Brainliest al que responda./Brainliest for the answer.
According to the next functions, do the operations developing the algebraic operations and indicate the result in the most simplified way possible.
De acuerdo con las siguientes funciones, realizar las operaciones indicadas desarrollando las operaciones algebraicas correspondientes e indicando el resultado de la forma mas simplificada posible.

Funciones/functions:
\(f(x)=3x^{3} +6x^{2} +5x\\g(x)=x^{2} +3x\)

Operaciones/operations:
1.-\(f+g\)
2.-\(f o g\)
3.-\(gof\)
4.-\(g-f\)
5.-\(g*f\)
6.-\(\frac{f}{g}\)
7.-\(f-g\)

Answer:

a) The vertex of the graph is \((h,k) = (0, 31)\), b) \(a = -16\), c) The equation of the parabola is \(f(t) = -16\cdot t^{2}+31\).

Step-by-step explanation:

a) The tennis ball experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from Earth's rotation and air viscocity are negligible. The height of the ball in time is represented by a second order polynomial. Hence, the vertex of the parabola is the initial point highlighted in graph.

The vertex of the graph is \((h,k) = (0, 31)\).

b) If we know that \((h,k) = (0, 31)\), \(f(t) = a\cdot (t-h)^{2} + k\) and \((t,f(t)) = (1,15)\), then the value of \(a\) is:

\(f(t) = a\cdot (t-h)^{2} + k\)

\(15 = a\cdot (1-0)^{2}+31\)

\(15 = a\cdot 1 + 31\)

\(a = 15-31\)

\(a = -16\)

c) The equation of the parabola is \(f(t) = -16\cdot t^{2}+31\).

It might be 2 not 100 percent sure

Answer:

isosceles (based on sides) and right triangle (based on angles)

Step-by-step explanation:

This is an isosceles triangle because two of the sides are the same distance (it is in cm.). This is also a right triangle because at point B the two lines are perpendicular (using their slopes).

(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Learn more about factorization click;

https://brainly.com/question/14452738

#SPJ1

Answer:

1.) 256 miles

2.) 2 1/2 ( 2.5 ) pages a day

Step-by-step explanation:

1.) ( 256 * 2.4 = 640 )

2.) 250 / 20 = 2.5

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

For more such information on: expression

https://brainly.com/question/28602085

#SPJ8

Answer: 3.

Step-by-step explanation:

\(\left \{ {{4x-3y=3 \ |[*(-4)]} \atop {5x-4y=3} \ |[*3]} \right. \ = > \ \left \{ {{-16x+12y=-12} \atop {15x-12y=9}} \right. \ = > \ \left \{ {{y=3} \atop {x=3}} \right.\)

Answer: 12 and 13

Step-by-step explanation:

a(a + 1) = 156

\(a^{2} + a - 156 = 0\)

(a + 13)(a - 12) = 0

a1 = -13 (Room number can't be negative so this is impossible)

a2 = 12, a2 + 1 = 12 + 1 = 13

So the room numbers are 12 and 13

The equation of the axis of symmetry of the parabola is equal to x = 4.

In this problem we find the representation of a parabola whose axis of symmetry is parallel with y-axis. The axis of symmetry passes through the vertex of the parabola. The definitions of the vertex and the axis of symmetry are, respectively:

Vertex

(x, y) = (h, k)

Axis of symmetry

x = h

If we know that h = - 4, then the equation of axis of symmetry is x = 4.

To learn more on parabolae: https://brainly.com/question/29267743

#SPJ1

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

Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

To learn more about y-axis on:

brainly.com/question/27946240

#SPJ1

The set builder notation of the solution inequality represented on the number line is; {x: 3< x <=5}.

It follows from the task content that at point positive 3, there's an open circle which signifies that the number 3 is less than the solution.

And since the number line is shaded from positive 3 to 5, it follows that the maximum value in the solution set is 5.

The representation is therefore; {x: 3< x <=5}.

Read more on inequalities;

https://brainly.com/question/24644930

#SPJ4

On the number line, the solution inequality is represented by the notation x: 3=5, which is the set builder notation of the inequality.

This is further explained below.

Given the information provided in the job, it is logical to conclude that at point positive 3, there will be an open circle. This will indicate that the number 3 will be lower than the answer.

And since the shading on the number line goes from positive 3 to 5, it follows that the highest value that can be found in the set of solutions is 5.

As a result, the representation is written as:

"x: 3 x = 5."

Learn more about the topic of inequality.

brainly.com/question/24644930

Answer: Radical Republicans

Step-by-step explanation:

Answer:

conservative Democrats

Step-by-step explanation:

Answer:

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

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

Answer:

n=90

Step-by-step explanation:

80% as a decimal is 0.80

0.80n = 72

n = 72/0.80

n = 90

look on the top and see a answer with apple)

have a nice night!

Answer:

the answer was 7.71

Step-by-step explanation:

hope this helps

A fraction is usually split into two parts: the first part is the number on top, called the numerator; and the second part is the number on the bottom, called the denominator. These are both separated by a line called the “divisor line”. We can use the division method help to solve this question: to get a decimal, simply divide the numerator 54 by the denominator 7 (which you can enter in any calculator):

54 (numerator) ÷ 7 (denominator) = 7.71

And finally, you get 7.71 as your answer when you convert 7 5/7 (or 54/7) to a decimal.

Answer:

7.71

Step-by-step explanation:

Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with \(\frac{dollars}{student}\):

\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)

The rate is 5 dollars per student.

Answer:

41200

Step-by-step explanation:

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

How to find the soccer portion of the pie chart?

In mathematics, the complete pie chart is 360° and to calculate the soccer portion using standard formula which states that the division of the total hours spent on soccer and total sports hours multiply with 360°.

According to the question, the given data states that the pie chart is 360° which represents the total sports hours as 50 hours.

Therefore, the soccer portion is:

= Total hours spent on walking / Total sports hours x 360°

= 10 / 50 x 360°

= 72°

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

To learn more about the soccer portion calculation from the given link:

https://brainly.com/question/26851221

#SPJ13

Answer:

22 cents per mile

Step-by-step explanation:

to get this answer, divide 17.60 by 4 to get the unit rate, or the rate when x=1.

Answer:

\(Probability = 0.734\)

Step-by-step explanation:

Given

Represent the event that a bulb is defective with p.

So:

\(p =6\%\)

Required

Determine the probability that all 5 are fully functioning

Represent the event that a bulb is defective with q.

So:

\(p + q = 1\)

Make q the subject

\(q = 1 - p\)

Substitute 6% for p

\(q = 1 - 6\%\)

Convert % to decimal

\(q = 1 - 0.06\)

\(q = 0.94\)

If 5 were selected and all are functioning, the event is represented as: q q q q q

And the probability is:

\(Probability = q * q * q * q *q\)

\(Probability = q^5\)

Substitute 0.94 for q

\(Probability = 0.94^5\)

\(Probability = 0.7339040224\)

\(Probability = 0.734\) --- approximated

Answer:1+1

Step-by-step explanation:

1+1=2

Answer:

20

Step-by-step explanation:

your welcome!!

Answer:

18

Step-by-step explanation:

Because 5/8×18 is 11 1/4

Answer:

what he said

Step-by-step explanation: