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2 years ago

If you walk from the train station to the

Mathematics

1 answer:

Ray Of Light [21]2 years ago

7 0

Since the miles are not given, I am writing the steps for you so that you can solve it on your own!!

<h3>Steps:</h3>

Take the miles from train station to library then library to park and then park to train station.
Add all the distances
And there you go, You have the total distance!!

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A language arts test is worth 100 points. There is a total of 26 questions. There are spelling word questions thatare worth 2 po

Ostrovityanka [42]

Answer:

Spelling word questions = 10

vocabulary word questions = 16

Step-by-step explanation:

Let

Spelling word questions = x

vocabulary word questions = y

Total points = 100

Total questions = 26

x + y = 26 (1)

2x + 5y = 100 (2)

From (1)

x = 26 - y

Substitute x = 26 - y into

2x + 5y = 100

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

- 2y + 5y = 100 - 52

3y = 48

y = 48 / 3

= 16

y = 16

Substitute y = 16 into

x + y = 26

x + 16 = 26

x = 26 - 16

= 10

x = 10

Spelling word questions = 10

vocabulary word questions = 16

7 0

3 years ago

HELP AS SOON AS POSSIBLE NEEDS ANSWERS ASAP

likoan [24]

Answer:

C. The mean will increase and ty e median will remain the same.

6 0

3 years ago

Show all work to identify the asymptotes and zero of the function f(x) = 6x / x^2 - 36

eduard

Answer:

Zero of the function f(x) is at x = 0

Vertical Asymptotes at x = ±6

Horizontal Asymptotes at y = 0

Step-by-step explanation:

<h3>Vertical Asymptotes </h3>

For a given function f(x):

Vertical Asymptotes are obtained at those values of x, where the function f(x) tends to infinity, I.e.,

When x approaches some constant value but the curve moves towards infinity.

If f(x) is a fraction, it'll tend to infinity when it's denominator becomes zero.

Vertical Asymptotes of the given function can be obtained by walking thru the following steps:

Step I

(Factorise the numerator and denominator)

$\mathsf{ f(x) = \frac{6x}{ {x}^{2} - 36 } }$

x² - 36 can be factorised into (x + 6)(x - 6)

and, ofcourse, we can write 6x as 6(x - 0)

$\mathsf{ f(x) = \frac{6(x - 0)}{ (x + 6)(x - 6) } }$

Step II

(Reduce the fraction to its simplest form by canceling out the common factors)

There aren't any common factors in the numerator and denominator in this case.

Step III

(Look for the values of x which cause the denominator to be zero)

If we put x = 6

denominator becomes 0

Also,

If we substitute x with -6

denominator becomes 0.

The two values of x indicate the two Vertical Asymptotes of the function f(x).

Therefore,

Vertical Asymptotes of the given function f(x) are:

$\boxed{ \mathsf{x = \pm6}}$

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<h3 /><h3>Horizontal Asymptotes:</h3>

Horizontal Asymptotes are obtained When x tends to infinity and y approaches some constant value.

I'll be using the concept of limits for this.

$\mathsf{y = \frac{6x}{ {x}^{2} - 36 } }$

dividing and multiplying by x² (Yep! so if x becomes infinity 1/ x and 1/ x² all such terms become 0, 'cause 1/ ∞ is 0)

$\implies \mathsf{y = lim_{x \rightarrow \infty }( \frac{ \frac{6x}{ {x}^{2} } }{ \frac{ {x}^{2} - 36 }{ {x}^{2} } } ) }$

$\implies \mathsf{y = lim_{x \rightarrow \infty }( \frac{ \frac{6}{ x } }{ 1- \frac{36 }{ {x}^{2} } } ) }$

Substitute x with ∞, you get zero/ 1

$\implies \boxed{\mathsf{y = 0}}$

So, the horizontal Asymptote of the function is y = 0, that is the x axis

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<h3>Zeroes of a function:</h3>

The values of x that reduces f(x) to zero are called the zeroes of f(x).

Here, only x = 0 acts as the zero of the function.

[NOTE:

For finding Vertical Asymptotes,Equate the denominator to 0. And
For finding Zeroes, Equate the numerator to 0]

__________________

[That's what it's graph looks like. ]

3 0

3 years ago

The sum of twice a number and 13 is 75

sveta [45]

Sum means add. Then we get twice. This means to multiply by 2. Twice a number means we have 2x. And is what we need to add to that 2x, so it is 2x + 13. Is means equals, so answer is 2x + 13 = 75.

7 0

4 years ago

The sum of 3y and 5 is 47

Musya8 [376]

3y + 5 = 47

Subtract the 5 so you have 3y on the left side and move it to the other side.

Now it’s:

3y = 47-5

3y = 42

Now, divide 3y by 3, so we get y by itself. Do the same thing to the other side.

y = 14

8 0

3 years ago