help im stuck on this

The solution is Option C.

The inverse of the function is f⁻¹ ( x ) = ( x + 5 )² and the domain is x ≥ 0

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is given as

f ( x ) = √x - 5   be equation (1)

On simplifying the equation , we get

y = √x - 5

To calculate the inverse of the function , solve for x , we get

Adding 5 on both sides of the equation , we get

√x = y + 5

Taking the square on both side of the equation , we get

x = ( y + 5 )²

Substitute the value of x = f⁻¹ ( x ) and y = x , we get

f⁻¹ ( x ) = ( x + 5 )²

And , the domain of the function is [ 0 , ∝ ]

Hence , the function is f⁻¹ ( x ) = ( x + 5 )²

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If you divide 63 by 3 you get 21.

If you divide 42 by 2 you get 21.

63 / 3 = 21

42 / 2 = 21

Therefore, the GCF(Greatest Common Factor)is 21.

Answer:

7^3

Step-by-step explanation:

since seven is being multiplied by itself 3 times, it is being cubed. So it needs to be raised to the third power.

hope this helps!!! :3

Answer: (-7)(-7)(-7) is equal to -7^3 (just imagine that the three is on the top right outer corner of the 7)

Step-by-step explanation:

A power is when you multiply a number by itself a certain number of times, in this case, we are multiplying the number 7 by itself 3 times. Every time it is multiplied by its self, the power of that number goes up (if you are using a power of one for any number, it will stay the same). Here is an example:

-7 to the first power is just -7.

-7 to the second power, or squared is just (-7)(-7) or (-7) x (-7).

-7 to the third power, or cubed, is just (-7)(-7)(-7) or (-7) x (-7) x (-7).

Hope this helps!!!

The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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Answer:

The answer is x = 2. To solve for x, divide both sides of the equation by 8 to get x = 16/8 = 2.

Step-by-step explanation:

Answer:

[tex]8x = 16 \\ x = 16 - 8 \\ x = 8[/tex]

The value of the expression 23.97 x √(0.7124) ÷ 3.877 x 52.18 is 0.1000069342.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

A phrase: 23.97xsquare root of 0.7124 divided by 3.877x52.18.

In numeric form,

23.97 x √(0.7124) ÷ 3.877 x 52.18.

= 0.1000069342.

Therefore, the value is 0.1000069342.

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Therefore , the solution of the given problem of compound statements comes out to be choice D is right.

Like in any language, connectives are used to combine simpler statements to create complex statements in mathematics. And, or, if... then, and if and only if are the connectives that are frequently employed in mathematics. The truth value of the a compound statement is determined by variable the truth values of its simpler parts.

Here,

Given :function

To discover the true values

Which compound statement,

if p →q  is true, will have the same truth value?

The formulation of the logic biconditional link

p ↔ q, which is "p → q and q → p," provides the direct connection to the solution.

As a result, choice D is right.

Therefore , the solution of the given problem of  compound  statements comes out to be choice D is right.

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Answer: The inverse of the function k(x)=x²-3 is k^(-1)(x)=±√(x+3). The domain restrictions for the inverse are x≥-3, since the square root is only defined for non-negative values.

The inverse of a function is the reflection of the original function over the line y=x. To find the inverse of k(x)=x²-3, we first swap the x and y variables: y=x²-3. Then, we solve for x: x=±√(y+3). This gives us the inverse function k^(-1)(x)=±√(x+3).

However, it is important to note that the square root function is only defined for non-negative values. Therefore, we must restrict the domain of the inverse function to x≥-3. This means that the inverse function can only be applied to input values that are greater than or equal to -3. For values less than -3, the inverse function is undefined.

