A 25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?

Answer: [tex]f^{-1}(x)=\frac{x}{5}[/tex]

Step-by-step explanation:

By definition the domain of an inverse function [tex]f^-1(x)[/tex] is the range of f(x) and the range of the inverse function is equal to the domain of the principal function f(x).

If you have a function [tex]f(x)=5x[/tex], then to find the inverse function, follow these steps:

1. Make [tex]y=f(x)[/tex]

 [tex]f(x)=y=5x[/tex]

 [tex]y=5x[/tex]

2. Solve for the variable "x":

[tex]x=\frac{y}{5}[/tex]

3. Exchange the variable "x" with the variable "y":

[tex]y=\frac{x}{5}[/tex]

4. Exchange "y" with[tex]f^{-1}(x)[/tex]. Then the inverse function is:

[tex]f^{-1}(x)=\frac{x}{5}[/tex]

Answer:

The scale factor of their side lengths is 4:7.

Step-by-step explanation:

Let the side length of two squares are p and q.

The area of a square is

[tex]A=a^2[/tex]

Using this formula, we get the area of both squares.

[tex]A_1=p^2[/tex]

[tex]A_2=q^2[/tex]

It is given that the areas of two similar squares are 16m and 49m.

[tex]\frac{p^2}{q^2}=\frac{16}{49}[/tex]

[tex](\frac{p}{q})^2=\frac{16}{49}[/tex]

Taking square root both the sides.

[tex]\frac{p}{q}=\sqrt{\frac{16}{49}}[/tex]

[tex]\frac{p}{q}=\frac{4}{7}[/tex]

Therefore the scale factor of their side lengths is 4:7.

To find the scale factor of the side lengths, we can take the square root of the ratio of the areas. In this case, the scale factor is √7/2.

To find the scale factor of the side lengths of the squares, we can take the square root of the ratio of their areas. In this case, the ratio of their areas is 49m:16m, which simplifies to 7:4. Taking the square root of this ratio gives us the scale factor of their side lengths. So, the scale factor is √(7/4) = √7/√4 = √7/2. Therefore, the scale factor of the side lengths is √7/2.

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Answer:

C

Step-by-step explanation:

Given data are :

{1,2,2,2,2,4,4,5,6,6,8,8,8,10}

1 appears only once so there will be 1 point above number 1 in the dot plot.

Then choice B or C or D are possible choices.

2 appears 4 times so there will be 4 points above number 4 in the dot plot.

Then choice B or C or D are possible choices.

4 appears 2 times so there will be 2 points above number 2 in the dot plot.

Then choice C or D are possible choices.

5 appears once once so there will be 1 point above number 5 in the dot plot.

Only choice that satisfies those results is C.

Hence correct answer is C.

Answer:

The correct answer is the amount the average person spends in a month on gasoline.

Step-by-step explanation:

When comparing the amounts spent on the purchase of two items, we must need to see the price difference between the products first, then we will see the consumption of those products. Here the two items that are being compared have different purchase prices. A cup of Coffee is far cheaper than purchasing a tank of gasoline. If coffee is purchased on daily basis, even then the amount spent on purchasing coffee would be much lesser than the amount spent on buying the gasoline. For example, the cup of coffee costs $1 and a tank of gasoline costs $50. If coffee is purchased daily, then monthly amount spent on it will be $30, and if gasoline is purchased twice in a month, the amount spent on it will be $100. So an average person spends more amount on gasoline than on purchasing coffee.

Answer:

Step-by-step explanation:

29-3(5)

29-15

14

X=14

Answer:X=11/10

Step-by-step explanation:

2x2-10x+7=0

4-10x+7=0

11-10x=0

-10x= -11

Divide both side by -10

-10x/-10.  -11/-10

Answer= 11/10

Answer:

x₁ = 5 + √11

         2

x₂ = 5 - √11

          2

Step-by-step explanation:

quadratic formula is given by

x = -b ±√b² - 4ac

             2a

a = 2, b = -10, c = 7

x = -(-10) ± √-10² - 4*2*7

                  2*2

x = 10 ± √100 - 56

           4  

x = 10 ± √44   = 2(5 ± √11)  = 5 ± √11

             4                   4               2

x₁ = 5 + √11

           2

x₂ = 5 - √11

           2

To solve any questions relating to ages, I find it easier to make a table, like in the picture below.

