Which function has an inverse that is also a function?
Og(x)=2x-3
Ok(x) = -9x²
Of(x) = x + 21
Ow(x) = -20

Answer:

640

Step-by-step explanation:

Answer:

=297/7

PEMDAS Hope this helps :)

All the lengths in the original figure are multiplied by the same number to get a scaled replica.

Every length in the original figure is multiplied by the same number in a scaled copy, which is a copy of the original figure. For instance, triangle ABC is a scaled version of triangle DEF.

To find the matching side length on triangle DEF, each side length on triangle ABC was multiplied by 1.5. A figure that is geometrically identical to the original figure is called a scale copy. This indicates that the scale copy and the original figure are identical in shape but may vary in size.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

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Solving the equation

An equation is a mathematical expression that shows the relationship between two variables.

Since together donal, yolanda, and iris made 27 birdhouses for a school fair. yolanda made n birdhouses. donal made one more birdhouse than yolanda, and iris made one more than donal. So, we solve the equation n +(n + 1) + (n + 1 + 1) = 27 to find the number of birdhouses each one made.

So, n + (n + 1) + (n + 1 + 1) = 27

Colecting like terms, we have that the equation is

n + (n + 1) + (n + 1 + 1) = 27

n + n + n + 1 + 1 + 1 = 27

3n + 3 = 27

Subtracting 3 from both sides of the equation, we have

3n = 27 - 3

3n = 24

Dividing oth sides by 3, we have

n = 24/3

n = 8

So, n + 1 = 8 + 1 = 9

and n + 1 + 1 = 8 + 1 + 1 = 10

So,

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Answer:

HERE ARE FOLLOWS

Step-by-step explanation:

The population of a city was five-sevenths of a million in 2010 and five million in 2016. The population growth can be described as an arithmetic sequence. Find its common difference, which represents the annual growth of the population.

In this question, we’re told that we have an arithmetic sequence. This is a special type of sequence that has a common difference between each term. For example, the sequence two, seven, 12, 17, and so on has a common difference of five, as we add five each time to get the next term. The general term of any arithmetic sequence, written sub , is equal to sub one plus minus one multiplied by , where sub one is the first term in the sequence and is the common difference. It is this common difference that we are trying to calculate in this question.

In this question, we are told that the initial population in 2010 was five-sevenths of a million. So, we will let sub one, the first term, be five-sevenths. We are also told that the population in 2016 was five million. We can see that this would correspond to the seventh term in our sequence. This means that sub seven is equal to five. We can now substitute our values into the formula for the general term. The seventh term five is equal to five-sevenths plus seven minus one multiplied by . The right-hand side simplifies to five-sevenths plus six .

Noting that we can write five as 35 over seven, when we subtract five-sevenths from both sides of our equation, we get thirty sevenths is equal to six . We can then divide both sides of this equation by six, giving us is equal to 30 over 42. Both the numerator and denominator of our fraction are divisible by six. As 30 divided by six is five and 42 divided by six is seven, our fraction simplifies to five-sevenths.

We can therefore conclude that the common difference which represents the annual growth of the population is five-sevenths of a million.

Answer:

48 free throws

Step-by-step explanation:

25:36 is the ratio

Now divide 25 by 36 to find the probability of the basketball player scoring:

25/36=0.694

Now multiply this probability with the total number of free throws (70) in order to get the number of free throws that would be made:

70 * 0.694 = 48.6

You can't make 48.6 free throws, so you have to round down to the nearest integer since you can't make 0.6 free throws.

Hence, 48.6 ==> 48 free throws

The probability that the Canadian Rounders have 0 players injured for their next match is 1/4 or 25%.

This implies the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happeing of the event.

The total number of matches = 4+5+2+3+2

The total number of matches = 16

Total, that has zero injured players = 4

The probability will be:

= 4 / 16

= 0.25

The probability is 0.25.

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Complete question

The following frequency table summarizes this year's injuries on the Canadian Rounders cricket team.

Number of injured players Number of matches

0 | 4

1 | 5

2 | 2

3 | 3

4 | 2

Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have 0 players injured for their next match?

