what is the prime factorization of 225 in exponent form

The simplified expression of the function \(f (x)= \frac{x-4}{x^2+13x+36}\) is

\(f (x)= \frac{x-4}{(x+9)(x+4)}\). f(x) is increasing for all x > –4

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

\(f (x)= \frac{x-4}{x^2+13x+36}\)

Expand the denominator

\(f (x)= \frac{x-4}{x^2+4x+9x+36}\)

Factorize the denominator

\(f (x)= \frac{x-4}{x(x+4)+9(x+4)}\)

Factor out x + 9

\(f (x)= \frac{x-4}{(x+9)(x+4)}\)

Hence, the simplified expression of the function \(f (x)= \frac{x-4}{x^2+13x+36}\) is

\(f (x)= \frac{x-4}{(x+9)(x+4)}\).  f(x) is increasing for all x > –4

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Answer: f(x) is increasing for all x > -4

Proof of validity is shown below.

Answer: I think the greatest common factor is 4x^2

Step-by-step explanation:

Find the numerical common factors. Which are 8, -12, and 20. Find the variable common factors for x^4, x^3, and x^2. Multiply them together. Then break down the factors on both sides and pick the biggest one. Finally multiply them together. (I’m sorry, I’m very bad at explaining things.)

The exponential equation 3² = 9 is written in logarithmic  form as :-

\(\boxed{\log_{3}9=2}\)

_____

RainbowSalt2222 ☔

Answer:

G(f(x))=2(3x^2-5x+13)-7

G(f(x))=6x^2-10x+26-7

G(f(x))=6x^2-10x+19 =>A

Step-by-step explanation:

The correct option that indicates the quadrant that contains the translation of the shaded figure is the option B

B. III

A translation is a transformation in which the size, relative position of the points on the pre-image, are preserved but the location of the pre-image changes to obtain the image.

The shape of the shaded figure is an L-shape

The geometric figure in quadrant II and IV are a reflection of the shaded figure, across the y-axis and across the x-axis, respectively which is not a translation transformation.

The geometric figure in quadrant III can be obtained from the shaded figure by a translation 4 units to the left and 5 units downwards, which can be expressed as <-4, -5>, which is a translation transformation, therefore;

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The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:

line of symmetry: x = -3

intercepts...

x - intercept: (-4, 0) and (-2, 0)

y - intercept: (0, 8)

vertex: (-3, -1)

Step-by-step explanation:

The image isn't that clear but what I can get is what listed

line of symmetry is the line straight down the middle as if the graph is reflected to the other side

intercepts...

x - intercept is when y = 0, note there is 2 of these a negative and positive root

y - intercept is when x = 0

vertex is the turning point

for an upward curve its a min

for a downward curve it a max

I attached an example of each on of these

3 x 3 = 9

Y x y = y^2

3y x 3y = 9y^2

Answer:

9y²

Step-by-step explanation:

\(=3y*3y\\\\=(3y)^{2} \\\\=9y^{2}\)

Answer:

5 glasses: 20 oranges

8 glasses: 32 oranges

Step-by-step explanation:

12 ÷ 3 = 4

4 oranges for each glass of juice.

Answer:

The chosen topic is not meant for use with this type of problem. Try the examples below.

2 = |3x|

−4/5x + 1/25 = 0

3x = 4 − x

Answer

Step-by-step explanation:

This has to be equal to something in order to solve it. I'm going to guess that it is equal to 0

(3x-15)(2x+7) = 0

That means that

3x - 15 = 0

3x = 15

x = 15/3

x = 5

or

2x + 7 = 0

2x = - 7

x = -7/2

x = - 3.5

The only other thing I can think of that this could equal is multiplying the two binomials together.

3x * 2x = 6x^2

3x*7 = 21x

-15*2x = - 30x

-15 * 7 = - 105

6x^2 - 7x - 105

But that does not solve for x.

A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).

Degree of the polynomial function is equal to 3.

Zero's of the polynomial function is equal to 2, -3 , 5 .

And f(3) = 6

If 2, -3, and 5 are zeros of f(x), then we can write function as,

f(x) = a(x-2)(x+3)(x-5)

where a is some constant.

To determine the value of a, we can use the fact that f(3) = 6.

Substituting x = 3 into the equation above, we get,

f(3) = a(3-2)(3+3)(3-5)

     = -12a

Here we have,

f(3) = 6, so we can set these two expressions equal to each other and solve for a,

⇒ -12a = 6

⇒ a = -1/2

Now we can substitute this value of a back into the equation for f(x) that we found earlier,

⇒ f(x) = -1/2 (x-2)(x+3)(x-5)

Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).

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Answer:

Step-by-step explanation:

25

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

The answer is 2

From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

200

Step-by-step explanation:

it was found that the ratio of people who liked Arithmetic and Algebra is 9 : 8. If 25% liked the both, 80 liked none of these and 20% liked arithmetic only, find the total number of people participated in the survey. Ans: 200

The solutions of the equation of the graph is -4 and 2.

An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.

We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.

In the given graph the point of intersection of the two equations are at x = -4 and x = 2.

Hence, the solutions of the equation of the graph is -4 and 2.

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The complete question is:

Answer:

10p

Step-by-step explanation:

p + 2p + 3p + 4p

= 10p

Answer:

10p

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

p + 2p + 3p + 4p

Step 2: Simplify

Answer:

Sin X = 15/17

Cos X = 8/17

Tan X = 15/8

Step-by-step explanation:

Recall, SOHCAHTOA.

Thus:

Sin X = opp/hyp

opp = 15

hyp = 17

✅Sin X = 15/17

Cos X = adj/hyp

Adj = 8

Hyp = 17

✅Cos X = 8/17

Tan X = opp/adj

Opp = 15

Adj = 8

✅Tan X = 15/8

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

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Answer: The rule is when rotating 90 degrees, it's (-y, x), 180 degrees is (-x, -y), and 360 degrees is (y,  -x). Just plug in the numbers accordingly, and you should get the correct answer. It worked for me <3.

Based on the information and diagram of the question, you can use the tangent function to get the value of x. Notice that you have a right triangle in the figure.

Then, you have:

tan x = opposide side/adjacent side

tan x = 130 mi/171 mi

tan x = 0.76

to solve for x, apply tan⁻¹ both sides:

tan⁻¹(tan x) = tan⁻¹(0.76)

x = tan⁻¹(0.76)

x = 37.24°

Hence, the pilot should turn an angle of 37.24° to fly directly to the airport, which is approximately 37.2°

The simplified exponential expression for this problem is given as follows:

D. 1/49.

The exponential expression for this problem is defined as follows:

\(7^{-\frac{5}{6}} \times 7^{-\frac{7}{6}}\)

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.

Hence the exponent is given as follows:

-5/6 - 7/6 = -12/6 = -2.

The negative exponent is moved to the denominator, hence:

1/7² = 1/49.

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The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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Answer: 315 miles

Step-by-step explanation:

let onward speed = x mph, then distance = 7x

return speed = (x+18) mph, (same) distance = 5(x+18)

equating the two,

7x = 5(x+18)

2x = 90 ==> x = 45 mph

so distance = 7*45 = 315 miles