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IrinaVladis [17]
3 years ago
6

Which is an irrational number?

Mathematics
1 answer:
erica [24]3 years ago
5 0

A. is the answer it can't be rational

Step-by-step explanation:

√21 is irrational.

Let's assume that √21 is rational. So √21 can be expressed in the form p/q form.

p/q is the reduced form of rational number so p and q have no common factors other than 1, i.e. they are co-prime numbers.

√21 = p/q

21 = p^2/q^2... (squaring both the sides)

21q^2 = p^2

p^2 is even. p^2 is a factor of 2...(1)

p=2t p^2=4t^2 t belongs to I

2q^2 = 4t^2 (2q^2=p^2)

q^2 = 2t^2

q^2 is even

q is even

2 is a factor of q.

From the statements (1) and (2), 2 is a common factor of p and q both.

This is contradictory because in p/q, we have assumed that p and q have no common factors other than 1.

That is, our assumption that √21 is rational is wrong.

Therefore, √21 is irrational.

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F(x)=x^2+9x-16<br><br><br> What is vertex <br><br> Axis of semetry
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Answer:

axis of symmetry is x=\frac{-9}{2}.

The ordered pair of the vertex is (\frac{-9}{2},\frac{-145}{4}).

Step-by-step explanation:

Your function is a quadratic.

Compare x^2+9x-16 to ax^2+bx+c.

You should see that a=1,b=9,c=-16.

The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing \frac{-b}{2a}.

So here we go!

The axis of symmetry is x=\frac{-9}{2(1)}=\frac{-9}{2}.

When you write your axis of symmetry be sure to write it as an equation.

That is the axis of symmetry is x=\frac{-9}{2}.

Now that was also the x-coordinate of your vertex.  To find the corresponding y-coordinate of the vertex, plug your value for x into

y=x^2+9x-16.

y=(\frac{-9}{2})^2+9(\frac{-9}{2})-16

Put into calculator:

y=\frac{-145}{4} when x=\frac{-9}{2}

The ordered pair of the vertex is (\frac{-9}{2},\frac{-145}{4}).

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3 years ago
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1. Solve.
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Answer:

1. \dfrac{c}{6}-\dfrac{7}{6}

2. m

3. 6w

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5. 75x - 153

Step-by-step explanation:

1. The product of −2c+14 and the multiplicative inverse of −12 is

(-2c+14)\cdot \dfrac{1}{-12}

Use distributive property:

(-2c+14)\cdot \dfrac{1}{-12}\\ \\=-\dfrac{1}{12}\cdot (-2c)-\dfrac{1}{12}\cdot 14\\ \\=\dfrac{c}{6}-\dfrac{7}{6}

2. Solve 10+(m−10)

Open the brackets remembering that the sign before brackets is "+":

10+(m-10)\\ \\=10+m-10

Combine the like terms usin commutative property:

10+m-10\\ \\=(10-10)+m\\ \\=0+m \\ \\=m

3. Solve 6w+3−3

Combine the like terms:

6w+3-3\\ \\=6w+(3-3)\\ \\=6w+0\\ \\=6w

4. Write the expression in standard form 13(3x+6).

Use distributive property:

13(3x+6)\\ \\=13\cdot 3x+13\cdot 6\\ \\=39x+78

5. Write the expression in standard form 15(5x−10)−3.

Use distributive property:

15(5x-10)-3\\ \\=15\cdot 5x-15\cdot 10-3\\ \\=75x-150-3

Combine the like terms:

=75x+(-150-3)\\ \\=75x-(150+3)\\ \\=75x-153

8 0
3 years ago
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