We know that the volume of a rectangular box is given by length times width times height. So, we have:

V = x * (x - 5) * (x + 2) = 180

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

We can use this equation to find the length of the box.

Expanding the equation:

x^3 - 5x^2 + 2x = 180

Solving for x using a calculator or an algebraic equation solver we can find that x = 9.52

So the length of the box is 9.52 inches.

The answer is B. 9.52 in

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The value of the trigonometric relation tan D = 15/8 = 1.875

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as CDE

The triangle CDE is a right triangle with ∠CDE = 90°

Now , the measure of side CD = 8 units

The measure of side CE = 15 units

The measure of side DE = 17 units

From the trigonometric relations ,

tan θ = opposite / adjacent

Substituting the values in the equation , we get

tan D = 15 / 8

Hence , the value of tan D = 15/8

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On solving the provided question, we can say that - the of the function f(x) = 0.5x + 7.8 = 9.8

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

here, we are provided with the function -

f(x)= 0.5x + 7.8

and given from question, x = 4

f(x) =  2 + 7.8 = 9.8

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The area of the deck in terms of s is 2s^2 + 7s + 15. The expression can be written in standard form as A = 2s^2 + 7s + 15.

The area of the deck can be expressed in terms of s using the standard form of a rectangular area equation, A = lw, where l is the length and w is the width. The side length of the pool is s and the length of the deck is twice the side length of the pool plus 5, or 2s+5. The width of the deck is 3 units longer than the side length of the pool, or s+3. Substituting these values into the area equation gives us:

A = (2s+5)(s+3)

A = 2s^2 + 7s + 15

Therefore, the area of the deck in terms of s is 2s^2 + 7s + 15.

The expression can be written in standard form as A = 2s^2 + 7s + 15.

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The area of the rectangular deck built around the square pool of side, s in terms of s is 2s² + 11s + 15.

Therefore the answer is 2s² + 11s + 15.

The pool has side length s. The length of the deck is 5 units longer than twice the side length of the pool, that is

l = 2s + 5

The width of the deck is 3 units longer than the side length of the pool, that is

b = s + 3

Deck is in rectangular shape, thus the area of the deck in terms of s can be calculates by

A = lb = (2s + 5)×(s + 3)

= 2s² + 6s + 5s + + 15

= 2s² + 11s + 15

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The metal is most likely to be Silver (Ag).

Density, d = 10.5 g/cm3.

z = 4 (as it is an FCC)

a = edge length = 409 pm = [tex]4.09 * 10^{-8} cm[/tex]

We have to find the Atomic Mass (M).

Perhaps the most common crystal structure is Face-Centered Cubic (FCC). The crystal structure is based on the Bravais lattice of the same name, with a single atom at each lattice point on the cube’s corners and faces. FCC is one of the most stable crystal structures and has the highest packing density. In some textbooks, FCC may also be abbreviated as CCP, which stands for Cubic Close-Packed.

The formula for density, d =

[tex]D = \frac{z * M}{N_{A} * V }[/tex]

where, V = volume.

Volume, V = a x a x a = a^3

V =[tex](4.09 * 10^{-8}) ^ 3 = 68.417 * 10^{-24} = 6.841 * 10^{-23}[/tex]

Using the density formula,

[tex]M = \frac{d * N_{A} * V }{z}[/tex]

[tex]M = \frac{10.5 * 6.023 * 10^{23} * 6.841 * 10^{-23} }{4}[/tex]

[tex]M = 108.15 amu[/tex]

The atomic weight is close to that of Silver (Ag).

Thus, the metal is most likely to be Silver (Ag).

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Equation reads C=25n+2500, and the price to make 3000 toys is $77,500. Additionally, 1200 toys may be created for $32500.

A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.

Let's use the equation y=mx+b, where n is the number of toys and C is the overall cost. The total cost of producing n toys would be equal to the initial development cost plus the production cost of each toy.

The cost to make a toy will equal m since m is multiplied by n, the quantity of toys. B will always equal the development cost since it is a constant and its value is unaffected by the number of toys.

Therefore, [tex]C=25n + 2500[/tex]

by above, equation put

[tex]n=1750\\C= 25(3000) + 2500\\C= $77,500[/tex]

Now, again by same equation, but C instead of n.

