How do you know if the inverse of a function is a function?.

Correct option is A, The foci of the hyperbola is (0,±√17).

A hyperbola is a plane curve that is produced by a point that is moving so that the difference between the distances from two fixed points is constant. It is created when a double right circular cone intersects with a plane that cuts through both ends of the cone.

The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.

Given the equation of hyperbola is [tex]\frac{y^2}{12} - \frac{x^2}{5} = 1[/tex]

In this equation,

a² = 12

b² = 5

Using the relation c² = a² + b²

c = √(12 + 5)

c = √ 17

As, the hyperbola is vertical,

The value of foci will be (0,±√17)

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The dividend is influenced by both the quotient and the divisor when the remainder is zero.

Any integer that divides a different number is the divisor. A factor, on the other hand, is a divisor that completely divides a number and leaves no remainder. Therefore, all factors are also divisors of a number. But not every divisor will also be a factor. The factors of 20 in the aforementioned case are 4 and 5.

We are left with a value after division if a number (dividend) cannot be divided entirely by another number (divisor). The term "remainder" refers to this amount.

When the remainder is zero, the dividend is affected by both the quotient and the divisor. When the remainder does not equal zero, neither the quotient nor the divisor are dividend factors.

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"Segment GT is congruent to segment PD on the number line." this statement is True.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

The number line is used to represent the coordinates G, T, Y, B, M, P, D, W.

The point of G is -10 and the point of T is -9.

To get the measurement subtract G from T -

= -9 - (-10)

= -9 + 10

= 1

The point of P is 5 and the point of D is 6.

To get the measurement subtract P from D -

= 6 - 5

= 1

The measurement of GT and PD both is 1.

Therefore, segment GD is congruent to segment PD on the number line.

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Answer:

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side.

Step-by-step explanation:

Answer:

200.96

Step-by-step explanation:

Pi(8 to the power of 2)

Answer:

Sum of Interior Angles = (8-2) * 180 = 1080 degrees

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

Step-by-step explanation:

The sum of the interior angles in a polygon can be found using the formula (n-2)*180, where n is the number of sides in the polygon.

In the case of an octagon (8 sides), the sum of the interior angles is (8-2)*180 = 1080 degrees.

The measure of the eighth interior angle can be found by subtracting the sum of the known interior angle measures from the total sum of the interior angles.

So,

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

In short,

Sum of Interior Angles = (8-2) * 180 = 1080 degrees

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

Answer:

25°

Step-by-step explanation:

Please see the attached document for how I set up this problem. I used the law/theorem of alternate interior angles to solve for the missing angle we're looking for, and knowing that a straight line will also have an angle measure of 180 degrees. We can also check the answer we arrive at by adding up all the angles that we have and seeing if they add up to 360 degrees, just as all the angles in a four-sided shape would.

The angle of KLM is 50 degrees. The opposite angle, MJK, is also 50 degrees. JKL and LMJ have the same angle of 130 degrees. When we add this together, we reach 360 degrees, letting us know our answer is correct.

Answer:the a would be 10

and the b would be 6

Step-by-step explanation:

Step-by-step explanation:

for questions about % always find out first what 100% or what 1% are.

everything else can be calculated out of these 2 numbers.

in our case here

100% = 389 ml

1% = 100%/100 = 389/100 = 3.89 ml

18.6% = 18.6×1% = 18.6 × 3.89 = 72.354 ml

so, there are 72.354 ml of acid in the solution.

FYI

as you can see, we can combine both steps into one and do any of the following

18.6% = 18.6 × 100%/100 = 18.6 × 389/100 =

= (18.6/100) × 389 = 0.186 × 389

Answer:

Because the plane is flying due east, it has to turn 90º to face south, before it turns the extra 35.31º to fly towards the airport. 90° + 35.31° = 125.31º It actually turns through the exterior angle of the triangle :

Step-by-step explanation:

hope this helps B)

Answer:

  55°

Step-by-step explanation:

You want to know the additional angle a plane must turn through to be going south after it took off going east, then turned right 35°.

The initial bearing angle was 90° (straight east). After turning right 35°, the airplane now has a heading of (90+35)° = 125°. To be going south (180°), the bearing must increase by ...

  180° -125° = 55°

The airplane will have to turn 55° more to be heading due south.

The volume and value of x is x>9.

Since x represents the width, it clearly must be greater than zero since a box must have each dimension be positive which makes the lower bound. The question is whether (17-2x) and (4-2x) represent the other 2 dimensions or not.

If so, then (4-2x) must also be greater than zero which makes the possible range of x as 0<x<1.5

If not, then in addition to the above range, values of x such that both 4-2x and 17-2 evaluate to negative still result in a positive volume.

Therefore, additional values of x are x>9.

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a)  Pam overtime wage for that week is 110.625

b) Pam works a basic week of 40 hours her basic wage is 150.

c)  Pam gross wage for that week during Christmas 114.375.

What is Basic wages?

An employee may not legally sell their labor for less than the minimum wage, which is the lowest compensation a business may pay their staff. By the turn of the 20th century, minimum wage laws were in place in the majority of nations.

