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lidiya [134]
3 years ago
14

What is the resulting ordered pair if the value of the independent variable is 2?

Mathematics
1 answer:
quester [9]3 years ago
5 0
To find f(2), put 2 where the variable is, then do the arithmetic. It might be easier to factor out x^2:
  f(x) = (-6x-4)·x^2
  f(2) = (-6·2-4)·2^2
  = -16·4
  = -64

Then the ordered pair (x, f(x)) for x=2 is
  B. (2, -64)
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Someone please help i dont know how to solve for 6 and 7 <br> :(
Sphinxa [80]

If I remember correctly, the solutions are only on the solid line or in the shaded area? therefore Answers could be:

6.) (-3,0.5) (-4,0) (-2,0) (-2,-5) (-3,-5) (-4,-1) (-3,-1) (-2,-1)

7.) (-1,0) (-2,0) (-3,0) (0,-1) (-4,-1)

7 0
2 years ago
Find an equation of the line containing the centers of the two circles whose equations are given below.
Anna35 [415]

Answer:

<h2><em>3y+x = -5</em></h2>

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1  =0  and x²+y²+4x+2y+4  =0, to  get the centre of both circles,<em> we will compare both equations with the general form of the equation above as shown;</em>

For the circle with equation x²+y²−2x+4y+1  =0:

2gx = -2x

2g = -2

Divide both sides by 2:

2g/2 = -2/2

g = -1

Also, 2fy = 4y

2f = 4

f = 2

The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4  =0:

2gx = 4x

2g = 4

Divide both sides by 2:

2g/2 = 4/2

g = 2

Also, 2fy = 2y

2f = 2

f = 1

The centre of the circle is (-2, -1)

Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

m is the slope

c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

from both centres, x₁= 1, y₁= -2, x₂ = -2 and y₂ = -1

m = -1-(-2)/-2-1

m = -1+2/-3

m = -1/3

The slope of the line is -1/3

To get the intercept c, we will substitute any of the points and the slope into the equation of the line above.

Substituting the point (-2, -1) and slope of -1/3 into the equation y = mx+c

-1 = -1/3(-2)+c

-1 = 2/3+c

c = -1-2/3

c = -5/3

Finally, we will substitute m = -1/3 and c = 05/3 into the equation y = mx+c.

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

y = -x/3-5/3

Multiply through by 3

3y = -x-5

3y+x = -5

<em>Hence the equation of the line containing the centers of the two circles is 3y+x = -5</em>

5 0
3 years ago
How many are there write answer and how you solved
V125BC [204]

Answer:

5.2 hours

Step-by-step explanation:

To find the solution, you need to multiply Aretha's time by 1.6, since Neal takes 1.6 as long to run the marathon.

3.25 × 1.6 = 5.2

In other words, Neal takes 5.2 hours to run the marathon. Let me know if I can help you with anything else, 'kay?

6 0
2 years ago
There is a bag filled with 2 blue, 4 red and 3 green marbles.
NISA [10]

Answer:

5 out of 9

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Find the nth term of this quadratic sequence<br> 3, 11, 25, 45, .
Hoochie [10]

The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Given,

In the question:

The quadratic sequence is :

3, 11, 25, 45, ...

To find the nth term of the quadratic sequence.

Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

11-3 = 8

The difference between the second and third terms can be calculated as follows:

25-11 = 14

The difference between the third and fourth terms can be calculated as follows:

45-25 = 20

The sequence is expressed as follows:

3,3+8,11+11,25+20,...

The difference between consecutive terms expands by 6.

Use the principle of mathematical induction.

6(\frac{n(n+1)}{2} )

= 3n(n+1)

The sequence's nth term can be calculated as follows:

term = 3n(n+1) - 4n + 1

             = 3n² - n + 1

Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Learn more about Principle of mathematical induction at:

brainly.com/question/29222282

#SPJ1

6 0
1 year ago
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