[tex]= > 32500= 25n +2500\\= > 30000=25n\\= > n = 1200[/tex]

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The line ED has a length of 4 units.

Given,

Points E and D in the ΔCAB

equation represent the midpoints of the segments AC and BC, respectively.

AB is 8 units as well.

The length of segment ED needs to be determined.

We are aware that a triangle's third side and the line segment connecting its midpoint are both said to be parallel to the triangle's third side and to be half its length. The mid point theorem is what is known as this.

E and D are the midpoints of AC and BC in the equation CAB, and E's length is equal to half of AB's length is

=> 8/2  

=> 4 units

so the length of the segment ED is 4 units

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The measure of segment ED is 4 units.

4 units

We know that the measure of segment AB is 8 units and that point E is the midpoint of segment AC and point D is the midpoint of segment BC. This means that the measure of segment AC is 8/2, or 4 units. Since point E is the midpoint of segment AC, it is also the midpoint of segment ED, meaning that the measure of segment ED is 4 units.

The measure of segment ED is 4 units.

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Answer:

In solving any mathematical equation carrying x,we mainly begin by first understanding the question and breaking them down little by little and solving them separately to know which to add to get x,or which to subtract to get x,e.t.c,as the case may be

The solution of the algebraic equation is 37/2

An algebraic equation is a statement that says that two algebraic expressions are equal. For example, the equation 3x + 2 = 6x

The algebraic expression 4/(x-4) -3/(x²-16) = 6/(x+4)

To solve this algebraic equation, you need to find the value of x.

4/(x-4) -3/(x²-16) = 6/(x+4)

4/(x-4) -3/(x-4)(x+4) = 6/(x+4)

The LCM of (x-4) and (x-4)(x+4) is (x-4)(x+4):

(4(x+4) -3)/(x-4)(x+4) = 6/(x+4)

(4x+16 -3)/(x-4)(x+4) = 6/(x+4)

4x+13/(x-4)(x+4) = 6/(x+4)

Multiply both sides by (x+4):

4x+13/(x-4) = 6

4x+13 = 6(x-4)

4x+13 = 6x-24

6x-4x = 13+24

2x = 37

x = 37/2

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Number of green chairs in the inventory is 208.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total number of chairs in the inventory = 520

Fraction of chairs that are green = 2/5 of 520

2 parts out of 5 parts are green.

Number of green chairs = 2/5 × 520

                                        = 1040 / 5

                                        = 208

Hence there are 208 green chairs in the inventory.

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An image is always formed at the back of a mirror. Thus, the flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = opposite / adjacent

         = 1.65 / 1.7

Tan θ = 0.9706

θ =  Tan⁻¹(0.9706)

 = 44.2°

θ = 44.2°

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = opposite / adjacent

        = h / 8.75

0.9706 = h / 8.75

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m tall.

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From a point (x, y) on a circle with radius r , we know that cos θ represents tha ratio  of x/r .Therefore, cos θ = x/r. On the unit circle the radius of the circle is 1, which means x = cosθ.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

From the figure below,

We see that,

The point (x, y) = (x, 0)

Cos θ = x/r

Unit circle means r = 1.

So,

Cos θ = x/1

Cos θ = 1

Thus,

The given statement is filled as above.

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Applying the perpendicular bisector theorem, the values of the measures are:

y = 12

x = 7

PQ = 29

SR = 32

PT = 18

PR = 36

The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment.

In other words, if a point P is the perpendicular bisector of line segment AB, then the distances from P to points A and B are equal. This is true no matter where point P is located on the perpendicular bisector.

Since QT is the perpendicular bisector of PR, we would therefore have the following based on the above stated theorem:

PQ = QR

Substitute:

5y - 31 = 2y + 5

5y - 2y = 31 + 5

3y = 36

3y/3 = 36/3

y = 12

SP = SR

Substitute:

4x + 4 = 7x - 17 [congruent segments]

4x - 7x = -4 - 17

-3x = -21

x = 7

PQ = 5y - 31 = 5(12) - 31 = 29

SR = 7x - 17 = 7(7) - 17 = 32

PT = 6x - 2y = 6(7) - 2(12)

PT = 18

PR = 2(PT)

PR = 2(18)

PR = 36

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The equation of this function is f(x) = 2(x - 2) / x - 1

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

The parent function is given as:

y = 1.

we can see that the function is translated 3 units down and  2 units right.

