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3 years ago

(x÷(y÷z))÷((x÷y)÷z)also the variables are not specified.

1 answer:

4 0

The answer is: z² .
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Given: <span>(x÷(y÷z))÷((x÷y)÷z) ; without any specified values for the variables;
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we shall simplify.
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We have:
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</span>(x÷(y÷z)) / ((x÷y)÷z) .
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Start with the first term; or, "numerator": (x÷(y÷z)) ;
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x ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) = [(xz) / y ]
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Then, take the second term; or "denominator":
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((x ÷ y) ÷z ) = (x / y) / z = (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)]
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So (x÷(y÷z)) / ((x÷y)÷z) = (x÷(y÷z)) ÷ ((x÷y)÷z) =

[(xz) / y ] ÷ [x / (zy)] = [(xz) / y ] / [x / (zy)] =
[(xz) / y ] * [(zy) / x] ;
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The 2 (two) z's "cancel out" to "1" ; and
The 2 (two) y's = "cancel out" to "1" ;
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And we are left with: z * z = z² . The answer is: z² .
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Jet001 [13]

Answer:

Corresponding angles are equal so,

m<6= 110° (being the corresponding angle)

.°. m<6= 110°

Hope this helps you!

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2 years ago

Determine the truth value of each of these statements if thedomainofeachvariableconsistsofallrealnumbers.

hoa [83]

Answer:

a)TRUE

b)FALSE

c)TRUE

d)FALSE

e)TRUE

f)TRUE

g)TRUE

h)FALSE

i)FALSE

j)TRUE

Step-by-step explanation:

a) For every x there is y such that $x^2=y$ :

TRUE

This statement is true, because for every real number there is a square number of that number, and that square number is also a real number. For example, if we take 6.5, there is a square of that number and it equals 39.0625.

b) For every x there is y such that $x=y^2$ :

FALSE

For example, if x = -1, there is no such real number so that its square equals -1.

c) There is x for every y such that xy = 0

TRUE

If we put x = 0, then for every y it will be xy=0*y=0

d)There are x and y such that $x+y\neq y+x$

FALSE

There are no such numbers. If we rewrite the equation we obtain an incorrect statement:

$x+y \neq y+x\\x+y - y-y\neq 0\\0\neq 0$

e)For every x, if $x \neq 0$ there is y such that xy=1:

TRUE

The statement is true. If we have a number x, then multiplying x with 1/x (Since x is not equal to 0 we can do this for ever real number) gives 1 as a result.

f)There is x for every y such that if $y\neq 0$ then xy=1.

TRUE

The statement is equivalent to the statement in e)

g)For every x there is y such that x+y = 1

TRUE

The statement says that for every real number x there is a real number y such that x+y = 1, i.e. y = 1-x

So, the statement says that for every real umber there is a real number that is equal to 1-that number

h) There are x and y such that

$x+2y = 2\\2x+4y = 5$

We have to solve this system of equations.

From the first equation it yields x=2-2y and inserting that into the second equation we have:

$2(2-2y)+4y=5\\4-4y+4y=5\\4=5$

Which is obviously false statement, so there are no such x and y that satisfy the equations.

FALSE

i)For every x there is y such that

$x+y=2\\2x-y=1$

We have to solve this system of equations.

From the first equation it yields $x=2-y$ and inserting that into the second equation we obtain:

$2(2-y)-y=1\\4-2y-y=1\\4-3y=1\\-3y=1-4\\-3y=-3\\y=1$

Inserting that back to the first equation we obtain

$x=2-1\\x=1$

So, there is an unique solution to this equations:

x=1 and y=1

The statement is FALSE, because only for x=1 (and not for every x) exists y (y=1) such that

$x+y=2\\2x-y=1$

j)For every x and y there is a z such that

$z=\frac{x+y}{2}$

TRUE

The statament is true for all real numbers, we can always find such z. z is a number that is halway from x and from y.

5 0

3 years ago

Which function is undefined for x = 0? y=3√x-2 y=√x-2 y=3√x+2 y=√x=2

Mkey [24]

For this case, we have to:

By definition, we know:

The domain of $f (x) = \sqrt [3] {x}$ is given by all real numbers.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root. Thus, it will always be defined.

So, we have:

$y = \sqrt [3] {x-2}$ with $x = 0$ : $y = \sqrt [3] {- 2}$ is defined.

$y = \sqrt [3] {x+2}$ with $x = 0:\ y = \sqrt [3] {2}$ is also defined.

$f (x) = \sqrt {x}$ has a domain from 0 to ∞.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.

Thus, we observe that:

$y = \sqrt {x-2}$ is not defined, the term inside the root is negative when $x = 0$ .