See picture for answer and clear diagram.

-----------------------------------------------------------------

Notes/Explanations + answer in written form

Let's say that Halley's age now is:              x

That means that her age in 18 years is:      x + 18

It also means that her age 2 years ago is:   x - 2

In the question, we are told that when Halley is 18 years older than her current age,  she will be 5 times the age she was when she was 2 years younger than her current age

That means:

Halley's current age + 18 years = 5 times (Halley's current age - 2 years)

So we get this equation (which we solve to get the answer) :

x + 18 = 5 * (x -2)                      ( expand the brackets)

x + 18 = 5x - 10                          (subtract x from both sides)

18 = 4x - 10                                 (add 10 to both sides)

28 = 4x                                       (now divide both sides by 4)

7 = x

Therefore, Halley's current age is 7 years

-------------------------------------------------

Note: equation is:   x + 18 = 5 * (x -2)    

1÷81 because you square it

9^ -2 = 1/9^2 = 1/81

It would be 13.

3x4 = 12

25-12

G= 13

Answer:

13

Step-by-step explanation:

g=25-3r

r=4

3 x 4 = 12

25-12= 13

the answer is 13

Answer:

$71

Step-by-step explanation:

First

61.72 times .15= 9.258

Second

61.72+9.258= 70.978

Answer:

Yes

Step-by-step explanation:

3 x - 2 y = 10

( - 2 , - 8 )

We know that coordinates are put in the form ( x , y ) and from that we can work out that x = -2 and y = -8

Now we just substitute x = -2 and y = -8 into 3 x - 2 y = 10

3 x - 2 y = 10

{ 3 × ( - 2 ) } - { 2 × ( - 8 ) } = 10

{ - 6 } - { - 16 } = 10

- 6 + 16 = 10 True

Answer:

yes

Step-by-step explanation:

To determine if the ordered pair is a solution to the equation.

Substitute the x and y values into the left side of the equation and if equal to the right side then the pair are a solution

3x - 2y = 3(- 2) - 2(- 8) = - 6 + 16 = 10

Hence (- 2, - 8) is a solution to the equation

Answer:

Equation: x/9 + 2 = 8

Solution: x = 54

Step-by-step explanation:

I'd imagine the question is asking "two more than the quotient of a number and 9 is 8." Let's break this down:

- two more than means we're going to be adding two to the following quantity in the sentence.

- the quotient of a number and 9 we can interpret as a division expression. We don't know what "a number is," so we can give it a label (I'll pick n), and we can now write it is x/9. Taken with that last bullet point, our expression becomes x/9 + 2.

- Finally, we're told that the result of this expression is 8, so we can write the compete equation as x/9 + 2 = 8.

Now, if we want to solve this:

We can start by subtracting 2 from either side, giving us

x/9 = 6

And multiplying either side by 9 gives us the solution

x = 54.

Answer:

20

Step-by-step explanation:

Answer:

x=21.4

Step-by-step explanation:

As we know the values of:

Perpendicular=10

Angle=25 degrees

And

Base=x

As the triangle is a right angled triangle, we will use the trigonometric ratios to find the value of x. As we have to find base and we know the values of perpendicular and angle, we will use a ratio that will include base and perpendicular.

So,

tan ⁡x=Perpendicular/Base

tan⁡ 25=10/x

x=10/tan ⁡25  

x=10/0.4663

x=21.4454

Rounding off to the nearest tenth

x=21.4

Answer:

see below

Step-by-step explanation:

the pattern between the numbers is that you add;

4+1=5

5+2=7

7+3=10

10+4=14

14+5=19

19+6=25

hope this helps

You add 6 to 19 in order to get to 25

Answer:

1/4

Step-by-step explanation:

Answer is

16

8

36

Explanation..multiply each by 4

The center of the circle is (-1.5, -2) and the radius is 3.205.

