers

Multiply by -2.
x > -8

_____
Multiplying or dividing by a negative number causes the direction of the relationship to change.

What is greater than 1 kg

Answers

2kg is greater than 1kg if thats what you're asking

a puppy weighs 9/10 pound. it's mother weighs 8 times as much. how much does the mother weigh?

Answers

the answer would be 72/10 or 7 2/10

The answer would be 7 2/10 or 72/10 or 7.2

which is smaller, half of 36 or one-seventh of 42

Answers

half of 36 = 36/2 = 18

one seventh of 42 = 42/7 = 6

one seventh of 42 is smaller than half of 36 by 12

hope this helps

Jalen plots two integers on a horizontal number line. The leftmost integer is negative. Which must be true of the second integer?
The second integer is negative.
The second integer is positive.
The second integer is greater than the first integer.
The second integer is less than the first integer.

Answers

The second integer is greater than the first integer

Answer:

c)The second integer is greater than the first integer

Step-by-step explanation:

In mathematics, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.

A number line can be extended infinitely in any direction and is usually represented horizontally, with 0 in the middle and negative numbers on the left and positive numbers to the right of zero.

Thus a number line can be used to represent both positive and negative rational numbers as well as integers.

The numbers to the left are less than that to the right

Hence here the option c) is right

Find all integer solutions to the pair of congruences (if any) x ≡ 17 (mod 23) 70x ≡ 3 (mod 93).

Answers

First, note that [tex]93=3\times31[/tex], which gives

[tex]70x\equiv3\pmod{93}\implies\begin{cases}70x\equiv3\equiv0\pmod3\\70x\equiv3\pmod{31}\end{cases}[/tex]

so in fact we're dealing with the system

[tex]\begin{cases}x\equiv17\pmod{23}\\70x\equiv0\pmod3\\70x\equiv3\pmod{31}\end{cases}[/tex]

Now, 3, 23, and 31 are relatively prime, so we can use the Chinese remainder theorem. But before we do that, we need to rework and ultimately eliminate the coefficients of [tex]x[/tex].

From the second equivalence, it follows immediately [tex]x[/tex] is some multiple of 3; this is because [tex]70x[/tex] is divisible by 3, but 3 doesn't divide 70, so it must divide [tex]x[/tex].

For the third equivalence, we can write [tex]70x=62x+8[/tex]. Then modulo 31, we have that [tex]62x\equiv0[/tex], which leaves us with [tex]8x\equiv3\pmod{31}[/tex]. We want a congruence of the form [tex]x\equiv\cdots[/tex], and to get that we can multiply [tex]8x[/tex] and 3 by the inverse of 8 modulo 31.

To find this inverse, we solve for [tex]y[/tex] in the relation

[tex]8y\equiv1\pmod{31}[/tex]

by using the Euclidean algorithm, or making just making the observation that [tex]8\times4\equiv32\equiv1\pmod{31}[/tex], so [tex]8^{-1}\equiv4\pmod{31}[/tex]. Distributing 4 across the third equivalence in our system gives [tex]x\equiv4\pmod{31}[/tex].

So to recap, we now have

[tex]\begin{cases}x\equiv17\pmod{23}\\x\equiv0\pmod3\\x\equiv12\pmod{31}\end{cases}[/tex]

and we're ready to use the CRT.

As a starting point, let's take

[tex]x=(17)+(23)+(23)=63[/tex]

It's clear that taken modulo 23, the latter two terms vanish and we have a remainder of 17, as desired. 63 is already a multiple of 3, but just to avoid doing more work later, let's multiply each term by 3 anyway to keep getting a remainder of 0:

[tex]x=(17\times3)+(23\times3)+(23\times3)=146[/tex]

Now multiply the first two terms by 31 to make sure they vanish when taken modulo 31. Meanwhile, [tex]23\times3\equiv69\equiv7\pmod{31}[/tex], but we want to get 12, so we would multiply this term by the inverse of 7 mod 31, and again by 12.

We can make a quick observation that [tex]7\times9=63=31\times2+1[/tex], so [tex]7^{-1}\equiv9\pmod{31}[/tex]. Alternatively, you can use the Euclidean algorithm to find this inverse. Either way, we get

[tex]x=(17\times3\times31)+(23\times3\times31)+(23\times3\times9\times12)=11,172[/tex]

So we're told that

[tex]x=11,172+(23\times3\times31)k=11,172+2139k[/tex]

is our solution set, where [tex]k\in\mathbb Z[/tex]. We can "simplify" this slightly by finding the least positive residue modulo the product of our moduli, which would be

[tex]11,172\equiv477\pmod{2139}[/tex]

so we end up with

[tex]x=477+2139k[/tex]

for integers [tex]k[/tex].

plz help ill give you brainlist plz help

Answers

The equation for the Area of a rectangle is
A = l * w
in this case A = 108 and w = 9

108 = 9l
l = 12 ft

If a number is located farther right on the number line than another, then it is larger. True False

Answers

True. When you go right, the number value increases so yes, it is larger

Answer:

it is TRUE my homei

Step-by-step explanation:

The dimensions of an office conference room are 10 feet by 18 feet. If the conference room blueprint dimensions are 5 centimeters by 9 centimeters, what is the scale of the blueprint?
A. 1 centimeter = 9 feet
B. 1 centimeter = 2 feet
C. 1 centimeter = 5 feet
D. 1 centimeter = 10 feet

Answers

1 centimeter = 2 feet

if 5 lemons cost £1 and a bag of 4 oranges cost £1.80, how much more does one orange cost than the lemon?

Answers

One orange costs 0.45 so a lemon costs 55 cents more than one orange

One lemon cost 20 cents and one orange cost 45 cents then 45-20 is 25 cents

Alex is decorating a large box with pieces of ribbon. He needs 7 sections of ribbon with a length of (3/4) yard. He is going to cut the 7 pieces from a roll of ribbon that is 30.2 yards long

Answers

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
SEE ATTACHED IMAGE.
For this case what you need to know is how much tape Alex needs.
We have then:
"He needs 7 sections of ribbon with a length of 3/4 yard"
In other words:
(7) * (3/4) = 5.25 yards.
Therefore, the amount of tape that will be left over will be:
30.2-5.25 = 24.95 yards.
Answer:
after Alex cuts the 7 pieces will remain 24.95 yards of ribbon

What is the value of log0.5^16? a.–4.00 b.–0.25 c.1.51 d.2.41

Answers

the answer for your question is a. -4

Answer:

The correct option is a.

Step-by-step explanation:

The given expression is,

[tex]log(0.5)^{16}[/tex]

Use property of logarithm

[tex]loga^b=bloga[/tex]

[tex]log(0.5)^{16}=16\times log(0.5)[/tex]

The value of log(0.5) is -0.30103.

[tex]log(0.5)^{16}=16\times -0.30103[/tex]

[tex]log(0.5)^{16}=-4.81648[/tex]

The value of given expression is -4.81648.

If the final answer appromatted to preceding integer, then the correct option is -4.00.

what is -10+2 because this is really confusing to me.

Answers

-8 hope this helps btw i am a pro at this kinda stuff lol have a nice day

If you need explaining think of it as....a number line. Zero is in the middle with negative numbers going down the left and positive numbers going down the right. Put a mark on -10 and move to the right 2 times. That would give you an answer of -8.

Hope this helps!
Let me know if i'm wrong.

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