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3 years ago

Is √17 a rational or irrational number Thank you for helping

Mathematics

1 answer:

Yakvenalex [24]3 years ago

7 0

Answer:

Not Rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

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Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

$y=a(x-h)^2+k$

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

Helppppppp pleasssseeeeee

Svet_ta [14]

$14mi-5\frac{7}{10}mi=[(14-5)-\frac{7}{10}]mi=(9-\frac{7}{10})mi=(8+1-\frac{7}{10})mi\\\\=(8+\frac{10}{10}-\frac{7}{10})mi=(8+\frac{10-7}{10})mi=(8+\frac{3}{10})mi=\boxed{8\frac{3}{10}mi}\\\\other\ method\\\\14mi-5\frac{7}{10}mi=14mi-5.7mi=(14-5-0.7)mi\\\\=(9-0.7)mi=\boxed{8.3mi}$

6 0

3 years ago

F(x)= x +4 g(x) = 3x Work out the value of gf (5).

MrMuchimi

The value of gf(5) for the given two expressions is 135.

According to the question,

We have the following information:

f(x)= x +4

g(x) = 3x

Now, in order to find the value of gf(5), we will first find the value of gf.

Now, we will multiply these two expressions:

3x(x+4)

Now, the terms outside the brackets need to multiplied inside the bracket:

$3x^{2} +12x$

Now, we will put the value of x in this expression as 5 and solve the expression further by multiplication and addition:

3*5*5+12*5

75+60

135

Hence, the value of gf(5) for the given two expressions of f(x) and g(x) is 135.

To know more about value here

brainly.com/question/20562282

#SPJ1

8 0

1 year ago

HELP ASAP PLS.

Sindrei [870]

Step-by-step explanation:

I have no idea if I'm doing it right but my guess would be to take the values that we get from f(x) and g(x) when x = 1. Therefore we get that f(x) is equal to 4 and g(x) is equal to -1. We than just do f/g which is 4/-1 which gives us the final answer of -4 which is option B.

Answer: Option B, -4

5 0

2 years ago

If m = -2 and p=3, then (4p-m)/mp is

ddd [48]

Answer:

-2 1/3

Step-by-step explanation:

((4 * 3) - (-2) /(-2*3)

(12 + 2 ) / (-2 * 3)

14 / -6

-2 1/3

7 0

2 years ago