Step-by-step explanation:

Answer:

Inverse function: [tex]\pm \sqrt{x + 3}[/tex]

Domain: [tex]x \ge -3[/tex]

Step-by-step explanation:

[tex]k(x) = x^2-3[/tex]

To find the inverse, set y = k(x)

==> y = x² - 3

Swap x and y

x = y² - 3

Add 3 to both sides
x + 3 = y²

y² = x + 3

[tex]y = \pm \sqrt{x + 3}[/tex]

or, in other words:

[tex]y = \sqrt{x +3} \:\;and\; y = -\sqrt{x + 3}[/tex] are the two solutions

Replace Swap x and y again to get the inverse as a function of x
[tex]k^{-1}(x) = \sqrt{x+3},\:-\sqrt{x+3}[/tex]

Since square roots of negative numbers are not defined, the term under the square root must be ≥ 0

x + 3 ≥ 0

==> x ≥ -3

There is no restriction on the upper bound it can go upto infinity

Domain of [tex]\sqrt{x + 3} : \:x\ge \:-3[/tex]

Given that point T is the center of dilation, we know that the length of line segments TX' and TY' are proportional to the length of line segments TX and TY, respectively.

We can express this as:

TX' = k * TX

TY' = k * TY

where k is the scale factor.

We are given the lengths of TX' and TY':

TX' = 6

TY' = 9

So, we can solve for k:

9 / k = 6

k = 9 / 6 = 3 / 2

Now that we know the value of k, we can find TY:

TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9

Next, we are given the length of XX':

XX' = 2

And using the dilation formula, we can find XX:

XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)

Finally, we can find TX by using the Pythagorean theorem:

TX^2 = TY^2 + XX^2

TX^2 = 9^2 + (2 * (2 / 3))^2

TX^2 = 81 + (4 / 3)^2

TX^2 = 81 + 16 / 9

TX^2 = 81 + 16 / 9

TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97

So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.

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TX' = k * TX

TY' = k * TY

TX' = 6

TY' = 9

So, we can solve for k:

9 / k = 6

k = 9 / 6 = 3 / 2

Now that we know the value of k, we can find TY:

TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9

XX' = 2

XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)

TX^2 = TY^2 + XX^2

TX^2 = 9^2 + (2 * (2 / 3))^2

TX^2 = 81 + (4 / 3)^2

TX^2 = 81 + 16 / 9

TX^2 = 81 + 16 / 9

TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97

So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.

Answer:

28

Step-by-step explanation:

The slope of a line represents the rate of change between two variables. In the case of Superior Segway Tours, the cost of the tour is changing as the number of hours for the tour changes. The rate of change can be calculated by dividing the change in the dependent variable (cost) by the change in the independent variable (hours). In this case, the slope is $28 per hour. This means that for every hour that is added to the tour, the cost will increase by $28.

The slope of this situation can be represented as the change in cost (y-axis) per unit change in time (x-axis). The slope in this case would be $28 per hour.

A perpendicular bisector is a line that intersects a given line segment at a 90°.

 A perpendicular bisector is a line segment, ray, or line that goes through the middle of a given line segment and crosses it at a 90° angle.

A line, ray, or line segment is a perpendicular bisector if it divides another line segment in half proportionately and makes a right angle (90o) with it at its halfway.

In other words, the perpendicular bisector serves as both a perpendicular line to the line segment and a bisector, cutting it in half.

The intersection of the perpendicular bisector with the line segment represents its midpoint.

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Answer:

E. - 11

Step-by-step explanation:

This is by the simple quantum physics moving by the gravitational carbon dioxide in the air that causes the numbers to evolve into the number 11 while mixed together

Answer:

15 percent

Step-by-step explanation:

There are total 40 students in class because 6 plus 12 plus 14 plus 20 is 40. Fraction would be 6/40

Using basic arithmetic operations, the missing terms are a)  7/5 and b) 19/14.

There are four basic arithmetic operations which are addition, subtraction, multiplication, and division. These operations can be applied to whole numbers and fractions.

a) 14/16  x  8/7= y x  5/7

In order to solve for y, the numerator and denominator on LHS are simplified and multiplied:

14/16  x  8/7=  7/8  x  8/7 = (7 x 8)/(8 x 7)

As there are same numbers in both numerator and denominator, they are cancelled:

(7 x 8)/(8 x 7)=1

Hence,

1= y x  5/7

Multiply both side by 7/5

7/5  x 1= y x  5/7  x  7/5

y=  7/5

b) 1/2+  4/7= y -2/7

In order to solve for y, add the fraction on LHS:

1/2+  4/7=  ((7 x 1)+(4 x 2))/((2 x 7)) = (7+8)/14=15/14

Hence,

15/14= y -2/7

Add 2/7 to both sides:

15/14+  2/7= y -2/7  +  2/7

y = (15+4)/14=19/14

Note: The question is incomplete. The complete question probably is:  Find the missing terms:

a) 14/16  x  8/7= y x  5/7

b) 1/2+  4/7= y -2/7

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Answer:

I don't know. I hope this helps!