What is Gross wages?

The total of the base salary, overtime compensation, commissions, bonuses, and other regular cash payments is referred to as the monthly gross wage. It does not include employer CPF contributions, bonuses, stock options, other lump sum payments, or payments-in-kind. It is prior to deducting employee CPF contributions and personal income tax.

Given that;

a)Calculation for  Pam overtime wage for that week ;

So, 25% of 3.75 = 0.9375

and add it to 3.75.

then 0.9375 + 3.75 = 4.6875

Since she worked 6 hours at that new wage,

then 6 x 4.6875 = 28.125

Now for 50% of 3.75 =1.875

and add it to 3.75

then  1.875 + 3.75 = 5.625

Since she worked 8 hours at that new wage,

then 8 x 5.625 = 45

She works double time, which means she receives two times her regular pay.

Since she worked five hours at the wage, double her basic wage by two and then by five.

then  2 x 3.75 x 5 = 37.5

So, Pam overtime wage for that week is ;

28.125 + 45 +  37.5 = 110.625

b) Pam works a basic week of 40 hours  her basic wage is ;

    40 x 3.75 = 150

c) Pam gross wage for that week during Christmas is ;

  total wages + overtime wages

⇒110.625 + 3.75 = 114.375

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The conjecture regarding a number and it's absolute value being always opposites is incorrect.

The counterexample is that the absolute value of any positive number is always the own number.

The absolute value of a number is the number without the signal, representing the difference between the number and zero.

For example:

|-2| = |2| = 0.

Hence the conjecture is false, as the absolute value of any positive number is always the own number.

The conjecture would be true if it stated this only for negative numbers, then the absolute value of a negative number is in fact always the opposite of the number.

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Answer:

1 kilogram

Step-by-step explanation:

The equation 3x - 5y = 12 could be used to represent the function y = f(x), which is NOT one-to-one.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given that function f(x) is not one-to-one

That means the given equation will have only one solution for the one value of x,

Since Quadratic equations have two values at the one value of x that means option a would not satisfy

option c also makes an exponential graph which means it also has more than one value at x

Since Option (b ) 3x - 5y = 12 has a linear function and linear functions do not have more than one value at a value of x

Therefore, the function y = f(x) is NOT one-to-one, the equation could represent f(x) as 3x - 5y = 12.

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Complex numbers are those whose representation is given by the notation a+ib, where a, b are real numbers and I is a made-up expressions called a "iota." I'm equal to (-1).

If complex numbers are required to answer an equation, it is considered complex. Complex numbers are made up of both imaginary and real parts. This is how it is stated: The letters A and B in the preceding equation both represent numerical values. A complex number is something like 4+3i.

In order to attain vague goals that cannot be met through conventional actions, complex issue solving is a collection of self-regulated psychological processes and activities. It takes a variety of tactics and inventive knowledge combinations.

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The value x = 0 is zero of function p(x) = x²

Consider given function  p(x) = x²

We know that from the definition of zeros of function, the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.

Here we need to check whether x = 0 is zero of function p(x)

If for x = 0, p(x) = 0 then x = 0 is zero of function p(x).

Substitute x = 0 in given function p(x)

⇒ p(x) = x²

⇒  p(0) = 0²

⇒ p(0) = 0

Thus x = 0 is a zero of given function.

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The complete question is:

Is x = 0 a zero of p(x)=x² ?

No, 36 is not a prime number. Because the number 36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, 36.  

A prime number is a natural number more than 1 that has no positive divisors aside from 1 and itself. Prime numbers have several important properties and applications in mathematics, such as the fundamental theorem of arithmetic, which states that every positive integer can be written as a unique product of primes. They are also used in number theory, cryptography, and coding theory.

In addition, prime numbers are of interest in studying patterns and properties in the distribution of numbers, such as the distribution of twin primes and Mersenne primes. They play a crucial role in number theory, which is a branch of mathematics that studies the properties of integers. Prime numbers are infinite in number, and it is an open question whether there are infinitely many prime pairs or twin primes, which are pairs of prime numbers that differ by 2.

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The probability of forgetting iClicker device in each class = 1/4 = 0.25 = p

The probability of remembering iClicker device in each class = 1-p = 0.75

(a) Given that she is sure she has the iClicker device after leaving the first class.

The probability that she left it in second class = 1(0.25) = 0.25

The probability that she left it in third class = 1(0.75)(0.25) = 0.1875

The probability that she left it in fourth class = 1(0.75)(0.75)(0.25) = 0.1406

The probability that she left it in fifth class = 1(0.75)(0.75)(0.75)(0.25) = 0.1055

The total probability that she left iClicker given that she is sure she has the iClicker device after leaving the first class is:

0.25 + 0.1875 + 0.1406 + 0.1055 = 0.6836

Given that she is sure she has the iClicker device after leaving the first class, the probability that she left it in the 5th class is:

0.1055/0.6836 = 0.154

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The inverse of 8 is 1/8.

