Consider the function g(x)=x−1‾‾‾‾‾√3. What is the range of this function's inverse?

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

Answer:

Step-by-step explanation:

To create a frequency distribution with a first class of 13-19 and a class width of 7, we need to determine the boundaries for each class. The first class has a lower boundary of 13 and an upper boundary of 19. The upper boundary of each subsequent class is obtained by adding 7 to the previous upper boundary.

Using these boundaries, we can count how many values fall into each class:

Class Boundaries Tally Frequency

1             13-19  

2            20-26  

3            27-33  

4           34-40  

5           41-47  

6          48-54  

7          55-61  

8         62-68  

9         69-75  

To obtain the frequency, we count the number of values that fall into each class. The tally column is used to keep track of the values as they are counted.

Answer:

F, J, and K

Step-by-step explanation:

The others are negative so they can't be exponential

The exponential function can't be negative or irrational, so options A, D, and E are correct.

The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras. The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

As we discussed above, the exponential function can't be negative or irrational  so, look at the options only,

f(x) = 10(1/7)ˣ,

j(x) = 8(4.13)ˣ,

k(x) = 12(8)ˣ are the exponential functions, whereas

g(x) = 4(-3)ˣ,

h(x) = 4(-13)ˣ are negative, so they can't be exponential functions.

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Answer:

6

Step-by-step explanation:

-15+6 means it goes minus basically its 15-6(-15+6)=-9

Answer:

n=24

Step-by-step explanation:

First add 15 to the right side equaling 24. Therefore n=24

Answer:

0.66 melones por niño o 2/3

Step-by-step explanation:

10/15=2/3=0.66

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

13, 21, 29

Step-by-step explanation:

You are adding 8 to each term. -27 + 8 = -19 + 8 = -11 + 8 = -3, etc.

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer:

Step-by-step explanation:

Its is

6CM wide. as to find the area we have to times the length x height :)

Answer:

wide = 6 cm

Step-by-step explanation:

\(t=tall=10\)

\(w=wide=?\)

\(P=perimeter=32\)

The equation:

\(P=2t+2w\)

\(32=2(10)+2w\\32=20+2w\)

\(32-20=2w\\12=2w\)

\(\frac{12}{2} =w\)

\(6=w\)

Hope this helps.

Answer:

15

Step-by-step explanation:

Answer:

A= equilateral triangle

B= right triangle

C= obtuse triangle

Answer:

Step-by-step explanation:

For the first box, B would be incorrect, since an equilateral triangle's angle measurements would all be equal. 62+62 is 124, and a triangle needs to add up to 180. As the final angle is 56, it can't be equilateral!

For the second box, C is the incorrect answer, since it is both a right triangle and scalene. The first angle is 22, the second is 90, and the third is unknown. As it needs to add up to 180, it wouldn't be possible for the unknown angle to be 158.

For the third box, C is also incorrect, since it needs to add up to 180. 108+72+72 is not possible, since that would be much higher than the 180 total.  

Answer: 15,000

Step-by-step explanation:

40 percent *37500

= (40/100)*37500

= (40*37500)/100

= 1500000/100 = 15,000

Answer:

Well lizzie stevens from Greys better stop running if she got cancer

Step-by-step explanation:

Answer:

12= ax - x + b

Step-by-step explanation:

5x -4(x - 3) - 8 = ax + b

5x -4x + 12 - 8 = ax + b

x + 12 = ax + b

12= ax - x + b

An inequality to represent the cost of Jason’s food for the party is

An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is

The two options for buying wings and hot dogs include the following:

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:

Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;

7x + 5y ≤ 40

Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;

y ≥ 5

Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.

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Answer:

refer to attachment

Step-by-step explanation:

Answer:

1.6

Step-by-step explanation:

i used calculator

Answer:  1.6

Step-by-step explanation:

The interquartile range of this data, in the stem and leaf plot would be 22

First, order the numbers out from the stem and leaf plot, using the key of 1 | 5 means 15.

The numbers are :

10, 23, 23, 28, 33, 45, 70, 90

The Interquartile range is:

= Third quartile - First quartile

First quartile :

= 25 % x 8

= 2 nd position which is 23

Third quartile :

= 75 % x 8

= 6 th position which is 45

The interquartile range is:

= 45 - 23

= 22

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Answer:5

Step-by-step explanation:

5098

Answer:

Step-by-step explanation:

x         6         a

8       48        c  

-4        b       20

Let the unknown numbers of the multiplication grid are a, b and c.

1). 6 × 8 = 48

2). (-4)×6 = b

    b = -24

3). (-4) × a = 20

   a = -5

4). 8 × a = c

    8 × (-5) = c

    c = -40

Therefore, missing in the given multiplication grid are,

x         6        -5

8       48       -40  

-4      -24       20

Answer:

A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)

Step-by-step explanation:

You would take three fourths of each coordinate to get the x and y values.

Answer:

A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)

Step-by-step explanation:

You would take three fourths of each coordinate to get the x and y values.

Answer:

5th term = - 10

Step-by-step explanation:

5th term

Here,

n = 5

d ( n ) = 6 - 4 ( n - 1 )

d ( 5 ) = 6 - 4 ( 5 - 1 )

         = 6 - 4 ( 4 )

         = 6 - 16

d ( 5 ) = - 10

The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.

The general form of an equation for a sinusoidal function is presented below.

y = a×sin[b*(x - h)] + c

The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.

y = a×sin[b*(x - h)] + c

y = 8sin[(27/2π)*(x - 4)] + c

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Weight of Omar after 4 weeks is 9.4375 pounds.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Weight of Omar at the time of birth = 8 pound 3 ounces

Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces

New weight of Omar

= (8 lb 3 ounces) + 20 ounces

= 8 lb + 23 oz

As, we know 16 ounces = 1 pound

23 ounces = 1.4375 pound

Now, total weight of Omar after 4 weeks = 8 lb + 23 oz

                                                                  ≈ 8 lb + (1.4375) lb

                                                                   ≈ 9.4375 pounds

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

The given function is :

\(\qquad \tt \dashrightarrow \:f(x) = \frac{1}{x} \)

here, for each value of x there is an unique value of f(x), so we can infer that it's a " one - one " function.

but it isn't an onto function because for value of x as 0, we have no value of f(x) [ undefined ]

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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Answer:

unless I am mistaken r=7

Step-by-step explanation:

you subtract 10 from each side and boom done