Step-by-step explanation:

Answer:

Tuna sandwich to likely

chicken sandwich to unlikely

Egg sandwich to impossible

Step-by-step explanation:

there is a lot more tuna than chicken sandwiches so it's likely

there is no egg sandwiches so it's impossible

The area of the base of the pyramid is 35/4 m².

The volume of the pyramid is 14 m³.

A pyramid is a three-dimensional geometric shape that has a base and triangular sides that meet at a common point, called the apex.

The formula for the area of the base of the pyramid is given as:

A = 1/2 bh

where b and h are the base and height of the triangle at the base of the pyramid.

Given b = 7/3 meters and h = 15/2 meters

A = 1/2 * 7/3 * 15/2

A = 35/4 m²

That is B = 35/4 m²

The formula for the volume of the pyramid is given as:

V = 1/3 Bh

where h is the height of the pyramid and h = 24/5 meters

V = 1/3* 35/4 * 24/5

V = 14 m³

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Answer:

Step-by-step explanation:

-2/11

Answer:

-1/5 × 10/11 = -2/11

Step-by-step explanation:

If you multiply -1/5 by 10/11, it becomes the fraction -2/11 or 0.1818...

After maxing x as a subject the solution becomes: x = z³ + √d 3a. This can be solved using the concept of solving equation.

Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

For instance, two equations with the identical variables, x and y, are x + y = 12 and 2x + 5y = 8. They are an equalization system.

Given that,

[tex]\sqrt{d} =\frac{ x - z^3}{3a}[/tex]

or, x - z³ = √d 3a

or, x = z³ + √d 3a

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Answer:

Step-by-step explanation:

2

BECUASE YEA

Answer:

Step-by-step explanation:

h(x) = -x + 1

h(x) = 0

0 = -x + 1

-1 = -x

x = 1

The projection of vector v on u is =[tex]\=109/\sqrt{113}(2i+10j+3k)[/tex]

Sometimes the inner product and the dot product are considered to be the same. The formal definitions of projection and rejection employ the inner product rather than the dot product whenever they don't coincide. The concepts of projecting a vector onto another and rejecting a vector from another can be applied to the concepts of projecting a vector onto a plane and rejecting a vector from a plane for a three-dimensional inner product space.

A vector's orthogonal projection on a plane is the vector's projection on that plane. A vector is rejected from a plane when it is projected in an orthogonal direction on a straight line. They're both vectors. The first is orthogonal to the plane, while the second is parallel.

we have v=10i+8j+3k and u=2i+10j+3k,

[tex]The\ projection\ v\ on\ w= ((v.u)/|u|)u\\\\the \proj=((20+80+9)/\sqrt{4+100+9})(2i+10j+3k)\\\\=109/\sqrt{113}(2i+10j+3k)[/tex]

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Answer: 324/4

Step-by-step explanation:

I know i'm doing this totally wrong I don't know.

People who dislike cantaloupe are marginally more likely to be (0.455) likely to be.

The joint relative frequencies in a row or column of a data table are added in this case.

Therefore, we will create a representation of the table using the findings from the survey of 200 randomly selected individuals as follows:

Watermelon The total is not a watermelon

Cantaloupes: 93, 16, and 109

Not a cantaloupe 66 25 91

Total 159 41 200

The marginal relative frequency for those who dislike cantaloupe is therefore 0.455.

The complete complete question is,

How common are those who dislike cantaloupe, on a relative basis? startfraction 91 over 200 endfraction startfraction 25 over 91 endfraction startfraction 66 over 200 endfraction startfraction 91 over 200 endfraction.