The multiplicative inverse of a number for any n is simply 1/n. It is denoted as:

1/x (or) x⁻¹

It is also called the reciprocal of a number and 1 is called the multiplicative identity.

The reciprocal of a number obtained is such that when it is multiplied by the original number, the value equals identity 1.

There are a few steps to find the inverse of a number:

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The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.

A. Let "r" be the number of state representatives and "s" be the number of state senators. We know from the problem that:

r + s = 181 (the sum of the number of representatives and senators is 181)

r - s = 119 (the difference of the number of representatives and senators is 119)

So the system of equations is:

r + s = 181

r - s = 119

B. To solve this system of equations, you can use the first equation to solve for one of the variables in terms of the other. Let's solve for "r" in terms of "s":

r = 181 - s

Now we can substitute this expression for "r" into the second equation:

(181 - s) - s = 119

Simplifying, we get:

181 - 2s = 119

2s = 62

s = 31

So there are 31 state senators in the Texas State Legislature. To find the number of representatives, we can use the first equation and substitute in the value of "s" that we just found:

r + 31 = 181

r = 150

So there are 150 state representatives in the Texas State Legislature.

Therefore, The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.

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The equation A = 2x²y + 4x²y² is a polynomial

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2x²y + 4x²y²   be equation (1)

On simplifying the equation , we get

A = 2xy ( x + 2xy )

Now , it is a mathematical expression with variables and coefficients

Hence , the equation A = 2x²y + 4x²y² is a polynomial

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Answer:

Choose whichever format you want to give the answer

[tex]\boxed{\dfrac{2}{9} \textrm{ hour}}[/tex]

[tex]\boxed{0.2222 \textrm{ hour}}[/tex]

[tex]\boxed{13.3333 \textrm{ minutes}}[/tex]

Step-by-step explanation:

[tex]\sf{Travel\: time = \dfrac{Distance}{Speed}}[/tex]

The time taken to travel the first 600 km

[tex]= \dfrac{600}{90} = \dfrac{20}{3}\; \sf{hours}[/tex]

This leaves 200 km which was travelled at a speed of 100 km/hr

Time taken for this stretch = 200/100 = 2 hours

If the entire trip were driven at 90 km/h, it would take the same time as the first case. Therefore we only need to be concerned about the last 200km

If the last 200km were traveled at 90 km/h instead of 100 km/h, time taken

[tex]=\dfrac{200}{90} = \dfrac{20}{9}\\\\[/tex]

The difference in time then would be:
[tex]=\dfrac{20}{9} - 2\\\\\\= \dfrac{20}{9} - \dfrac{18}{9}\\\\=\dfrac{2}{9}\; hour[/tex]

= 0.22 hour in decimal

= 13.33 minutes

Adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

Let the fractions be 1/8 and 1/12

8 = 2 × 4

12 = 3 × 4

By using LCM, we get

[tex]$2 \times 3 \times 4=24 \quad\{L C M\}$[/tex]

= 1/8 + 1/12

simplifying the equation, we get

[tex]$=\frac{1 \times 3}{8 \times 3}+\frac{1 \times 2}{12 \times 2}$[/tex]

= 3/24 + 2/24

= 5/24

Therefore, adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.

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The set of potential output values of a function is often referenced by the range () function.

A built-in Python function called range() can be used to produce a series of numbers. The range() function's parameters can be supplied by the user if they want to generate a series of numbers given the starting and ending values.

It can be used to generate a list of numbers or to iterate over a series of numbers in for loops.

For example, range(5) will generate a sequence of numbers from 0 to 4, and range(2, 5) will generate a sequence of numbers from 2 to 4.

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The perimeter of your new patio is 52.

Given that,

In order to match the shape of your backyard, your family has decided to build a rectangular patio there. The dimensions of your backyard are 20 feet wide by 45 feet long. Your new patio measures 18 feet in length.

To find :  The perimeters of your backyard and of the patio.

The dimensions of the yard are length 45 and width 20.

The patio is going to have the same shape, only smaller.

The length of the patio is 18 feet.

The ratio of the length of the patio to the length of the yard is 18/45.

Since the patio and the yard are to have the same shape, then that same ratio of 18/45, applied to the width of 20, gives you a patio width of 18/45* 20 = 8

Therefore, The perimeter of your new patio is 2 * (18 + 8) = 2 * 26 = 52.

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Step 1: The greatest common factor (GCF) in this equation is x^3. So we can factor it out:

y = x^3(x - 343)

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Step 2: We can not take root of a³ and b as there is no square term in the equation.

Step 3:

a= x^3

b= - 343

Step 4: Plugging in a and b into the original equation, we get

y = x^3(x - 343)

This is the simplified form of the equation.

So, the equation is a polynomial equation of degree 4, with the leading coefficient a = x^3 and the constant term b = -343, and it can be written as y = a(x-b) which is y = x^3(x-343)

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Answer: 7 seats in each row.

Step-by-step explanation:

14 / 2 = 7 seats in each row.

The number of regular sodas served is 12.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.

Number of regular sodas served = percentage of regular sodas served x number of sodas served

= 25% x 48

= 25/100 x 48 = 12

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