Consider the function f(x) = 10x and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)?

If the 72% of its original amount of C-14. Then the number of years will be 3285.

The complete question is attached below.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.

Then the function is given below.

[tex]\rm N= N_0 \ e^{-kt}[/tex]

Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.

[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]

We have N = 0.72N₀, the time will be

[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]

Take log on both side, then we have

ln 0.72 = -0.001 × t × ln e

  -0.33 = -0.001 × t

         t = 3285 years

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Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, In the graph,

we can see that we have a vertical asymptote at x = -1.

Hence, This means that the denominator of the rational equation becomes zero when x = -1.

So the equation must be:

⇒ y = 1 / (x + 1)

Here, The denominator is x + 1, and as expected, it becomes zero when, x = -1.

Then, we conclude that the correct option is C.

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Answer:

The answer would be (0, 2/3) or (0, Two-thirds)

Answer:

0, 2/3

Step-by-step explanation:

Answer:

Sam is correct

Step-by-step explanation:

6 divided by 1/4.

This is asking how many times can 1/4 go into 6?  This might be a calculation needed if Sam brought 6 pies to the party of 24 people.  How should Sam cut the pies so that each person gets an equal share, and there is none left over.  This is a serious issue because Sam only knows how to cut pies into quarters.  He always gets confused when having to split a pie into 5, 6, 7, 8 or even 9 equal pieces.  Sam decided that if he cuts the pies into quarters, that he'll have exactly 24 pieces of pie, all equal in size, and exactly enough to feed everyone.

Sam says 24 is wrong.  I don't see the figure that Sam has in mind, but it apparently is not 24.

When a pie is cut into quarters, it will serve 4 people.  If one has 6 pies, and everyone takes only one slice, then there would be 4 x 6 or 24 pieces of pie, exactly what is needed:  one for each person.

Answer:

the answer pf x its 15

by adding the middle sum to 90 degreess and by dividing 6 and 90 you get 15

7.7278 g/ml is the most accurate density of the substance.

It is define as the quantity per unit volume, unit area, or unit length.

i.e. the mass of a substance per unit volume.

Mathematically,

[tex]\rho =\frac{m}{v}[/tex]       ----- equation  (1)

Where,

p is the density

m is the mass

v is the volume

According to the question,

Mass = 27.82 grams  

Volume = 3.6 ml

By substituting the Value of m and v in equation 1.

[tex]\rho =\frac{27.82}{3.6}[/tex]

[tex]\rho = 7.7277777 g/ml[/tex]

Therefore,

The most accurate density of the substance in g/ml is  7.7277777 g/ml.

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The value of z is 119° and the value of y is 28°.

When two parallel lines meet any other line, comparable angles are generated in matching corners or corresponding corners with the transversal, these angles are called corresponding angles.

If the given diagram is modified a bit it will look as shown below, the two angles will be 61° because the two angles are corresponding angles.

Now, since 61° and x lie on the same side of the line, therefore, the sum of the two angles will be,

61° + x = 180°

x = 119°

Also, the angles measured at 61° and (3y-23)° lie on the same side of the transversal, therefore, these two angles are corresponding angles. Thus,

61° = (3y-23)°

61 = 3y - 23

y = 28

Hence, the value of z is 119° and the value of y is 28°.

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Answer:

if a and b are both negative numbers, the product is a positive number

The coordinates of point N are (3, 5).2 the answer is 2/1 but just write 2.

We have given that,

Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

The coordinates of point M are (2, 4), and the coordinates of point N are (3, 5)

Therefore we get,

2 the answer is 2/1 but just write 2.

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Explanation:

She has already ran 8 miles, so she has 26-8 = 18 miles left to go.

She runs at a pace of 7.5 mph, which means she has 18/(7.5) = 2.4 hours left to go.

I used the equation distance = rate*time, and solved for time to get time = distance/rate.

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

Another approach:

Here's how you can use algebra.

x = time she has left in hours

7.5x = distance covered in those x hours

7.5x+8 = total distance

7.5x+8 = 26

7.5x = 26-8

7.5x = 18

x = 18/(7.5)

x = 2.4

Answer:

The man is 27 years old.

Step-by-step explanation:

You can create a system of equations.
Let x = the age of the man
Let y = the age of his son
You can create the following equations based on what was given in the problem:
1. x = y + 18
2. (x - 3) = 4(y - 3)
You can simplify the second equation:
x - 3 = 4y - 12
x = 4y - 9
Then, solve the system of equations:
x = y + 18
-
x = 4y - 9
____________
0 = -3x + 27
The son's age is 9, therefore the father is 27 years old.

Answer:

B

Step-by-step explanation:

Used elimination method.

first plugged in (0,0)which remove A,D

than saw the line is not solid so chose B

Answer: [tex]g(x) = 3^{x-6}[/tex]

Step-by-step explanation:

Think about it like doing

x - 6 = 0

x = 6

That is how you know that it will be shifted 6 units right (how you can tell the difference between right and left shift)

Answer:

trapezoid

the horizontal side lengths wont touch each other if you extend them out

Answer:

The number after - 2 is - 3.5.