To find the center and radius of the circle, we can use the formula for the distance between two points in a coordinate plane. The two points given are (-3, -4) and the origin (0, 0), which represents the diameter of the circle. The center of the circle is the midpoint of the diameter, which can be found by taking the average of the x-coordinates and the y-coordinates. So, the center is ( (-3+0)/2 , (-4+0)/2 ) = (-1.5, -2). The radius of the circle is half the length of the diameter, which can be found using the distance formula as the distance between the center and one of the endpoints of the diameter. So, the radius is the distance between (-1.5, -2) and (-3, -4), which is √((-3-(-1.5))² + (-4-(-2))²) = √(2.5² + 2²) = √(6.25 + 4) = √10.25 = 3.205.

Answer:

1+6i

Step-by-step explanation:

Given:

f(x)=x^4 - 2x^3 + 38x^2 - 2 + 37

zero of f(x) = 1-6i

another zero of function = ?

Conjugate Zero theorem:

As per conjugate zero theorem, if a function f(x) has real coefficients and one of zero is a complex number then the conjugate of that complex number will also be a zero of that function i.e. complex zeroes will occur in complex conjugate pairs.

conjugate of 1-6i is 1+6i

hence another zero of f(x) will be 1+6i !

Answer:

1/2 - 2/6 = 1/6

Step-by-step explanation:

to answer two that are different simply take the lesser up or higher down example: 1/2-2/4 this would be zero because 2 x 1/2 = 2/4

1/2-2/6= 0.16

hope this helps

The frequency  is    1 /period =    1 / [ 2 pi ]

Final answer:

The frequency of the function f(x) = 2cos(x) - 4 is 1/(2π), meaning the function completes one full cycle every 2π units along the x-axis.

Explanation:

The frequency of a function in mathematics describes how often the function repeats its pattern over a certain interval. In the case of the function f(x) = 2cos(x) - 4, the frequency is determined by the coefficient of x inside the cosine function. The standard form of the cosine function is cos(bx), where the frequency is |b|/(2π), because a sine or cosine function oscillates between +1 and -1 every 2π radians, as denoted in Figure 16.10.

In this instance, b = 1 since there is no coefficient multiplying x inside the cosine. Therefore, the frequency of the function f(x) is |1|/(2π), which simplifies to 1/(2π). This frequency means that the function completes one full cycle every 2π units along the x-axis.

Answer:

[tex]y\geq 0[/tex] or [tex][0, \infty)[/tex]

Step-by-step explanation:

By definition the function

[tex]y = log (x)[/tex] has a domain of [tex]x> 0[/tex].

Since the function is not defined for the values of x negative or equal to zero.

The range of this function is all the real numbers.

Since [tex]y <0[/tex] when [tex]0 <x <1[/tex] and [tex]y\geq0[/tex] when [tex]1\leq x<\infty.[/tex]

In this case we have the function [tex]y = log ^ 2 (x-6)[/tex]

Therefore since the log function is squared then its range is now [tex]y\geq 0[/tex]

Answer:

Ans: All real numbers

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

1. Shape of a nonagon: 9 (root non-)

2. Total exterior angle: 360° (constant for all polygons)

3. Given that this polygon is regular, the one exterior angle of an nonagon is 360°/9 = 40°.

Answer:

Step-by-step explanation:

An exterior angle and an interior angle are supplementary angles.

Two Angles are Supplementary when they add up to 180°.

Therefore the measure of exterior angle is equal to different between 180° and an interior angle.

Method 1:

You can use the formula of the measure of interior angle of the regular polygon with n-sides:

[tex]\alpha=\dfrac{180^o(n-2)}{n}[/tex]

We have a nonagon. Therefore n = 9. Substitute:

[tex]\alpha=\dfrac{180^o(9-2)}{9}=(20^o)(7)=140^o[/tex]

[tex]180^o-140^o=40^o[/tex]

Method 2:

Look at the picture.

[tex]\alpha=\dfrac{360^o}{9}=40^o[/tex]

[tex]2\beta[/tex] - it's an interior angle

We know: The sum of measures of these three angles of any triangle is equal to 180°.