This means that the transformation rule

(x, y) -> (x - 2, y - 3)

So, we have graph contains the point (-1, 2) and the y-intercept is less than 2.

Since the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

Hence, the equation of the graph is

f(x) = 2(x - 2) / x - 1

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Answer:1/4

Step-by-step explanation:3/8-1/8=1/4

The values of f ◦ g is equal to (x + 2)^2 + 1 and g ◦ f is equal to x^2 + 3.

f ◦ g is the composition of functions f and g, which means that for any x in the domain of g, we substitute g(x) into f(x) to get f(g(x)) = (x + 2)^2 + 1.

g ◦ f is the composition of functions g and f, which means that for any x in the domain of f, we substitute f(x) into g(x) to get g(f(x)) = x^2 + 1 + 2

So f ◦ g = (x + 2)^2 + 1 and g ◦ f = x^2 + 3

It's important to notice that the order of the functions matters when composing them, f ◦ g is not the same as g ◦ f. The composition of functions is a fundamental concept in mathematics and it's used to chain multiple functions together to create a new function.

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Answer:

2x + 40

Step-by-step explanation:

Given ,

L = x

B = 20cm

To Find: Expression that represents the Perimeter

Perimeter of rectangle = 2(l+b)

                                       = 2(x+20)

                                        = 2x + 40

Answer:

Graph 1- No, Graph 2- No, Graph 3- Yes, Graph 4- Yes, Graph 5- No, Graph 6- No

Answer:

3.75

Step-by-step explanation:

Just divide 1.5 by 0.4

just ask your teacher for extra help if needed

The function is defines for all (x,y,z) ∈ R³

Hence the domain of this equation is,

D = {(x, y, z) | 9x² + 9y² + z² ≤ 81

The function is bound by sphere.

The set of inputs that a function will accept is known as the domain of the function in mathematics.  (f),  " (f), where f is the function, are other ways to refer to it.

More specifically, the domain of f is X given a function  Xto Yfcolon Xto Y. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.

The function f can be graphed in the Cartesian coordinate system in the particular situation where X and Y are both subsets of  R  In this instance, the graph's x-axis shows the domain as the projection.

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Answer:

1, 5 6 10 15 30 because these numbers times certain numbers can also give 30 for instance 1 by 30 is30, 5 by6 is 30 6 by 5 is 30 10 by 3 is 30 15 by 2 is 30 30 by 1 is 30

At the point where x = 0, the equation simplifies to 8e^y = 8e, which can be rearranged to e^y = 1. This means that y = 0.

1. Substitute x = 0 into the equation: xy + 8e^y = 8e

2. Simplify the equation: 8e^y = 8e

3. Rearrange the equation to isolate the exponent: e^y = 1

4. Take the natural logarithm of both sides: y = ln(1)

5. Evaluate the natural logarithm: y = 0

At the point where x = 0, the given equation simplifies to 8e^y = 8e. Rearranging this equation to isolate the exponent on the left hand side, we get e^y = 1. Taking the natural logarithm on both sides, we get y = ln(1). Finally, evaluating the natural logarithm of 1, we get y = 0. Therefore, the value of y" at the point where x = 0 is 0.

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The number for the expression is 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = x

Now,

50 + x = 6x

Subtract x on both sides.

50 = 5x

Divide 5 into both sides.

x = 10

Thus,

The number is 5.

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The equivalent expression when we apply distributive property is -10w -20

You should understand that distributive property states that every term inside a grouping symbol multiplied by every term outside the grouping symbol yields the same result.

To this effect, the formula to do this is x(y+z) = xy+xz

The given expression is

5×(−2w−4)

= 5*-2w- 5*4

= -10w -20

In the expression every term outside the symbol is multiplied by every term inside the symbol to give the result of the expression

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