Step-by-step explanation:

Follow the pattern

Let the number be  after -2

as in the question after 4 we have 2.5 then 1 and so on.

if we subtract 4 from 2.5 we get

2.5 - 4 = -1.5

similarly:  1 - 2.5 = -1.5

-0.5 - 1 = -1.5

and now

x -(-2) = - 1.5

x = - 1.5 -2

x = - 3.5

so the number after - 2 is - 3.5.

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Answer:

x2

Step-by-step explanation:

x2

The attached graph represents the piecewise function h(x)

Which of the following is the graph of the piecewise function

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The function is given as:

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The above means that the piecewise function has 3 domains

Next, we plot the graph using a graphing tool

See attachment for the graph of the piecewise function h(x)

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The statements that are true about the pyramid are

From the question, we are to determine the statements that are true about the pyramid

The diagram shows a square pyramid,

The length of a side of its base is 756 ft

and

The height / altitude of a triangular face is 612 ft

Since the pyramid is a square pyramid,

Then, the base must be a square with each side measuring 756 feet

∴ The first statement is true

Since the height of a triangular face is 612 ft,

Then,

∴ The slant height of the pyramid is 612 feet

NOTE: Slant height of a pyramid is the altitude of the triangle comprising a lateral face

Thus, the second statement is true

Since the triangular faces each have a base of 756ft and a height of 612 ft,

Then,

All four triangular faces are congruent

∴ The fourth statement is true

NOTE: Lateral sides of a solid are the faces on the sides of the shape

The pyramid has four lateral faces which are each a triangle

∴ The last statement is true

Hence, the statements that are true about the pyramid are

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Answer:

38.667°

Step-by-step explanation:

the total sum of 3 angles in a triangle is 180

in triangle PQR this means:

P+Q+R = 180

so:

64+x+2x=180

64+3x=180

3x=116

x=116/3=38.667

So Q=X=38.667

The slope of the line parallel to the line on the graph (0,-3) (5,-4) is - 1 / 5

Parallel lines have the same slope.

Therefore,

slope = m = y₂ - y₁ / x₂ - x₁

Therefore,

x₁ = 0

x₂ = 5

y₁ = -3

y₂ = -4

Therefore,

slope = -4 - (-3)  / 5 - 0

slope = -4 + 3 / 5

slope = - 1 / 5

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The equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3

The ordered pairs are given as:

(1, 4), (–1, 2), and (0, 3)

From the above ordered pairs, we can see that the difference between the x and y values is 3.

This means that:

y - x = 3

Add 3 to both sides

y = x + 3

Hence, the equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3

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The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

y = 2x+5

Compare the equation with the standard equation;

[tex]\rm y = mx+ c[/tex]

where,

m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;

m = 2

The product of the slope of the two-line perpendicular to each will be -1.

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is;

y = -2x+c.

m₁=2

m₂=-2

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is y = -2x+5.

Hence, option B is correct.

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Answer:

They are the same angle.

Step-by-step explanation:

We have a diagonal line and two 180° parallel lines running through it. The x and y values should be identical because of the placement. The diagonal on the right and right above the 180° angle.

Option 2: Corresponding angles.

Hope this helps!

If not, I am sorry.

Answer:

Function

Step-by-step explanation:

Yes, the graph is a function. For each x value, there is a unique y value that corresponds with it.

A graph can also be tested as a function by using the popular "vertical-line test".

Answer:

Step-by-step explanation:do i know u

Answer:

x= 5.8125

Step-by-step explanation:

Given: [tex]\frac{12x-7}{4} =\frac{5x+18}{3}[/tex]

Since we have one fraction equal to another fraction, we can cross multiply.

(12x -7)(3)= 4(5x +18)

Expand:

36x -21= 20x +72

Bring all the x terms to one side, constant to the other:

36x -20x= 72 +21

Simplify:

16x= 93

Divide both sides by 16:

[tex]x= \frac{93}{16}[/tex]

x= 5.8125

Additional:

Here is a similar question which you may wish to check out

Answer:

No, the table does not represent a function.

Step-by-step explanation:

By definition, a function will not have 2 or more results for the same input.

The table shows two values of y for the same x:  (2,1) and (2,4).  The same input, 2, results in two different values, 1 and 4.

See attached image.

The slope of the line in its simplest form is 3.

The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].

We need to find the slope of the line in its simplest form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.

Select any two points on the line like A and B.

From the below figure it is clear that

Rise = Change in y = -2-(-5) = 3

Run = Change in x = 9-0 = 9

Now, [tex]\frac{9}{3} =3[/tex]

Therefore, the slope of the line in simplest form is 3.

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The area of the swimming pool on the scale drawing will be 300 sq. centimeters.

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

For the given scale drawing 1 centimeter represents 2 meters, therefore, the length of 40 meters in one scale drawing will be equal to,

40 meters = 40/2 centimeters = 20 centimeters

The width of 30 meters one scale drawing will be equal to,

30 meters = 30/2 centimeters = 15 centimeters

Now, the area of the swimming pool on the scale drawing will be,

Area= 20 centimeters × 15 centimeters = 300 sq. centimeters

Hence, the area of the swimming pool on the scale drawing will be 300 sq. centimeters.

The complete question is:

A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters. then what is the area of the swimming pool on the scale drawing?

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Answer:

add 2 to each side of the equation

Step-by-step explanation:

x-2=10

To solve for x, we need to add 2 to each side of the equation

x-2+2 = 10+2

x = 12