Therefore:

[tex]\alpha+2\beta=180^o\to2\beta=180^o-\alpha[/tex]

Substitute:

[tex]2\beta=180^o-40^o=140^o[/tex]

[tex]\theta[/tex] - it's a exterior angle

[tex]2\beta+\theta=180^o\to\theta=180^o-2\beta[/tex]

substitute:

[tex]\theta=180^o-140^o=40^o[/tex]

Answer:

Final step: Division Property of Inequality

Step-by-step explanation:

–2(5 – 4x) < 6x-4

-10 + 4x < 6x - 4          :  Distributive property

4x < 6x + 6                 :  Addition Property of Inequality (Add 10 to both sides)

-2x < 6                         :  Subtraction Property of Inequality (Subtract 6x from both sides)

  x > - 3                        :  Division Property of Inequality (Divide both sides by -2, flip the symbol sign)

Answer

I don't see the options here so the final step is Division Property of Inequality

Answer:

7k -7

Step-by-step explanation:

-k-(-8k+7)

Distribute the minus sign to all terms in the parentheses

-k--8k-7

Ad negative negative is a positive

-k + 8k -7

Combine like terms

7k -7

Answer:

The answer is 7k-7

Step-by-step explanation:

Hope this helps!!!

- The answer is simply ( 1, 3 ) and ( 4, 0 ), Nishishi~

- Ouma

Answer:

c on edge nuity

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-y=4&\text{add}\ y\ \text{to both sides}\\x+2y=-2\end{array}\right\\\\\left\{\begin{array}{ccc}x=4+y&(1)\\x+2y=-2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(4+y)+2y=-2\qquad\text{combine like terms}\\\\4+(y+2y)=-2\qquad\text{subtract 4 from both sides}\\\\3y=-6\qquad\text{divide both sides by 3}\\\\y=-2\\\\\text{put the value of}\ y\ \text{to (1):}\\\\x=4+(-2)\\\\x=2[/tex]

Answer:

C. y = -9, -3, 0, 5, 7

Step-by-step explanation:

The given function is represented by the set of ordered pairs

{(-2,0,) (-4, -3,) (2, -9,) (0,5,) (-5,7)}

The range of this function is the set of all the y-values.

The set of the y-values are:

{-9,-3,0,5,7}

Therefore the range is y = -9, -3, 0, 5, 7

The correct option is C

The value of tan 25° to the nearest hundredth​ is: 0.47

There are three main trigonometric ratios which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find tan 25° to the nearest hundredth​

The value of tan 25 degrees in decimal is 0.466307658

Approximating to the nearest hundredth gives:

tan 25° = 0.47

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Answer:

3 1/3

Step-by-step explanation:

First find the mean which is (2+6+8+12+12)/5=8 then find the distance from the mean and all the numbers in the data set.

For example 2 is 6 away from 8 and so on

Remember it's called the mean absolute deviation so it has to be the absolute value of the distances.

Distances: 6, 2, 0, 4, 4,

Then do 6+2+0+4+4/5 because even though 0 doesn't add anything, it is still a value in the distances. You get 3 1/3

Answer:

f(- 1) = 7

Step-by-step explanation:

To evaluate f(- 1) substitute x = - 1 into f(x)

f(- 1) = 5(- 1) + 12 = - 5 + 12 = 7

For this case we have a function of the form[tex]y = f (x)[/tex], where:

[tex]f (x) = 5x + 12[/tex]

We must find the value of the function when x = -1.

That is, [tex]f (-1)[/tex]:

[tex]f (-1) = 5 (-1) +12\\f (-1) = - 5 + 12[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]f (-1) = 7[/tex]

Answer:

[tex]f (-1) = 7[/tex]

The inverse of the function [tex]y = 3x^5 - 4[/tex] is [tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]

How to determine the inverse of the function

From the question, we have the following parameters that can be used in our computation:

[tex]y = 3x^5 - 4[/tex]

Swap the variabls x and y

So, we have

[tex]x = 3y^5 - 4[/tex]

Add 4 to both sides

This gives

[tex]3y^5 = x + 4[/tex]

Divide through by 3

[tex]y^5 = \frac{x + 4}{3}[/tex]

Take the 5th root of both sides

[tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]

hence, the inverse of the function is [tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]