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Answer: y = 5x + 70

Step-by-step explanation:

The table which represents a linear relationship that is also proportional is table 1.

There is a linear relationship between y and x when the rate of change of y with respect to x will be equal.

Table 1:

xy

00

42

84

When x = 4

y = kx

2 = k×4

2 = 4k

k = 2/4

k = 0.5

y = kx

y = 0.5x

when x = 8

y = 0.5(8)

y = 4

Table 2:

xy

01

23

45

y = kx

when x = 2

3 = k × 2

3 = 2k

k = 3/2

k = 1.5

when x = 4

y = 1.5x

y = 1.5(4)

y = 6

Therefore, table 1 is proportional and represents a linear relationship with the equation y = 0.5x.

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Answer:

79.4cm

Step-by-step explanation:

1cm = 10mm so 794mm / 10mm = 79.4cm

On a principal of $100,000.00 with compound interest accrued at a rate of 7% per year compounded continuously over 4 years, the total sum is $132,312.98.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given,  You have an inheritance of $100,000 from your grandparents, you must invest the money in a mutual fund until you are 21 years old, which will pay an annual interest rate of r% compounded continuously.

From the general formula of compound interest:

A = Pe^rt,

where P is the principal balance,

r is the interest rate,

n is the number of times interest is compounded annually,

t is the number of years

In our case,

P = 100,000

t = 21 - 17 = 4

n = 12 for compounded continuously

thus,

A = 100,000(2.71828)^r4

For the value of r = 7

A = 100,000.00(2.71828)^(0.07)(4)

A = $132,312.98

Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $100,000.00 at a rate of 7% per year compounded continuously over 4 years is $132,312.98.

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In a triangle ABC, angle B=90, angle C=60, angle A=30 and BC=12cm. The area of the triangle is 144 * (√3/2) sq cm

In a right triangle with a 90 degree angle, the length of the side opposite the 90 degree angle is the height, and the length of the other two sides form the base. If angle C = 60 degrees, then angle A = 90 - 60 = 30 degrees.

If BC = 12 cm, then the height AC is equal to AB * sin(30) = 12 * (√3/2).

The area of the triangle is equal to (1/2) * base * height = (1/2) * 12 * (12 * (√3/2)) = (12 * 12 * (√3/2))/2 = 144 * (√3/2) sq cm

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The complete question goes thus:

In a triangle ABC, angle B=90, angle C=60, angle A=30 and BC=12cm. What is the area of the triangle?

Jingle cites a situation in real life -Men make up about 95% of those detained by the police.

99 percent of bricklayers are men.

Men make up 99 percent of soldiers' fatalities.

When you want to know something, it is often apparent and overwhelming. But it's rarely brought up since "women" simply don't engage in those kinds of behaviors. Voluntarily.

Jordan Petersen uses these examples frequently to silence liberals who support equality of all kinds because they don't want to talk about how the equality they claim to want would actually be totalitarian and authoritarian.

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Assuming that interest for a given month is based on the balance for the previous month, it will take 6 months to pay off the credit card debt of $1,200 when making a net payment of $225.

An online finance calculator can determine the period for a compound interest system.

The length of payment uses the beginning credit card balance of $1,200 and the net payment of $225 (since a monthly payment of $300 is made when an additional charge of $75 is withdrawn from the card).

I/Y (Interest per year) = 18%

PV (Present Value) = $1,200

PMT (Periodic Payment) = $-225 ($300 - $75)

FV (Future Value) = $0

Results:

Period (N #) = 5.6

Sum of all periodic payments = $-1,260.08

Total Interest = $60.08

Thus, within six months you can pay off the credit card debt.

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Length of the diagonal of the rectangular prism is 14.69694. Here is the solution below

Given that the information:

Length of the rectangular prism - 10

Width of the rectangular prism - 4

Height of the rectangular prism - 10

Length of the diagonal of the rectangular prism -

Diagonal (d) = √l²+w²+h²= √10²+4²+10² =  14.69694

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid.

The correct answer of this question is 14.69

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