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amm1812
3 years ago
15

What is a rational number

Mathematics
1 answer:
siniylev [52]3 years ago
7 0

It's a number that can be expressed as a fraction, the numerator and the denominator of which, are integers.

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50 Points Please show graph
worty [1.4K]

Answer:

The solutions are x = -9 , x = -5

Step-by-step explanation:

* Lets find the vertex of the parabola

- In the quadratic equation y = ax² + bx + c, the vertex of the parabola

 is (h , k), where h = -b/2a and k = f(h)

∵ The equation is y = x² + 14x + 45

∴ a = 1 , b = 14 , c = 45

∵ h = -b/2a

∴ h = -14/2(1) = -14/2 = -7

∴ The x-coordinate of the vertex of the parabola is -7

- Lets find k

∵ k = f(h)

∵ h = -7

- Substitute x by -7 in the equation

∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4

∴ The y-coordinate of the vertex point is -4

∴ The vertex of the parabola is (-7 , -4)

- Plot the point on the graph and then find two points before it and

 another two points after it

- Let x = -9 , -8 and -6 , -5

∵ x = -9

∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0

- Plot the point (-9 , 0)

∵ x = -8

∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3

- Plot the point (-8 , -3)

∵ x = -6

∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3

- Plot the point (-6 , -3)

∵ x = -5

∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0

- Plot the point (-5 , 0)

* To solve the equation x² + 14x + 45 = 0 means find the value of

  x when y = 0

- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates

 of the intersection points of the parabola with the x-axis

∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)

∴ The solutions of the equation are x = -9 and x = -5

* The solutions are x = -9 , x = -5

5 0
3 years ago
Number of Tickets, X 2 5 10 13 Cost, y $8.50 $21.25 $42.50 $55.25​
brilliants [131]

Answer:

4.25

Step-by-step explanation:

Take your cost and divide it by the number of tickets.

55.25/13 = 4.25

21.25/5 = 4.25

No matter which pair you use, the answer is 4.25

4 0
3 years ago
Solve the following system y=-2 -2x-7y=24
Dafna1 [17]

Answer:

x = -5

y = -2

Step-by-step explanation:

<em><u>Since you have y, plug that into the equation:</u></em>

-2x - 7y = 24

-2x - 7(-2) = 24

-2x + 14 = 24

<u><em>Then, subtract 14 from both sides:</em></u>

-2x + 14 = 24

      - 14   - 14

__________

-2x = 10

<u><em>Finally, divide both sides by -2:</em></u>

-2x = 10

x = -5

So now you have, x = -5 and y = -2.

6 0
3 years ago
Evaluate the expression for the given values.
zmey [24]
Mx-ymx-y

m=5m=5
x=3x=3
y=8y=8
So... They all have to be 0 otherwise they are false so...

Hope this helps :)
8 0
3 years ago
Read 2 more answers
For two functions, m(x) and p(x), a statement is made that m(x) = p(x) at x = 7. What is definitely true about x = 7?
Shkiper50 [21]

For this case we have the following functions:

m (x)

p (x)

Where,

x: independent variable

m, p: dependent variables

For the value of x = 7 we have:

m (7)

p (7)

For this case it is true that:

m (7) = p (7)

Therefore, both functions have the same output argument for the same input value.

Answer:

C) Both m (x) and p (x) have the same output value at x = 7.

4 0
3 years ago
Read 2 more answers
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