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hodyreva [135]
3 years ago
13

Sam said the square root of a rational number must be a rational number. Jenna disagreed. She said that it is possible that the

square root of a rational number can be irrational. Who is correct and why?
Mathematics
2 answers:
Nat2105 [25]3 years ago
6 0
Jenna is correct.  This is because the square root of 2 is an irrational number.  And if the number is a prime number, the answer is less likely to have a rational square root.
Rzqust [24]3 years ago
3 0

Answer: Jenna is correct.

Step-by-step explanation:

We can prove this statement with help of two examples.

Since we know that 64 is the rational number.

And, the square root of 64 is \sqrt{64}.

Which is equal to 8 or -8.

And, they are integers, and we know that the integer are always a rational number.

Therefore \sqrt{64} is a rational number.

And, If we take a number 2 which is a rational number.

Since, when we do square root of 2, we get √2.

And, √2 is a irrational number.

Thus, we can say that we can obtain a rational or irrational number after doing the square root of rational number.

Therefore, Jenna is correct.



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Identify all factors of the expression 12x^2-14x-6
Evgen [1.6K]

Let's solve this by using the quadratic formula:

\frac{-b+-\sqrt{b^2-4ac} }{2a}


Note that we only use the coefficients so a=12, b=-14, and c=-6.

Plug values in the quadratic equation:

\frac{ -  ( - 14)± \sqrt{ {( - 14)}^{2} - 4(12)( - 6) } }{2(12)}

And so by evaluating those values we obtain:

\frac{14+-\sqrt{484} }{24}=\frac{14+-22}{24}  \\\\

Now we have two answers which are our factors one where we add another where we subtract and so:

First factor:

\frac{14+22}{24}=\frac{36}{24}=\frac{3}{2}


Second Factor:

\frac{14-22}{24}=\frac{-8}{24}=-\frac{1}{3}


And so your factors are

\frac{3}{2},-\frac{1}{3}

meaning that those are your roots/x-intercepts.


6 0
3 years ago
Find quadratic polynomial which best fits the function f(x)=e^x and x=0, in the sense that g(0)= f(0), and g'(0) = f'(0), and g"
Dmitriy789 [7]
Let g(x)=ax^2+bx+c. Then

\begin{cases}g(0)=c\\g'(0)=b\\g''(0)=2a\end{cases}

Meanwhile, since f(x)=e^x, you have f(0)=f'(0)=f''(0)=e^0=1.

It follows that a=\dfrac12, b=1, and c=1, so that the quadratic fit for f(x)=e^x that satisfies the given points is

g(x)=\dfrac12x^2+x+1

Note that this is just the second-order Taylor polynomial for e^x about x=0.
3 0
3 years ago
Find Z for the following sequence:<br> 210, 209, 213, 186, 202, Z
nikklg [1K]

Answer:

77

Step-by-step explanation:

as far as I can tell the steps between the given numbers are

-1

+4

-27

+16

1 can be expressed as 1³

4 can be expressed as 2²

27 can be expressed as 3³

16 can be expressed as 4²

my best guess is that next one is minus 5³ = -125

edit: technically the given steps can be expressed as

(-1)³

(-2)²

(-3)³

(-4)²

somewhat nicer pattern there

7 0
3 years ago
Trevor makes essential oil using 15 drops of rose oil for every 6 drops of lavender oil.
Black_prince [1.1K]

Answer:

Trevor will need 2 drops of lavender oil if he uses 5 drops of rose oil.

Step-by-step explanation:

If 15/5 = 3

Then, all we have to do is 6/3=2.

So hence, Trevor will need 2 drops of lavender oil if he uses 5 drops of rose oil.

Thanks

5 0
2 years ago
Read 2 more answers
A wire is first bent into the shape of a square. Each side of the square is 9cm long. Then the wire is unbent and reshaped into
EastWind [94]

Answer:

5 cm

Step-by-step explanation:

the perimeter of a square with sides of 9 cm is 36 cm so the rectangle must have the same perimeter

if the length of the rectangle is 13cm, its opposite side is also 13cm

add 13 + 13 to get 26

let 'n' = width of rectangle

perimeter = 26 + n + n

36 = 26 + 2n

2n = 10

n = 5

8 0
3 years ago
Read 2 more answers
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